Journal Papers

2026

MILUV: A Multi-UAV Indoor Localization dataset with UWB and Vision

Mohammed Ayman Shalaby, Syed Shabbir Ahmed, Nicholas Dahdah, and 3 more authors

International Journal of Robotics Research, 2026

Abs arXiv Code

This paper introduces MILUV, a Multi-UAV Indoor Localization dataset with UWB and Vision measurements. This dataset comprises 217 minutes of flight time over 36 experiments using three quadcopters, collecting ultra-wideband (UWB) ranging data such as the raw timestamps and channel-impulse response data, vision data from a stereo camera and a bottom-facing monocular camera, inertial measurement unit data, height measurements from a laser rangefinder, magnetometer data, and ground-truth poses from a motion-capture system. The UWB data is collected from up to 12 transceivers affixed to mobile robots and static tripods in both line-of-sight and non-line-of-sight conditions. The UAVs fly at a maximum speed of 4.418 m/s in an indoor environment with visual fiducial markers as features. MILUV is versatile and can be used for a wide range of applications beyond localization, but the primary purpose of MILUV is for testing and validating multi-robot UWB- and vision-based localization algorithms. The dataset can be downloaded at https://doi.org/10.25452/figshare.plus.28386041.v1. A development kit is presented alongside the MILUV dataset, which includes benchmarking algorithms such as visual-inertial odometry, UWB-based localization using an extended Kalman filter, and classification of CIR data using machine learning approaches. The development kit can be found at https://github.com/decargroup/miluv, and is supplemented with a website available at https://decargroup.github.io/miluv/.
Forward-Backward Extended DMD with an Asymptotic Stability Constraint

Louis Lortie, Steven Dahdah, and James Richard Forbes

Journal of Nonlinear Science, 2026

Abs arXiv

This paper presents a data-driven method to identify an asymptotically stable Koopman system from noisy data. In particular, the proposed approach combines system inputs and approximations of the system’s forward- and backward-in-time dynamics to reduce bias caused by noisy data while enforcing asymptotic stability. A Koopman model of an inherently asymptotically stable system can be unstable due to noisy data and a poor choice of lifting functions. To prevent identifying an unstable model, the proposed approach imposes an asymptotic stability constraint on the Koopman model. The proposed method is formulated as a semidefinite program and its performance is compared to state-of-the-art methods with a simulated Duffing oscillator dataset and experimental soft robot dataset.
Gaussian Variational Inference with Non-Gaussian Factors for State Estimation: A UWB Localization Case Study

Andrew Stirling, Mykola Lukashchuk, Dmitry Bagaev, and 2 more authors

IEEE Robotics and Automation Letters, 2026

Jointly accepted to ICRA.

Abs arXiv

This letter extends the exactly sparse Gaussian variational inference (ESGVI) algorithm for state estimation in two complementary directions. First, ESGVI is generalized to operate on matrix Lie groups, enabling the estimation of states with orientation components while respecting the underlying group structure. Second, factors are introduced to accommodate heavy-tailed and skewed noise distributions, as commonly encountered in ultra-wideband (UWB) localization due to non-line-of-sight (NLOS) and multipath effects. Both extensions are shown to integrate naturally within the ESGVI framework while preserving its sparse and derivative-free structure. The proposed approach is validated in a UWB localization experiment with NLOS-rich measurements, demonstrating improved accuracy and comparable consistency. Finally, a Python implementation within a factor-graph-based estimation framework is made open-source to support broader research use.
DIVO: Continuous-time DVL-Inertial-Visual Odometry for Unmanned Underwater Vehicles

Kyungmin Jung, Angad Bajwa, Junha Yoo, and 2 more authors

2026

2025

LCSS
Design of Input-Output Observers for a Population of Systems With Bounded Frequency-Domain Variation Using DK-Iteration

Timothy Everett Adams and James Richard Forbes

IEEE Control Systems Letters (LCSS), Sep 2025

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This letter proposes a linear input-output observer design methodology for a population of systems in which each observer uses knowledge of the linear time-invariant dynamics of the particular device. Observers are typically composed of a known model of the system and a correction mechanism to produce an estimate of the state. The proposed design procedure characterizes the population variation in the frequency domain and synthesizes a single robust correction filter. The correction filter guarantees a level of estimation performance for all systems compatible with the uncertainty characterization. This is accomplished by posing a robust performance problem using the observer error dynamics and solving it using DK -iteration. The design procedure is experimentally demonstrated on a flexible joint robotic manipulator with varied joint stiffnesses. It is shown that the proposed robust correction filter achieves comparable estimation performance to a method using a correction gain tailored toward each joint stiffness configuration.
@article{adamsDesignInputOutputObservers2025, title = {Design of {{Input-Output Observers}} for a {{Population}} of {{Systems With Bounded Frequency-Domain Variation Using DK-Iteration}}}, author = {Adams, Timothy Everett and Forbes, James Richard}, year = {2025}, month = sep, journal = {IEEE Control Systems Letters (LCSS)}, volume = {9}, pages = {2645--2650}, issn = {2475-1456}, doi = {10.1109/LCSYS.2025.3638270}, url = {https://ieeexplore.ieee.org/document/11271285}, urldate = {2026-03-07}, selected = true, bibtex_show = true }
pykoop: Python Library for Koopman Operator Approximation

Steven Dahdah and James Richard Forbes

Journal of Open Source Software, 2025

Abs Code

pykoop is a Python package for learning differential equations in discretized form using the Koopman operator. Differential equations are an essential tool for modelling the physical world. Ordinary differential equations can be used to describe electric circuits, rigid-body dynamics, or chemical reaction rates, while the fundamental laws of electromagnetism, fluid dynamics, and heat transfer can be formulated as partial differential equations. The Koopman operator allows nonlinear differential equations to be rewritten as infinite-dimensional linear differential equations by viewing their time evolution in terms of an infinite number of nonlinear lifting functions. A finite-dimensional approximation of the Koopman operator can be identified from data given a user-selected set of lifting functions. Thanks to its linearity, the approximate Koopman model can be used for analysis, design, and optimal controller or observer synthesis for a wide range of systems using well-established linear tools. pykoop’s documentation, along with examples in script and notebook form, can be found at pykoop.readthedocs.io/en/stable. Its releases are also archived on Zenodo (Dahdah & Forbes, 2024b).
Globally Optimal Data-Association-Free Landmark-Based Localization Using Semidefinite Relaxations

Vassili Korotkine, Mitchell Cohen, and James Richard Forbes

IEEE Robotics and Automation Letters, 2025

Jointly accepted to ICRA

Abs arXiv

This letter proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally optimal fashion. Relative position measurements to a fixed set of known landmarks are used, but the data association is unknown in that the robot does not know which landmark each measurement is generated from. The relaxation is shown to be tight in a majority of cases for moderate noise levels. The proposed algorithm is compared to local Gauss-Newton baselines initialized at the dead-reckoned trajectory, and is shown to significantly improve convergence to the problem’s global optimum in simulation and experiment. Accompanying software and supplementary material can be found at https://github.com/decargroup/certifiable_uda_loc.
Matrix Scheduling of QSR-Dissipative Systems

Sepehr Moalemi and James Richard Forbes

IEEE Transactions on Automatic Control, 2025

Abs arXiv Code

This article considers gain-scheduling of quadratic supply rate (QSR)-dissipative subsystems using scheduling matrices. The corresponding QSR-dissipative properties of the overall matrix-gain-scheduled system, which depends on the QSR properties of the subsystems scheduled, are explicitly derived. The use of scheduling matrices is a generalization of the scalar scheduling signals used in the literature, and allows for greater design freedom when scheduling systems, such as in the case of gain-scheduled control. Furthermore, this work extends the existing gain-scheduling results to a broader class of QSR-dissipative systems. The matrix-scheduling of important special cases, such as passive, input strictly passive, output strictly passive, finite L2 gain, very strictly passive, and conic systems are presented. The proposed gainscheduling architecture is used in the context of controlling a planar three-link robot subject to model uncertainty. A novel control synthesis technique is used to design QSRdissipative subcontrollers that are gain-scheduled using scheduling matrices. Numerical simulation results highlight the greater design freedom of scheduling matrices, leading to improved performance.
Robust Impedance Emulation Using Optimal Filter Approach for Power-Hardware-In-the-Loop Application

Dmitry Rimorov, James Richard Forbes, Olivier Tremblay, and 1 more author

IEEE Open Journal of the Industrial Electronics Society, 2025

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Power-hardware-in-the-loop (PHIL) simulation infrastructure is an invaluable tool for testing and validating emerging technologies expected to be connected to power grids. As such, PHIL closed-loop stability is a crucial factor to consider when designing its numerical interface. Recent work has shown that the transmission line method provides a robust solution to the PHIL interface stability problem while achieving a high level of PHIL closed-loop performance. However, to fully utilize its advantages, it requires a fast impedance emulation control loop. To solve this problem, this article proposes an H optimal filter approach for characteristic impedance emulation, which allows a systematic and tractable design procedure and produces a robust controller. Robust stability and performance are assessed through the positive realness check and by virtue of the structured singular value. The proposed method and the resulting controller are compared to an existing approach and validated on a 3-kVA, 208-V PHIL experimental testbed with different types of the device under test, including a residential solar inverter. The results demonstrate significant performance improvements that are crucial for the future megawatt-scale PHIL infrastructure.
The Harmonic Exponential Filter for Nonparametric Estimation on Motion Groups

Miguel Saavedra, Steven Parkison, Ria Arora, and 2 more authors

IEEE Robotics and Automation Letters, 2025

Abs arXiv

Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are all unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing nonparametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. This letter introduces a novel approach to nonparametric Bayesian filtering on motion groups, designed to handle multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the elementwise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and asymptotically exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter’s superior performance compared with established nonparametric filtering methods across a range of simulated and real-world localization tasks.
Asymptotically Stable Data-Driven Koopman Operator Approximation with Inputs using Total Extended DMD

Louis Lortie and James Richard Forbes

Machine Learning: Science and Technology, 2025

Abs arXiv

This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an infinite set of lifting functions. A Any further distribution finite-dimensional approximation of the Koopman operator can be identified from data by of this work must maintain attribution to choosing a finite subset of lifting functions and solving a regression problem in the lifted space. the author(s) and the title of the work, journal Existing methods are designed to identify open-loop systems. However, it is impractical or citation and DOI. impossible to run experiments on some systems, such as unstable systems, in an open-loop fashion. The proposed method leverages the linearity of the Koopman operator, along with knowledge of the controller and the structure of the closed-loop (CL) system, to simultaneously identify the CL and plant systems. The advantages of the proposed CL Koopman operator approximation method are demonstrated in simulation using a Duffing oscillator and experimentally using a rotary inverted pendulum system. An open-source software implementation of the proposed method is publicly available, along with the experimental dataset generated for this paper.

2024

An Adaptive Graduated Nonconvexity Loss Function for Robust Nonlinear Least-Squares Solutions

Kyungmin Jung, Thomas Hitchcox, and James Richard Forbes

IEEE Transactions on Robotics, 2024

DOI
Data-Driven Batch Localization and SLAM Using Koopman Linearization

Zi Cong Guo, Frederike Dumbgen, James Richard Forbes, and 1 more author

IEEE Transactions on Robotics, 2024

Jointly accepted to ICRA

Abs arXiv

In this article, we present a framework for modelfree batch localization and simultaneous localization and mapping (SLAM). We use lifting functions to map a control-affine system into a high-dimensional space, where both the process model and the measurement model are rendered bilinear. During training, we solve a least-squares problem using groundtruth data to compute the high-dimensional model matrices associated with the lifted system purely from data. At inference time, we solve for the unknown robot trajectory and landmarks through an optimization problem, where constraints are introduced to keep the solution on the manifold of the lifting functions. The problem is efficiently solved using a sequential quadratic program (SQP), where the complexity of an SQP iteration scales linearly with the number of timesteps. Our algorithms, called reduced constrained Koopman linearization localization (RCKL-Loc) and reduced constrained Koopman linearization SLAM (RCKL-SLAM), are validated experimentally in simulation and on two datasets: one with an indoor mobile robot equipped with a laser rangefinder that measures range to cylindrical landmarks, and one on a golf cart equipped with radio-frequency identification (RFID) range sensors. We compare RCKL-Loc and RCKL-SLAM with classic model-based nonlinear batch estimation. While RCKL-Loc and RCKL-SLAM have a similar performance compared to their model-based counterparts, they outperform the model-based approaches when the prior model is imperfect, showing the potential benefit of the proposed datadriven technique.
A Hessian for Gaussian Mixture Likelihoods in Nonlinear Least Squares

Vassili Korotkine, Mitchell Cohen, and James Richard Forbes

IEEE Robotics and Automation Letters, 2024

Jointly accepted to ICRA

Abs arXiv Code

This letter proposes a novel Hessian approximation for Maximum a Posteriori estimation problems in robotics involving Gaussian mixture likelihoods. Previous approaches manipulate the Gaussian mixture likelihood into a form that allows the problem to be represented as a nonlinear least squares (NLS) problem. The resulting Hessian approximation used within NLS solvers from these approaches neglects certain nonlinearities. The proposed Hessian approximation is derived by setting the Hessians of the Gaussian mixture component errors to zero, which is the same starting point as for the Gauss-Newton Hessian approximation for NLS, and using the chain rule to account for additional nonlinearities. The proposed Hessian approximation results in improved convergence speed and uncertainty characterization for simulated experiments, and similar performance to the state of the art on real-world experiments. A method to maintain compatibility with existing solvers, such as ceres, is also presented.
Decentralized State Estimation: An Approach using Pseudomeasurements and Preintegration

Charles Champagne Cossette, Mohammed Ayman Shalaby, David Saussié, and 1 more author

International Journal of Robotics Research, 2024

Abs arXiv

This paper addresses the problem of decentralized, collaborative state estimation in robotic teams. In particular, this paper considers problems where individual robots estimate similar physical quantities, such as each other’s position relative to themselves. The use of pseudomeasurements is introduced as a means of modeling such relationships between robots’state estimates and is shown to be a tractable way to approach the decentralized state estimation problem. Moreover, this formulation easily leads to a general-purpose observability test that simultaneously accounts for measurements that robots collect from their own sensors, as well as the communication structure within the team. Finally, input preintegration is proposed as a communication-efficient way of sharing odometry information between robots, and the entire theory is appropriate for both vector-space and Lie-group state definitions. To overcome the need for communicating preintegrated covariance information, a deep autoencoder is proposed that reconstructs the covariance information from the inputs, hence further reducing the communication requirements. The proposed framework is evaluated on three different simulated problems, and one experiment involving three quadcopters.
Closed-loop Koopman Operator Approximation

Steven Dahdah and James Richard Forbes

Machine Learning: Science and Technology, 2024

Abs arXiv Code

This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an infinite set of lifting functions. A finite-dimensional approximation of the Koopman operator can be identified from data by choosing a finite subset of lifting functions and solving a regression problem in the lifted space. Existing methods are designed to identify open-loop systems. However, it is impractical or impossible to run experiments on some systems, such as unstable systems, in an open-loop fashion. The proposed method leverages the linearity of the Koopman operator, along with knowledge of the controller and the structure of the closed-loop (CL) system, to simultaneously identify the CL and plant systems. The advantages of the proposed CL Koopman operator approximation method are demonstrated in simulation using a Duffing oscillator and experimentally using a rotary inverted pendulum system. An open-source software implementation of the proposed method is publicly available, along with the experimental dataset generated for this paper.
Spatial Roles in Hockey Special Teams

Jonathan Arsenault, Margaret Cunniff, Eric Tulsky, and 1 more author

Journal of Quantitative Analysis in Sports, 2024

Abs

Special teams (i.e. power play and penalty kill) situations play an outsized role in determining the outcome of ice hockey games. Yet, quantitative methods for characterizing special teams tactics are limited. This work focuses on team structure and player deployment during in-zone special teams possessions. Leveraging player and puck tracking data from the National Hockey League (NHL), a framework is developed for describing player positioning during 5-on-4 power play and 4-on-5 penalty kill possessions. More specifically, player roles are defined directly from the player tracking data using non-negative matrix factorization, and every player is allocated a unique role at every frame of tracking data by solving a linear assignment problem. Team formations naturally arise through the combination of roles occupied in a frame. Roles that vary on a per-frame basis allow for a fine-grained analysis of team structure. This property of the roles-based representation is used to group together similar power play possessions using latent Dirichlet allocation, a topic modelling technique. The concept of assignments, which remain constant over an entire possession, is also introduced. Assignments provide a more stable measure of player positioning, which may be preferable when assessing deployment over longer periods of time.
Laser-to-Vehicle Extrinsic Calibration in Low-Observability Scenarios for Subsea Mapping

Thomas Hitchcox and James Richard Forbes

IEEE Robotics and Automation Letters, 2024

Jointly accepted to ICRA40

Abs arXiv

Laser line scanners are increasingly being used in the subsea industry for high-resolution mapping and infrastructure inspection. However, calibrating the 3D pose of the scanner relative to the vehicle is a perennial source of confusion and frustration for industrial surveyors. This letter describes three novel algorithms for laser-to-vehicle extrinsic calibration using naturally occurring features. Each algorithm makes a different assumption on the quality of the vehicle trajectory estimate, enabling good calibration results in a wide range of situations. A regularization technique is used to address low-observability scenarios frequently encountered in practice with large, rotationally stable subsea vehicles. Experimental results are provided for two field datasets, including the recently discovered wreck of the Endurance.
Reducing Two-Way Ranging Variance by Signal-Timing Optimization

Mohammed Ayman Shalaby, Charles Champagne Cossette, Jerome Le Ny, and 1 more author

IEEE Transactions Aerospace and Electronic Systems, 2024

Abs arXiv

Time-of-flight-based ranging among transceivers with different clocks requires protocols that accommodate varying rates of the clocks. Double-sided two-way ranging (DS-TWR) is widely adopted as a standard protocol due to its accuracy; however, the precision of DS-TWR has not been clearly addressed. In this paper, an analytical model of the variance of DS-TWR is derived as a function of the user-programmed response delays, which is then compared to the Cramer-Rao Lower Bound (CRLB). This is then used to formulate an optimization problem over the response delays in order to maximize the information gained from range measurements. The derived analytical variance model and optimized protocol are validated experimentally with 2 ranging UWB transceivers, where 29 million range measurements are collected.
Multi-Robot Relative Pose Estimation and IMU Preintegration Using Passive UWB Transceivers

Mohammed Ayman Shalaby, Charles Champagne Cossette, Jerome Le Ny, and 1 more author

IEEE Transactions on Robotics, 2024

Abs arXiv

Ultra-wideband (UWB) systems are becoming increasingly popular as a means of inter-robot ranging and communication. A major constraint associated with UWB is that only one pair of UWB transceivers can range at a time to avoid interference, hence hindering the scalability of UWB-based localization. In this article, a ranging protocol is proposed that allows all robots to passively listen on neighboring communicating robots without any hierarchical restrictions on the role of the robots. This is utilized to allow each robot to obtain more range measurements and to broadcast preintegrated inertial measurement unit (IMU) measurements for relative extended pose state estimation directly on SE_2(3). Consequently, a simultaneous clock-synchronization and relative-pose estimator is formulated using an on-manifold extended Kalman filter (EKF) and is evaluated in simulation using Monte Carlo runs for up to seven robots. The ranging protocol is implemented in C on custom-made UWB boards fitted to three quadcopters, and the proposed filter is evaluated over multiple experimental trials, yielding up to 48% improvement in localization accuracy. Fig. 1. Experimental setup. (a) Custom-made board fitted with a DWM1000 UWB transceiver. (b) Uvify IFO-S quadcopter equipped with two UWB transceivers 45 cm apart.
DIVE: Deep Inertial-Only Velocity Aided Estimation for Quadrotors

Angad Bajwa, Charles Champagne Cossette, Mohammed Ayman Shalaby, and 1 more author

IEEE Robotics and Automation Letters, 2024

Jointly accepted to IROS

Abs Code

This letter presents a novel deep-learning-based solution to the problem of quadrotor inertial navigation. Visual-inertial odometry (VIO) is often used for quadrotor pose estimation, where an inertial measurement unit (IMU) provides a motion prior. When VIO fails, IMU dead reckoning is often used, which quickly leads to significant pose estimation drift. Learned inertial odometry leverages deep learning and model-based filtering to improve upon dead reckoning. Efforts for quadrotors, however, rely on sensors other than, or in addition to, an IMU, or have only been proven on a specific set of trajectories. The proposed generalizable approach regresses a 3D velocity estimate from only a history of IMU measurements, and the learned outputs are applied as a correction to an on-manifold Extended Kalman Filter. The proposed algorithm is shown to be superior to the state-of-the-art in learned inertial odometry. A 42% improvement in localization accuracy is shown over the state-of-the-art on an in-distribution testing set, and a 22% improvement is shown on an out-of-distribution testing set. Additionally, the proposed algorithm shows a 43% improvement over dead reckoning in VIO failure scenarios.

2023

Bayesian Filtering for Homography Estimation

Arturo Del Castillo Bernal, Philippe Decoste, and James Richard Forbes

IEEE Robotics and Automation Letters, 2023

Jointly accepted to ICRA

Abs arXiv

This letter considers homography estimation in a Bayesian filtering framework using rate gyro and camera measurements. The use of rate gyro measurements facilitates a more reliable estimate of homography in the presence of occlusions, while a Bayesian filtering approach generates both a homography estimate along with an uncertainty. Uncertainty information opens the door to adaptive filtering approaches, post-processing procedures, and safety protocols. In particular, herein an iterative extended Kalman filter and an interacting multiple model (IMM) filter are tested using both simulated and experimental datasets. The IMM is shown to have good consistency properties and better overall performance when compared to the state-of-the-art homography nonlinear deterministic observer in both simulations and experiments.
System Identification and Simulation of Soft Tissue Force Feedback in a Spine Surgical Simulator

Harriet Chorney, James Richard Forbes, and Mark Driscoll

Computers in Biology and Medicine, 2023

Abs

Surgical simulators are being introduced as training modalities for surgeons. This paper aims to evaluate dynamic models used to convey force feedback from puncturing the soft tissue during a spine surgical simulation. The force feedback of the tissue is treated as a dynamic system. This is done by performing classical system identification across a bandwidth of frequencies on a tissue analogue and fitting that behaviour to dynamic viscoelastic models. The models that are tested are an inverted linear model, the Maxwell model, the Kelvin-Boltzmann (KB) model, and a higher-order blackbox (HO) model. Several error metrics such as percent variance accounted for (%VAF) are determined to measure solution accuracy. The force feedback models are programmed into a surgical simulator and tested with study participants who rated them based on how well the identified models match the behaviour of the rubber tissue analogue. The highest %VAF is 82.64% when the tissue is modelled as the HO model. Statistically significant differences (p < 0.05) are found between all model ratings from participants except between the HO model and the KB model. However, the HO model has the highest percentage (37.8%) of participants who rank its performance as the closest to the tissue analogue compared to the other force feedback models. The more accurately the dynamic behaviour resembles the tissue analogue, the higher the model was rated by study participants. This study highlights the importance of utilizing dynamic signals to generate dynamic models of soft tissue for spine surgical simulators.
Combining DVL-INS and Laser-based Loop Closures in a Batch Estimation Framework for Underwater Positioning

Amro Al-Baali, Thomas Hitchcox, and James Richard Forbes

IEEE Journal of Oceanic Engineering, 2023

Abs arXiv

Correcting gradual position drift is a challenge in long-term subsea navigation. Though highly accurate, modern inertial navigation system (INS) estimates will drift over time due to the accumulated effects of sensor noise and biases, even with acoustic aiding from a Doppler velocity log (DVL). The raw sensor measurements and estimation algorithms used by the DVL-aided INS are often proprietary, which restricts the fusion of additional sensors that could bound navigation drift over time. In this letter, the raw sensor measurements and their respective covariances are estimated from the DVL-aided INS output using semidefinite programming tools. The estimated measurements are then augmented with laser-based loop-closure measurements in a batch state estimation framework to correct planar position errors. The heading uncertainty from the DVL-aided INS is also considered in the estimation of the updated positions. The pipeline is tested in simulation and on experimental field data. The proposed methodology reduces the long-term navigation drift by more than 30 times compared to the DVL-aided INS estimate.
Know What You Don’t Know: Consistency in Sliding Window Filtering with Unobservable States Applied to Visual-Inertial SLAM

Daniil Lisus, Mitchell Cohen, and James Richard Forbes

IEEE Robotics and Automation Letters, 2023

Abs arXiv

Estimation algorithms, such as the sliding window filter, produce an estimate and uncertainty of desired states. This task becomes challenging when the problem involves unobservable states. In these situations, it is critical for the algorithm to “know what it doesn’t know”, meaning that it must maintain the unobservable states as unobservable during algorithm deployment. This letter presents general requirements for maintaining consistency in sliding window filters involving unobservable states. The value of these requirements for designing navigation solutions is experimentally shown within the context of visual-inertial SLAM making use of IMU preintegration.
Improving Self-Consistency in Underwater Mapping through Laser-Based Loop Closure

Thomas Hitchcox and James Richard Forbes

IEEE Transactions on Robotics, 2023

Jointly accepted to ICRA

Abs arXiv

Accurate, self-consistent bathymetric maps are needed to monitor changes in subsea environments and infrastructure. These maps are increasingly collected by underwater vehicles, and mapping requires an accurate vehicle navigation solution. Commercial off-the-shelf (COTS) navigation solutions for underwater vehicles often rely on external acoustic sensors for localization; however, survey-grade acoustic sensors are expensive to deploy and limit the range of the vehicle. Techniques from the field of simultaneous localization and mapping, particularly loop closures, can improve the quality of the navigation solution over dead reckoning, but are difficult to integrate into COTS navigation systems. This article presents a method to improve the self-consistency of bathymetric maps by smoothly integrating loop-closure measurements into the state estimate produced by a commercial subsea navigation system. Integration is done using a white-noise-on-acceleration motion prior, without access to raw sensor measurements or proprietary models. Improvements in map self-consistency are shown for both simulated and experimental datasets, including a 3-D scan of an underwater shipwreck in Wiarton, ON, Canada.
Cascaded Model Predictive Control of a Tandem-Rotor Helicopter

Faraaz Ahmed, Ludwik Andrew Sobiesiak, and James Richard Forbes

IEEE Control Systems Letters, 2023

Abs arXiv

This letter considers cascaded model predictive control (MPC) as a computationally lightweight method for controlling a tandem-rotor helicopter. A traditional single MPC structure is split into separate outer and inner-loops. The outer-loop MPC uses an SE_2(3) error to linearize the translational dynamics about a reference trajectory. The inner-loop MPC uses the optimal angular velocity sequence of the outer-loop MPC to linearize the rotational dynamics. The outer-loop MPC is run at a slower rate than the inner-loop allowing for longer prediction time and improved performance. Monte-Carlo simulations demonstrate robustness to model uncertainty and environmental disturbances. The proposed control structure is benchmarked against a single MPC algorithm where it shows significant improvements in position and velocity tracking while using significantly less computational resources.

2022

Spacecraft Energy Management using Convex Optimisation

Martin Doff-Sotta, Mark Cannon, and James Richard Forbes

Energy Conversion and Management: X, 2022

Abs

This paper considers a spacecraft energy management strategy for optimally scheduling the power available for secondary tasks, such as communications and scientific payloads, while meeting the power demand for primary tasks, such as thermal management and propulsion, and adhering to operating constraints. A solution based on convex optimisation and model predictive control is proposed. Mathematical models of the various energy subsystems are used to formulate the energy management task over a future horizon as a constrained optimisation problem. We show that this problem can be formulated as a convex program and we derive an energy management strategy in the form of a model predictive control law. The convex problem formulation guarantees global optimality of the presented solution and opens the way for future onboard real-time implementations.
System Norm Regularization Methods for Koopman Operator Approximation

Steven Dahdah and James Richard Forbes

Proceedings of the Royal Society A, 2022

Abs arXiv Code

This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed H_2-H∞ optimal control.
System Identification and Two-Degree-of-Freedom Control of Nonlinear, Viscoelastic Tissues

Amanda Bianco, Raphael Zonis, Anne-Marie Lauzon, and 2 more authors

IEEE Transactions on Biomedical Engineering, 2022

Abs arXiv

Objective: This paper presents a force control scheme for brief isotonic holds in an isometrically contracted muscle tissue, with minimal overshoot and settling time to measure its shortening velocity, a key parameter of muscle function. Methods: A two-degree-of-freedom control configuration, formed by a feedback controller and a feedforward controller, is explored. The feedback controller is a proportional-integral controller and the feedforward controller is designed using the inverse of a control-oriented model of muscle tissue. A generalized linear model and a nonlinear model of muscle tissue are explored using input-output data and system identification techniques. The force control scheme is tested on equine airway smooth muscle and its robustness confirmed with murine flexor digitorum brevis muscle. Results: Performance and repeatability of the force control scheme as well as the number of inputs and level of supervision required from the user were assessed with a series of experiments. The force control scheme was able to fulfill the stated control objectives in most cases, including the requirements for settling time and overshoot. Conclusion: The proposed control scheme is shown to enable automation of force control for characterizing muscle mechanics with minimal user input required. Significance: This paper leverages an inversion-based feedforward controller based on a nonlinear physiological model in a system identification context that is superior to classic linear system identification. The control scheme can be used as a steppingstone for generalized control of nonlinear, viscoelastic materials.
Mind the Gap: Norm-Aware Adaptive Robust Loss for Multivariate Least-Squares Problems

Thomas Hitchcox and James Richard Forbes

IEEE Robotics and Automation Letters, 2022

Jointly accepted to IROS

Abs arXiv

Measurement outliers are unavoidable when solving real-world robot state estimation problems. A large family of robust loss functions (RLFs) exists to mitigate the effects of outliers, including newly developed adaptive methods that do not require parameter tuning. All of these methods assume that residuals follow a zero-mean Gaussian-like distribution. However, in multivariate problems the residual is often defined as a norm, and norms follow a Chi-like distribution with a non-zero mode value. This produces a “mode gap” that impacts the convergence rate and accuracy of existing RLFs. The proposed approach, “Adaptive MB,” accounts for this gap by first estimating the mode of the residuals using an adaptive Chi-like distribution. Applying an existing adaptive weighting scheme only to residuals greater than the mode leads to more robust performance and faster convergence times in two fundamental state estimation problems, point cloud alignment and pose averaging.
Model Predictive Control of a Tandem-Rotor Helicopter with a Non-Uniformly Spaced Prediction Horizon

Faraaz Ahmed, Ludwik Andrew Sobiesiak, and James Richard Forbes

IEEE Control Systems Letters, 2022

Jointly accepted to CDC

Abs arXiv

This letter considers model predictive control of a tandem-rotor helicopter. The error is formulated using the matrix Lie group SE_2(3). A reference trajectory to a target is calculated using a quartic guidance law, leveraging the differentially flat properties of the system, and refined using a finite-horizon linear quadratic regulator. The nonlinear system is linearized about the reference trajectory enabling the formulation of a quadratic program with control input, attitude keep-in zone, and attitude error constraints. A non-uniformly spaced prediction horizon is leveraged to capture the multi-timescale dynamics while keeping the problem size tractable. Monte-Carlo simulations demonstrate robustness of the proposed control structure to initial conditions, model uncertainty, and environmental disturbances.
Position and Attitude Tracking Control Using CCW and SNI System Theory With Applications to Multi-agent Systems

Ken Lee and James Richard Forbes

Automatica, 2022

Abs

This paper considers position and attitude tracking control. Counterclockwise (CCW) input-output maps from force and torque to position and attitude are established for rigid-body position and attitude motion. Using the properties of counterclockwise systems and negative imaginary (NI) systems, a stabilizing strictly negative imaginary (SNI) controller is shown to drive the tracking errors in position and attitude to zero. In addition, a method to synthesize the strictly negative imaginary controller in a H∞-optimal sense is presented. The control laws are then extended to the formation control problem in multi-agent systems. Numerical results are included.
Vectorial Parameterizations of Pose

Timothy Barfoot, James Richard Forbes, and Gabriele M.T. D’Eleuterio

Robotica, 2022

Abs arXiv

Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of a vector space are surjectively mapped to a matrix Lie group. For example, these vectorial representations can be employed for optimization as well as uncertainty representation on groups. The most common mapping is the matrix exponential, which maps elements of a Lie algebra onto the associated Lie group. However, this choice is not unique. It has been previously shown how to characterize all such vectorial parameterizations for SO(3), the group of rotations. Some results are also known for the group of poses, where it is possible to build a family of vectorial mappings that includes the matrix exponential as well as the Cayley transformation. We extend what is known for these pose mappings to the 4 x 4 representation common in robotics and also demonstrate three di erent examples of the proposed pose mappings: (i) pose interpolation, (ii) pose servoing control, and (iii) pose estimation in a pointcloud alignment problem. In the pointcloud alignment problem, our results lead to a new algorithm based on the Cayley transformation, which we call CayPer.
Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems

Zi Cong Guo, Vassili Korotkine, James Richard Forbes, and 1 more author

IEEE Robotics and Automation Letters, 2022

Jointly accepted to ICRA

Abs arXiv

We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of controlaffine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference computational cost that is independent of the number of training points. We lift the original nonlinear system into a higher-dimensional Reproducing Kernel Hilbert Space (RKHS), where the system becomes bilinear. The time-invariant model matrices can be learned by solving a least-squares problem on training trajectories. At test time, the system is algebraically manipulated into a linear time-varying system, where standard batch linear state estimation techniques can be used to efficiently compute state means and covariances. Random Fourier Features (RFF) are used to combine the computational efficiency of Koopman-based methods and the generality of kernel-embedding methods. KoopSE is validated experimentally on a localization task involving a mobile robot equipped with ultra-wideband receivers and wheel odometry. KoopSE estimates are more accurate and consistent than the standard model-based extended Rauch-Tung-Striebel (RTS) smoother, despite KoopSE having no prior knowledge of the system’s motion or measurement models. Fig. 1. Left: KoopSE concept flowchart. KoopSE uses training data to learn a high-dimensional system, allowing inference to be done by solving a linear state estimation problem. Right: Experimental setup for validating KoopSE. A Husky robot drives around in an indoor environment while receiving range measurements from ultra-wideband (UWB) anchors and logging wheel odometry.
Down-Speeding Diesel Engines with Two-Stage Turbochargers: Analysis and Control Considerations

Daryoush Mirza-Hekmati, William Heath, Judith Apsley, and 1 more author

International Journal of Engine Research, 2022

Abs

Diesel engines continue to be used in truck applications, so reducing fuel use and hence CO2 emissions, is a priority. Single-stage turbocharged diesel engines are known to be fuel efficient under steady load at low speeds. However, the engine’s ability to track load transients becomes limited by emission constraints due to the rate of production values for smoke and the resulting higher nitrogen oxides (NOx). Modern air-path solutions including a variable geometry turbine (VGT) and high pressure exhaust gas recirculation (EGR) can be used to improve dynamic response without increasing NOx emissions, but lead to complex interactions that can be difficult to control. This paper develops a two-stage, inseries, air-path configuration, which improves the typical part-load performance at low engine-speeds through adjustments to the turbine expansion ratios. Better EGR rates (for NOx reduction) at low engine speeds can be achieved whilst the engine transient response is maintained. The air-path system is simulated using Ricardo Wave software and analysed for steady-state and transient behaviour in order to identify the relationships, constraints and performance measures for different operating regions that specify the controller requirements.

2021

Heading Estimation Using Ultra-wideband Received Signal Strength and Gaussian Processes

Daniil Lisus, Charles Champagne Cossette, Mohammed Ayman Shalaby, and 1 more author

IEEE Robotics and Automation Letters, 2021

Jointly accepted to IROS

Abs arXiv

It is essential that a robot has the ability to determine its position and orientation to execute tasks autonomously. Heading estimation is especially challenging in indoor environments where magnetic distortions make magnetometer-based heading estimation difficult. Ultra-wideband (UWB) transceivers are common in indoor localization problems. This letter experimentally demonstrates how to use UWB range and received signal strength (RSS) measurements to estimate robot heading. The RSS of a UWB antenna varies with its orientation. As such, a Gaussian process (GP) is used to learn a data-driven relationship from UWB range and RSS inputs to orientation outputs. Combined with a gyroscope in an invariant extended Kalman filter, this realizes a heading estimation method that uses only UWB and gyroscope measurements.
Cascaded Filtering Using the Sigma Point Transformation

Mohammed Ayman Shalaby, Charles Champagne Cossette, Jerome Le Ny, and 1 more author

IEEE Robotics and Automation Letters, 2021

Jointly accepted to ICRA. Best student paper award finalist (1 of 4 finalists).

Abs arXiv

It is often convenient to separate a state estimation task into smaller “local” tasks, where each local estimator estimates a subset of the overall system state. However, neglecting cross-covariance terms between state estimates can result in overconfident estimates, which can ultimately degrade the accuracy of the estimator. Common cascaded filtering techniques focus on the problem of modelling cross-covariances when the local estimators share a common state vector. This letter introduces a novel cascaded and decentralized filtering approach that approximates the cross-covariances when the local estimators consider distinct state vectors. The proposed estimator is validated in simulations and in experiments on a three-dimensional attitude and position estimation problem. The proposed approach is compared to a naive cascaded filtering approach that neglects cross-covariance terms, a sigma point-based Covariance Intersection filter, and a full-state filter. In both simulations and experiments, the proposed filter outperforms the naive and the Covariance Intersection filters, while performing comparatively to the full-state filter.
Relative Position Estimation in Multi-Agent Systems Using Attitude-Coupled Range Measurements

Mohammed Ayman Shalaby, Charles Champagne Cossette, James Richard Forbes, and 1 more author

IEEE Robotics and Automation Letters, 2021

Jointly accepted to ICRA

Abs arXiv

The ability to accurately estimate the position of robotic agents relative to one another, in possibly GPS-denied environments, is crucial to execute collaborative tasks. Inter-agent range measurements are available at a low cost, due to technologies such as ultra-wideband radio. However, the task of threedimensional relative position estimation using range measurements in multi-agent systems suffers from unobservabilities. This letter presents a sufficient condition for the observability of the relative positions, and satisfies the condition using a simple framework with only range measurements, an accelerometer, a rate gyro, and a magnetometer. The framework has been tested in simulation and in experiments, where 40-50 cm positioning accuracy is achieved using inexpensive off-the-shelf hardware.
Relative Position Estimation Between Two UWB Devices with IMUs

Charles Champagne Cossette, Mohammed Ayman Shalaby, David Saussié, and 2 more authors

IEEE Robotics and Automation Letters, 2021

Jointly accepted to ICRA.

Abs arXiv

For a team of robots to work collaboratively, it is crucial that each robot have the ability to determine the position of their neighbors, relative to themselves, in order to execute tasks autonomously. This letter presents an algorithm for determining the three-dimensional relative position between two mobile robots, each using nothing more than a single ultra-wideband transceiver, an accelerometer, a rate gyro, and a magnetometer. A sliding window filter estimates the relative position at selected keypoints by combining the distance measurements with acceleration estimates, which each agent computes using an on-board attitude estimator. The algorithm is appropriate for real-time implementation, and has been tested in simulation and experiment, where it comfortably outperforms standard estimators. A positioning accuracy of less than 1 m is achieved with inexpensive sensors.

2020

Design and Configuration of Folded Platonic Strapdowns of Biaxial MEMS Accelerometers

Xiaowei Shan, Jorge Angeles, and James Richard Forbes

ASME Journal of Mechanical Design, 2020

Abs

The authors report on the design, configure, and test of isotropic accelerometer strapdowns for high-precision inertial measurement unit (IMU) and folded MEMS configuration. The biaxial low-g MEMS accelerometers are based on the Platonic solids. A Platonic strapdown is integrated into an embedded system for acceleration-array signal acquisition targeting rigid-body pose-and-twist estimation. The electromechanical properties for dynamic sensitivity are tested on a haptic manipulator, which shows that the position estimation matches reasonably well the encoder readouts. The Platonic strapdown is promising in folded MEMS IMU with chip-level miniaturization and high estimation precision.
Finite-Horizon LQR Control of Quadrotors on SE_2(3)

Mitchell Cohen, Khairi Abdulrahim, and James Richard Forbes

IEEE Robotics and Automation Letters, 2020

Jointly accepted to IROS

Abs arXiv

This letter considers optimal control of a quadrotor unmanned aerial vehicles (UAV) using the discrete-time, finitehorizon, linear quadratic regulator (LQR). The state of a quadrotor UAV is represented as an element of the matrix Lie group of double direct isometries, SE_2(3). The nonlinear system is linearized using a left-invariant error about a reference trajectory, leading to an optimal gain sequence that can be calculated offline. The reference trajectory is calculated using the differentially flat properties of the quadrotor. Monte-Carlo simulations demonstrate robustness of the proposed control scheme to parametric uncertainty, stateestimation error, and initial error. Additionally, when compared to an LQR controller that uses a conventional error definition, the proposed controller demonstrates better performance when initial errors are large.
The Invariant Rauch-Tung-Striebel Smoother

Niels Laan, Mitchell Cohen, Jonathan Arsenault, and 1 more author

IEEE Robotics and Automation Letters, 2020

Jointly accepted to IROS

Abs arXiv

This letter presents an invariant Rauch-Tung-Striebel (IRTS) smoother applicable to systems with states that are an element of a matrix Lie group. In particular, the extended RauchTung-Striebel (RTS) smoother is adapted to work within a matrix Lie group framework. The main advantage of the invariant RTS (IRTS) smoother is that the linearization of the process and measurement models is independent of the state estimate resulting in state-estimate-independent Jacobians when certain technical requirements are met. A sample problem is considered that involves estimation of the three dimensional pose of a rigid body on SE(3), along with sensor biases. The multiplicative RTS (MRTS) smoother is also reviewed and is used as a direct comparison to the proposed IRTS smoother using experimental data. Both smoothing methods are also compared to invariant and multiplicative versions of the Gauss-Newton approach to solving the batch state estimation problem.
Exactly Sparse Gaussian Variational Inference with Application to Derivative-Free Batch Nonlinear State Estimation

Timothy Barfoot, James Richard Forbes, and David Yoon

International Journal of Robotics Research, 2020

Abs arXiv

We present a Gaussian variational inference (GVI) technique that can be applied to large-scale nonlinear batch state estimation problems. The main contribution is to show how to fit both the mean and (inverse) covariance of a Gaussian to the posterior efficiently, by exploiting factorization of the joint likelihood of the state and data, as is common in practical problems. This is different than maximum a posteriori (MAP) estimation, which seeks the point estimate for the state that maximizes the posterior (i.e., the mode). The proposed exactly sparse Gaussian variational inference (ESGVI) technique stores the inverse covariance matrix, which is typically very sparse (e.g., block-tridiagonal for classic state estimation). We show that the only blocks of the (dense) covariance matrix that are required during the calculations correspond to the non-zero blocks of the inverse covariance matrix, and further show how to calculate these blocks efficiently in the general GVI problem. ESGVI operates iteratively, and while we can use analytical derivatives at each iteration, Gaussian cubature can be substituted, thereby producing an efficient derivative-free batch formulation. ESGVI simplifies to precisely the Rauch-Tung-Striebel (RTS) smoother in the batch linear estimation case, but goes beyond the ‘extended’ RTS smoother in the nonlinear case because it finds the best-fit Gaussian (mean and covariance), not the MAP point estimate. We demonstrate the technique on controlled simulation problems and a batch nonlinear simultaneous localization and mapping problem with an experimental dataset.
Navigation and Control of Unconventional VTOL UAVs in Forward-Flight with Explicit Velocity Wind Estimation

Mitchell Cohen and James Richard Forbes

IEEE Robotics and Automation Letters, 2020

Jointly accepted to ICRA

Abs arXiv

This letter presents a solution for the state estimation and control problems for a class of unconventional vertical takeoff and landing (VTOL) UAVs operating in forward-flight conditions. A tightly-coupled state estimation approach is used to estimate the aircraft navigation states, sensor biases, and the wind velocity. State estimation is done within a matrix Lie group framework using the Invariant Extended Kalman Filter (IEKF), which offers several advantages compared to standard multiplicative EKFs traditionally used in aerospace and robotics problems. An SO(3)-based attitude controller is employed, leading to a single attitude control law without a separate sideslip control loop. A control allocator is used to determine how to use multiple, possibly redundant, actuators to produce the desired control moments. The wind velocity estimates are used in the attitude controller and the control allocator to improve performance. A numerical example is considered using a sample VTOL tailsitter-type UAV with four control surfaces. Monte-Carlo simulations demonstrate robustness of the proposed control and estimation scheme to various initial conditions, noise levels, and flight trajectories.
The Complex-Step Derivative Approximation on Matrix Lie Groups

Charles Champagne Cossette, Alex Walsh, and James Richard Forbes

IEEE Robotics and Automation Letters, 2020

Jointly accepted to ICRA

Abs arXiv

The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is extended to be compatible with elements of matrix Lie groups. As with the standard complex-step derivative, the method is still able to achieve analytical accuracy, up to machine precision, with a single function evaluation. Compared to a central-difference scheme, the proposed complex-step approach is shown to have superior accuracy. The approach is applied to two different pose estimation problems, and is able to recover the same results as an analytical method when available.
Lagrangian Derivation of Variable-Mass Equations of Motion using an Arbitrary Attitude Parameterization

Charles Champagne Cossette, James Richard Forbes, and David Saussié

Journal of the Astronautical Sciences, 2020

Abs

Lagrange’s equation is a popular method of deriving equations of motion due to the ability to choose a variety of generalized coordinates and implement constraints. When using a Lagrangian formulation, part of the generalized coordinates may describe the attitude. This paper presents a means of deriving the dynamics of variable-mass systems using Lagrange’s equation while using an arbitrary constrained attitude parameterization. The equivalence to well-known forms of the equations of motion is shown.
Elastodynamics of a Parallel Schönflies-motion Generator

Zuyu Yin, Bruno Belzile, Jorge Angeles, and 1 more author

Transactions of the Canadian Society for Mechanical Engineering, 2020

Abs

The authors propose a model of the elastodynamics of the Peppermill Carrier, a parallel isostatic Schönflies-motion generator designed for pick-and-place operations. The Cartesian spring and the finite element method are used to build the elastodynamics model of the robot. The stiffness and mass matrices are introduced to obtain the natural frequencies of the robot along a test trajectory — the Adept test cycle — that serves to evaluate the performance of the robot with respect to the operation speed.
Conic Sector Analysis Using Integral Quadratic Constraints

Matthew Turner and James Richard Forbes

International Journal of Robust and Nonlinear Control, 2020

Abs

This paper interprets the Conic Sector stability results of Zames, and the multivariable generalizations provided by Safonov and Athans, in an integral quadratic constraint context. The ideas are formulated for the case where one element of a feedback interconnection is linear and the other satisfies a conic sector condition. This scenario allows the main stability results to be formulated using integral quadratic constraints, with all finite-sector cases being captured using this framework. The stability results are expressed using frequency domain inequalities or linear-matrix inequalities. Some examples show how the main technical result can, in the multivariable case, be used to provide a reduction in conservatism over standard results.
MIMO Nyquist Interpretation of the Large Gain Theorem

Ryan James Caverly, Leila Jasmine Bridgeman, Richard Pates, and 1 more author

International Journal of Control, 2020

Abs

The Large Gain Theorem is an input-output stability result with intriguing applications in the field of control systems. This paper aims to increase understanding and appreciation of the Large Gain Theorem by presenting an interpretation of it for linear time-invariant systems using the well-known Nyquist stability criterion and illustrative examples of its use. The Large Gain Theorem is complementary in nature to the Small Gain Theorem, as it uses a lower bound on the gain of the open-loop system to guarantee closed-loop stability, rather than an upper bound on the gain of the open-loop system. It is shown that the stipulations of the Large Gain Theorem ensure that the multi-input multi-output Nyquist stability criterion is satisfied. Numerical examples of minimum gain and systems that satisfy the Large Gain Theorem are presented, along with examples that make use of the Large Gain Theorem to guarantee robust closed-loop stability.

2019

A Novel Capacitive Sensing Structure for Simultaneous Detection of Biaxial Low-g Acceleration in a Commercial MEMS Process

Xiaowei Shan, Jorge Angeles, and James Richard Forbes

Microsystem Technologies, 2019

Abs

The authors report a novel MEMS capacitive sensing structure that utilizes a single-layer electroplated gold to achieve simultaneous sensing of biaxial acceleration with low cross-axis sensitivity. The capacitive sensing structure is designed for the in-plane biaxial accelerometer with high frequency ratio and low-g acceleration range. The etching precision of the large proof-mass suspension is guaranteed by the design of detachable supporting islands. Then, different locations are explored in arranging the capacitors, for which the corresponding estimation algorithms are derived. Finally, the proposed structure was fabricated under the commercial MicraGEM-Si platform based on silicon-on-insulator (SOI) technologies. In summary, the structural and fabrication designs of the MEMS capacitive sensing structure solve the problems in biaxial independent sensing, while offering: 3D connectivity of electrodes using planar fabrication technologies; large proof-mass fabrication precision; identical mobility range in all in-plane directions; and sensing algorithms for any regular polygonal shape.
Iterative H_2-Conic Controller Synthesis

Leila Jasmine Bridgeman and James Richard Forbes

International Journal of Robust and Nonlinear Control, 2019

Abs

This paper proposes a method to synthesize controllers that minimize an upper bound on the closed-loop H_2-norm while imposing desired controller conic bounds. An initial conic controller is synthesized and iteratively improved. Conic sectors can be used to characterize a variety of input-output properties, such as gain, phase, and minimum gain. If such plant properties hold robustly to uncertainty present, then closed-loop stability can be ensured robustly via the Conic Sector Theorem by imposing desired controller conic bounds. Consequently, this paper provides a versatile optimal and robust controller synthesis method. Moreover, it relies only on the solution of convex optimization problems subject to linear matrix inequality constraints, making it readily implementable.
Synthesis of Strictly Positive Real H_2 Controllers Using Dilated LMIs

James Richard Forbes

International Journal of Control, 2019

Abs

This paper considers strictly positive real (SPR) controller design via direct minimisation of an upper bound on the closed-loop H_2 norm. To realise a tractable design problem, an observer-based control structure is assumed and a state-feedback gain that renders the controller SPR while minimising an upper bound on the closed-loop H_2 norm is sought. A convex optimisation problem subject to linear matrix inequality (LMI) constraints is realised by using a common Lyapunov variable. By using dilated LMIs, a partial separation of design variables is possible thereby enhancing design freedom. Numerical results comparing the common Lyapunov variable solution, the dilated LMI solution and method presented in the literature are included.
Dynamic Modelling and Adaptive Control of a Flexible Cable-Driven Parallel Robot

Harsh Atul Godbole, Ryan James Caverly, and James Richard Forbes

ASME Journal of Dynamic Systems, Measurement and Control, 2019

Abs

This paper investigates the dynamic modeling and adaptive control of a single degree-offreedom flexible cable-driven parallel robot (CDPR). A Rayleigh-Ritz cable model is developed that takes into account the changes in cable mass and stiffness due to its winding and unwinding around the actuating winch, with the changes distributed throughout the cables. The model uses a set of state-dependent basis functions for discretizing cables of varying length. A novel energy-based model simplification is proposed to further facilitate reduction in the computational load when performing numerical simulations involving the Rayleigh-Ritz model. For control purposes, the massive payload assumption is used to decouple the rigid and elastic dynamics of the system, and a modified input torque and modified output payload rate are used to develop a passive input–output map for the naturally noncollocated system. A passivity-based adaptive control law is derived to dynamically adapt to changes in cable properties and payload inertia, and different forms of the adaptive control law regressor are proposed. It is shown through numerical simulations that the adaptive controller is robust to changes in payload mass and cable properties, and the selection of the regressor form has a significant impact on the performance of the controller.
Nonlinear Approaches to Linear- and Linear-Matrix-Inequality-Constrained State Estimation

Robin Aucoin, Stephen Alexander Chee, and James Richard Forbes

IEEE Transactions on Aerospace and Electronic Systems, 2019

Abs

This paper considers nonlinear state estimation subject to inequality constraints in the form of linear and linear-matrix inequalities. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. Additional constraints, such as weighted-norm- or linear-inequality constraints, that the state estimate must satisfy are easily augmented to the constrained optimization problem. The proposed constrained estimation methodology is applied in the extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) frameworks. Motivated by estimation problems involving a vehicle that can rotate and translate in space, multiplicative versions of the constrained EKF and SPKF formulations are discussed. Simulation results for a ground-based mobile robot operating in a constrained three-dimensional terrain are presented and are compared to results that use the traditional multiplicative EKF and SPKF, as well as filters that enforce inequality constraints by simply projecting the state estimate into the constrained domain along the shortest Euclidean distance.
Higher-Order Nonlinear Complementary Filtering on Lie Groups

David Evan Zlotnik and James Richard Forbes

IEEE Transactions on Automatic Control, 2019

Abs arXiv

Nonlinear observer design for systems whose state-space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model and corrects the propagated state estimate using an innovation term on the tangent space of the Lie group. In the proposed method, the innovation term is constructed by passing the gradient of an invariant cost function, resolved in a basis of the tangent space, through a linear time-invariant system. The introduction of the linear system completes the extension of linear complementary filters to nonlinear Lie group observers by allowing higher order filtering. In practice, the proposed method allows for greater design freedom and, with the appropriate selection of the linear filter, the ability to filter bias and noise over specific bandwidths. A disturbance observer that accounts for constant and harmonic disturbances in group velocity measurements is also considered. Local asymptotic stability about the desired equilibrium point is demonstrated. A numerical example that demonstrates the desirable properties of the observer is presented in the context of pose estimation.

2018

Gradient-Based Observer for Simultaneous Localization and Mapping

David Evan Zlotnik and James Richard Forbes

IEEE Transactions on Automatic Control, 2018

Abs

An observer for simultaneous localization and mapping is considered in this paper. The proposed observer is based on recent theoretical foundations in a gradient-based observer design on Lie groups. As such, the form of the observer is similar to recently developed nonlinear attitude and pose observers. Translational and angular velocity measurements, as well as relative position measurements of nearby landmarks, are used directly within the observer structure. The case of biased translational and angular velocity measurements is also considered. Stability results are presented that demonstrate an asymptotic convergence of the pose and map estimates. The proposed algorithm is implemented successfully in experiment.
H∞-Optimal Parallel Feedforward Control Using Minimum Gain

Ryan James Caverly and James Richard Forbes

IEEE Control Systems Letters, 2018

Abs

This letter presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system minimum phase by augmenting its output. The system output is perturbed the least amount possible by minimizing the gain of the parallel feedforward controller while ensuring the augmented system is minimum phase. This is done by minimizing the maximum singular value of a static parallel feedforward controller or the weighted H∞ norm of a dynamic parallel feedforward controller. Static and dynamic parallel feedforward controllers are synthesized using direct and indirect methods that involve bilinear matrix inequality constraints and are solved iteratively using linear matrix inequalities. The direct method enforces a minimum gain constraint directly on the augmented system, while the indirect method solves for an asymptotically stabilizing negative feedback controller that is inverted to obtain the parallel feedforward controller. Numerical examples are provided to demonstrate the effectiveness of the proposed controller synthesis methods.
Constrained Attitude Control on SO(3) via Semidefinite Programming

Alex Walsh and James Richard Forbes

AIAA Journal of Guidance, Control, and Dynamics, 2018

Abs

(No abstract.)
Design of a Biaxial High Frequency Ratio Low-g MEMS Accelerometer

Xiaowei Shan, Jorge Angeles, and James Richard Forbes

Microsystem Technologies, 2018

Abs

A micro/meso-scale monolithic architecture was designed, fabricated and tested for in-plane inertial sensing and actuation with isotropic stiffness in the sensitive plane and high frequency-ratios between the insensitive and sensitive directions. The architecture was designed to accommodate any regular polygonal shape with a proof-mass suspension made of a serial array of compliant parallelogram linkages. Structural optimization and finite element analysis were conducted to achieve high frequency ratios and a high degree of compliance in the sensitive directions, for low-g applications and in-plane sensing. Then, the elastically isotropic structure for any regular polygonal shape was modeled in the sensitive plane and validated numerically. Lame curves were introduced in the fillets to relax the stress concentration, while air-damping analysis was introduced to provide prediction of the high resistance in the insensitive out-of-plane motion. Next, the microfabrication process was devised and conducted for triangular and square structures based on the biaxial architecture. Special techniques were studied on the wafer bonding with large cavities and the adhesive influence during deep reactiveion etching (DRIE). Finally, techniques were studied on the reflectivity adjustment of the sample surface and the in-plane biaxial motion detection of the fundamental frequencies using a uniaxial laser-sensing system. Vibration tests conducted in the micro/meso prototypes validated the isotropic biaxial sensitivity and the size effect of the high squeezed-film air damping in the insensitive direction.
On Constrained Kalman Filtering

Anton de Ruiter, James Richard Forbes, and Maksims Demjanenko

AIAA Journal of Guidance, Control, and Dynamics, 2018

Abs

(No abstract.)
Very Strictly Passive Controller Synthesis with Affine Parameter Dependence

Alex Walsh and James Richard Forbes

IEEE Transactions on Automatic Control, 2018

Abs

This paper considers linear parameter-varying (LPV) control within a passive systems framework. A very strictly passive (VSP) controller is presented in state-space form where the state-space matrices have an affine dependence on plant parameters. The resulting controller is a VSP-LPV controller guaranteed to stabilize nonlinear passive systems via the passivity theorem. An H∞-inspired control synthesis method is presented along with an experimental comparison between the proposed VSP-LPV controller and a self-scheduled LPV controller. Experimental results demonstrate effective joint angle and rate tracking of a two-link flexible-joint manipulator when the proposed VSP-LPV controller is used.
Flexible Planar Cable-Driven Parallel Manipulator Control: Maintaining Positive Cable Tensions

Ryan James Caverly and James Richard Forbes

IEEE Transactions on Control Systems Technology, 2018

Abs

In this brief, a planar cable-driven parallel manipulator is controlled using a strictly positive real compensator, cable pretension is explicitly accounted for, and cable slack is avoided. A strictly positive real controller is implemented using actuator saturation prevention techniques and the solution to a linear programming problem to ensure that the cable tensions remain strictly positive. Pretension torque is directly accounted for when determining the input-output stability of the closed-loop system. Numerical simulations demonstrate that the controller can track high-acceleration trajectories with the same precision as a state-of-the-art controller from the literature, while maintaining positive cable tensions.
Comparative Study of Input-Output Stability Results

Leila Jasmine Bridgeman and James Richard Forbes

IEEE Transactions on Automatic Control, 2018

Abs

At present, many similar but disparate input-output (I-O) stability criteria exist. Without means for comparison, it is unclear which result is best used in any given application. This paper proposes a means for comparison between I-O stability results involving norms and inner products of inputs and outputs. The extended conic sector theorem provides a framework for determining which results are least conservative and most broadly applicable. In so-doing, numerous existing stability results are unified and revealed as more powerful than previously thought.
Conic-sector-based Analysis and Control Synthesis for Linear Parameter Varying Systems

Sivaranjani S, James Richard Forbes, Peter Seiler, and 1 more author

IEEE Control Systems Letters, 2018

Abs arXiv

We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closedloop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.

2017

Discrete-Time Minmax Filtering Subject to a Norm-Constrained State Estimate

Stephen Alexander Chee and James Richard Forbes

Automatica, Nov 2017

DOI: 10.1016/j.automatica.2017.07.024

Abs

This paper considers discrete-time minmax filtering when the state estimate, or part of the state estimate, is subjected to a norm constraint. Derivation and use of minmax filters are motivated by the desire to estimate systems’ states in a more robust manner. There are various methods for enforcing constraints on the state estimate using the Kalman filter, however, enforcing constraints on the state estimate in the minmax framework has been less explored. This paper presents the derivation of a minmax filter for a discrete-time system with a full or partial equality norm constraint on the state estimate. This is accomplished by modifying the minmax filter’s optimization problem using Lagrange multipliers to enforce the constraint on the state estimates.
Kalman Filter Based Unconstrained and Constrained Extremum-Seeking Guidance on SO(3)

Alex Walsh, James Richard Forbes, Stephen Alexander Chee, and 1 more author

AIAA Journal of Guidance Control and Dynamics, 2017

Special issue “The Kalman Filter and Its Aerospace Applications".

Abs

Extremum-seeking guidance endeavors to drive the output of a system to the extremum of an unknown objective function. This paper proposes an extremum-seeking guidance algorithm on 𝑆⁢𝑂⁡(3) for cases with and without inclusion and exclusion zones. The gradient of the unknown objective function is estimated via a Kalman filter so that the extremum of the objective function can be approximated. To satisfy inclusion and exclusion zone constraints, two different constrained Kalman filters are proposed. The first Kalman filter is a gain-projected Kalman filter, and the second is a novel linear matrix inequality based Kalman filter that is able to accommodate a larger class of constraints. The proposed extremum-seeking guidance algorithm is demonstrated using a performance objective that relates a spacecraft’s attitude to received power of an unknown radiation source using a patch antenna.
Conic Bounds for Systems Subject to Unknown Delay

Leila Jasmine Bridgeman and James Richard Forbes

IEEE Transactions on Automatic Control, 2017

Abs

Linear matrix inequality conditions implying conic bounds are developed for stable linear time-invariant systems with input, output, and/or state delays. Combined with the Conic Sector Theorem, this enables the design of output-feedback controllers ensuring closed-loop input-output stability that is robust to certain maximum delays. These contributions are used in a numerical example to design a nearly-optimal controller with guaranteed inputoutput-stability for a range of delays and improved performance relative to an H2 -optimal controller designed for the nominally undelayed system.
Dynamic Modeling, Trajectory Optimization, and Control of a Flexible Kiteplane

Ryan James Caverly and James Richard Forbes

IEEE Transactions on Control Systems Technology, 2017

Abs

This paper investigates dynamic modeling, trajectory optimization, and control of a flexible kiteplane used for wind energy harvesting. The individual components of the kiteplane, including flexible wings and a rigid fuselage, are modeled separately and then constrained together using the null-space method. The flexible wings of the kiteplane are modeled as flexible plates, and the Rayleigh-Ritz method is used to discretize the partial differential equation that describes the strain energy stored in the wing. The attitude of the kiteplane is described by the direction cosine matrix (DCM) directly and a proportional-integral-derivative control law that makes use of the DCM is implemented for attitude control. An unsteady aerodynamic model based on Theodorsen’s lift model is used in simulation to allow for an accurate model under transient conditions. An optimal trajectory is found using a simplified dynamic model and solving a finite-dimensional constrained optimization problem. Numerical simulations of the optimal trajectories are performed to demonstrate the kiteplane’s energy-harvesting capability.
Analysis and Synthesis of Input Strictly Passive Gain-Scheduled Controllers

Alex Walsh and James Richard Forbes

Journal of the Franklin Institute, Feb 2017

Abs

Gain-scheduling within a passive systems framework is considered. A novel input strictly passive gainscheduled controller is proposed. The scheduling signals, although bounded and square integrable on a finite time interval, are not constrained to be linear, but rather are permitted to be a nonlinear function of external parameters or time. Synthesis of the controller parameters is also considered. In particular, how to include state-feedback or observer gains individually designed about specific set points within the gain-scheduled controller is presented. The number of states associated with the controller is fixed. Adding set points within the scheduling algorithm does not increase the number of controller states numerically integrated online, reducing the computational burden associated with implementation. Although the input strictly passive gain-scheduled controller developed can be used to control any passive plant, the utility of the proposed architecture is highlighted by considering the control of flexible-link robotic manipulators. Numerical simulation results are presented, including a comparison to another passivity-based gain-scheduling algorithm.
Nonlinear Estimator Design on the Special Orthogonal Group using Vector Measurements Directly

David Evan Zlotnik and James Richard Forbes

IEEE Transactions on Automatic Control, 2017

Abs

The convergence properties of popular nonlinear attitude estimators can be traced to the choice of an attitude error function. This paper considers a nonlinear deterministic direction cosine matrix estimator whose form is derived from an alternate attitude error function. While the resulting estimator shares several properties with those previously presented in the literature, the careful selection of an attitude error function results in an estimator with superior convergence properties. The attitude estimate is propagated using a rate gyroscope measurement and corrected using two or more vector measurements. Simulation and experimental results are presented that highlight the desirable properties of the proposed estimator.

2016

Estimator Design for a Single Degree of Freedom Cable-Actuated System

Ryan James Caverly and James Richard Forbes

Journal of the Franklin Institute, 2016

Abs

In this paper, state estimation of a single degree of freedom flexible cable-actuated system governed by nonlinear equations of motion is considered. State estimation formulations are developed in discrete time using an extended Kalman filter (EKF) and an unscented Kalman filter (UKF). Measurements of the payload acceleration and either the angular position of one or both winches are obtained by an accelerometer mounted on the payload and angular winch encoders. These sensors are relatively small and inexpensive, and allow for operation in many different environments. This is an improvement over current estimation techniques for cable-actuated systems that typically rely on a position measurements of the payload that are obtained by large and expensive sensors that often only operate in a particular environment (e.g., motion capture system, GPS receiver). An EKF and UKF are implemented to estimate the states of the system using a nonlinear dynamic model. A proportional-derivative-based controller from the literature is used for control. Estimation of the tension in each cable is also performed, which demonstrates that additional sensors (e.g., load cells) are not needed to obtain an accurate estimate of the cable tensions. Consideration of sensors with different sampling rates is also included in the EKF and UKF formulations. Simulation results using the EKF and UKF along with the proportional-derivative controller in discrete time are presented.
Modeling of a Rolling Flexible Spherical Shell

Francois Robert Hogan and James Richard Forbes

ASME Journal of Applied Mechanics, 2016

Abs

The purpose of this paper is to develop the motion equations of a flexible spherical shell rolling without slip on a flat surface. The motivation for this paper stems from tumbleweed rovers, which are envisioned to roll, deform, and bounce on the Martian surface due to the flexible nature of their thin walls. The motion equations are derived using a constrained Lagrangian approach and capture the rolling without slip nonholonomic constraint. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the spherical shell on its trajectory.
Modeling and Control of Flow-Induced Vibrations of a Flexible Hydrofoil in Viscous Flow

Ryan James Caverly, Chenyang Li, Eun Jung Chae, and 2 more authors

Smart Materials and Structures, 2016

Abs

In this paper, a reduced-order model (ROM) of the flow-induced vibrations of a flexible cantilevered hydrofoil is developed and used to design an active feedback controller. The ROM is developed using data from high-fidelity viscous fluid-structure interaction (FSI) simulations and includes nonlinear terms to accurately capture the effect of lock-in. An active linear quadratic Gaussian (LQG) controller is designed based on a linearization of the ROM and is implemented in simulation with the ROM and the high-fidelity viscous FSI model. A controller saturation method is also presented that ensures that the control force applied to the system remains within a prescribed range. Simulation results demonstrate that the LQG controller successfully suppresses vibrations in both the ROM and viscous FSI simulations using a reasonable amount of control force.
A Very Strictly Passive Gain-Scheduled Controller: Theory and Experiments

Alex Walsh and James Richard Forbes

IEEE/ASME Transactions on Mechatronics, 2016

Abs

This paper considers gain-scheduled control within a passive systems framework. Inspired by the passivity theorem and linear parameter varying systems theory, a very strictly passive gain-scheduled controller is introduced. The proposed gain-scheduled controller is used in tandem with an actuator saturation prevention technique. The actuator saturation prevention technique does not violate the passive properties of the controller, can account for feedforward control, and can have variable saturation limits. Scheduling signals are bounded and square integrable on finite time intervals. They have no restrictions on their derivatives, can be nonlinear, and can be functions of system states, exogenous signals, or time. The controller is applied to a trajectory tracking problem of a two-link flexible manipulator’s heavy payload. The proposed controller is compared to two other gain-scheduling paradigms through experimentation. The theoretical and experimental results of this paper show that the proposed control architecture with a fixed number of integrating states is able to have improved stability properties over a traditional linear parameter varying controller without compromising performance. In addition, the proposed controller is able to asymptotically track a trajectory while avoiding actuator saturation.
Exponential Convergence of a Nonlinear Attitude Estimator

David Evan Zlotnik and James Richard Forbes

Automatica, Oct 2016

Abs

A nonlinear attitude estimator is presented. The estimator uses a minimum of two vector measurements and a rate-gyro to estimate the attitude and the rate-gyro bias. The estimator can be implemented using a low-cost inertial measurement unit such as those typically used on inexpensive aerial vehicles. Estimator design is based on an alternate attitude error function that yields an estimator with faster convergence properties than similar estimators previously considered in the literature. A proof of exponential stability about the desired equilibrium point is provided. Simulation and experimental results demonstrate the desirable properties of the proposed estimator.
The Extended Conic Sector Theorem

Leila Jasmine Bridgeman and James Richard Forbes

IEEE Transactions on Automatic Control, Jul 2016

Abs

Input-output stability theory is an indispensable tool in control engineering. However, classic results such as the Conic Sector Theorem, cannot be applied in some important cases. This technical note extends the original Conic Sector Theorem to apply to open-loop unstable systems and those with negative upper conic bounds and incorporates a careful treatment of degenerate conic systems and alterations accounting for nonzero initial conditions. Simulations highlight how the contributions facilitate robust control in the most challenging of circumstances.
Saturated Control of Flexible-Joint Manipulators Using a Hammerstein Strictly Positive Real Compensator

Ryan James Caverly, David Evan Zlotnik, and James Richard Forbes

Robotica, Jun 2016

Abs

In this paper the control of flexible-joint manipulators while explicitly avoiding actuator saturation is considered. The controllers investigated are composed of a bounded proportional control term and a Hammerstein strictly positive real angular rate control term. This control structure ensures that the total torque demanded of each actuator is bounded by a value that is less than the maximum torque that each actuator is able to provide, thereby disallowing actuator saturation. The proposed controllers are shown to render the closed-loop system asymptotically stable, even in the presence of modeling uncertainties. The performance of the controllers is demonstrated experimentally and in simulation.
Trajectory Tracking, Estimation, and Control of a Pendulum-Driven Spherical Robot

Francois Robert Hogan and James Richard Forbes

AIAA Journal of Guidance Control and Dynamics, 2016

Abs

(No abstract.)
Continuous-Time Estimation of Attitude Using B-Splines on Lie Groups

Hannes Sommer, James Richard Forbes, Roland Siegwart, and 1 more author

AIAA Journal of Guidance, Control, and Dynamics, 2016

Abs

Filtering algorithms are the workhorse of spacecraft attitude estimation, but recent research has shown that the use of batch estimation techniques can result in higher accuracy per unit of computational cost. This paper presents an approach for singularity-free batch estimation of attitude in continuous time using B-Spline curves on unit-length quaternions. It extends existing theory of unit-length quaternion B-splines to general Lie groups and arbitrary Bspline order. It is shown how to use these curves for continuous-time batch estimation using Gauss-Newton or Levenberg-Marquardt, including efficient curve initialization, a parameter update step that preserves the Lie group constraint within an unconstrained optimization framework, and the derivation of Jacobians of the B-spline’s value and its time derivatives with respect to an update of its parameters. For unit-length quaternion splines, the equations for angular velocity and angular acceleration are derived. An implementation of this algorithm is evaluated on two problems: spacecraft attitude estimation using a three-axis magnetometer, a sun sensor, and 1) a three-axis gyroscope, and 2) a continuous-time vehicle dynamics model based on Euler’s equation. Its performance is compared against a standard multiplicative extended Kalman filter and a recently published batch attitude estimation algorithm. The results show that B-splines have equal or superior performance over all test cases and provide two key tuning parameters, the number of knots and the spline order, that an engineer can use to trade off accuracy and computational efficiency when choosing a spline representation for a given estimation problem.

2015

Modeling of a Rolling Flexible Circular Ring

Francois Robert Hogan and James Richard Forbes

ASME Journal of Applied Mechanics, Nov 2015

Abs

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh-Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on a flat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat surface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring’s motion.
Modeling and Control of Flexible Telescoping Manipulators

Alex Walsh and James Richard Forbes

IEEE Transactions on Robotics, 2015

Abs

This paper considers modeling and control of a planar flexible two-link telescoping manipulator. The telescoping interface between the deploying and non-deploying portions of the links is discussed in detail. The equations of motion are derived using Lagrange’s equation and constrained using a projection method that eliminates the need to compute Lagrange multipliers explicitly. Passivity-based control of the telescoping manipulator is also investigated. It is shown that several passive input-output maps exist. In particular, by a suitable redefinition of the inputs and outputs, a modified tip-based control is made possible. The model is validated through numerical simulation, and the tip-based control is compared with joint-based control. Simulation results show that tip-based control has better closed-loop performance compared with joint-based control.
Generalized Euler Sequences Revisited

Anton de Ruiter and James Richard Forbes

Journal of the Astronautical Sciences, Mar 2015

Abs

It has previously been shown in the literature that the generalized Euler sequences (also known as Davenport sequences) provide a universal set of attitude representations. However, while these works assert the existence of generalized Euler angles for a given attitude, they do not provide explicit ranges that those angles must lie within. In addition, they do not generally provide physical insight into what a generalized Euler sequence is. This paper addresses these two points. As such, this paper contains a comprehensive self-contained treatment of generalized Euler sequences. In particular, a constructive approach is taken to proving that the generalized Euler sequences provide a universal set of attitude representations. In doing so, specific ranges that contain the generalized Euler angles are obtained, and physical insight is provided into the generalized Euler sequences. The singularity of the generalized Euler sequences is characterized, and it is shown that the generalized Euler angles are uniquely specified within their restricted ranges when away from the singularity condition.
Direction-Cosine-Matrix-Based Attitude Control Subject to Actuator Saturation

James Richard Forbes

IET Control Theory and Applications, 2015

Abs

Set-point attitude control of a rigid body explicitly preventing actuator saturation is considered. The attitude control approach developed does not employ any sort of direction-cosine-matrix (DCM) parameterisation, such as Euler angles or quaternions. Rather, the DCM is used directly within the feedback control algorithm. Together a proportional control term and an angular velocity control term make up the attitude controller. The angular velocity control is composed of a strictly positive real system subject to a special input non-linearity. The specific form of the proportional control and angular velocity control ensure control torques are below the saturation level of the on-board actuators. Two controller synthesis methods are considered. The first uses the linearised system, the solution to the linear quadratic regulator problem, and the Kalman-Yakubovich-Popov lemma to design the controller. The second employs a simple low-pass filter that is guaranteed to stabilise the closed-loop system; tuning the low-pass filter is also considered. Numerical simulation results demonstrate effective closed-loop control in the presence of plant disturbances and sensor noise.
Modeling of Spherical Robots Rolling on Generic Surfaces

Francois Robert Hogan and James Richard Forbes

Multibody System Dynamics, 2015

Abs

In this paper, the motion of a spherical robot rolling on a generic surface is considered. The motion equations are derived in matrix form using a Lagrangian approach, and quaternions are used to parametrize attitude. Focus is placed on a general formulation of the problem that facilitates the integration of the holonomic and nonholonomic constraints into the motion equations in a straightforward manner. The motion equations capture the nonholonomic nature of rolling without slipping, the contact requirement between the spherical rover and the generic surface, an additional constraint associated with an energy-harvesting pendulum, and the quaternion unit-length constraints. Numerical simulations involving Martian tumbleweed rovers are performed on complex three-dimensional surfaces resembling Martian craters and wave fields.
The Exterior Conic Sector Lemma

Leila Jasmine Bridgeman and James Richard Forbes

International Journal of Control, 2015

Abs

The conic sector theorem is a powerful input–output stability analysis tool, providing a fine balance between generality and simplicity of system characterisations that is conducive to practical stability analysis and robust controller synthesis. Without means to systematically identify and impose exterior conic properties, existing analysis and synthesis methods are limited to employing a special case of the conic sector theorem which may prove overly conservative when considering very strictly passive plants. This paper removes the current limitation by establishing the exterior conic sector lemma, which provides matrix inequalities equivalent to exterior conic bounds for linear time-invariant systems.
Dynamic Modelling and Passivity-Based Control of a Single Degree of Freedom Cable-Actuated System

Ryan James Caverly, James Richard Forbes, and Donya Mohammadshahi

IEEE Transactions on Control Systems Technology, 2015

Abs

In this paper, a lumped-mass dynamic model of a single degree of freedom cable-actuated system is derived, and passivity-based control is considered. The dynamic model developed takes into consideration the changing cable stiffness and mass as the cable is wrapped around a winch. In addition, the change in the winch inertia as the cable is wrapped around the winch is modeled. It is assumed that the mass of the payload is much greater than the mass of the cables and the equivalent mass of the winches, which allows for an approximation where the rigid dynamics can be decoupled from the elastic dynamics of the system. This approximation enables the definition of a modified input torque and modified output rate, allowing the establishment of passive input-output mappings. Passivity-based controllers are investigated, shown to render the closed-loop system input-output stable, and tested in simulation.
The Minimum Gain Lemma

Leila Jasmine Bridgeman and James Richard Forbes

International Journal of Robust and Nonlinear Control, 2015

Abs

This paper focuses on the newly developed notion of minimum gain and the corresponding Large Gain Theorem. The Large Gain Theorem is an input–output stability result particularly well suited to unstable plants connected in feedback with stable or unstable controllers. This paper aims to facilitate the practical application of these results. An altered definition of minimum gain broadens the applicability of the Large Gain Theorem, and the novel Minimum Gain Lemma provides LMI conditions that imply and are often equivalent to a minimum gain for LTI systems. Numerical examples are provided to clarify the differences between the existing and proposed definitions of minimum gain, highlight the utility of the newly established Minimum Gain Lemma, and demonstrate how the paper’s contributions may be employed in practice.
Attitude Control With Active Actuator Saturation Prevention

James Richard Forbes

Acta Astronautica, Feb 2015

Abs

Spacecraft attitude control in the presence of actuator saturation is considered. The attitude controller developed has two components: a proportional component and an angular velocity component. The proportional control has a special form that depends on the attitude parameterization. The angular velocity control is realized by a strictly positive real system with its own input nonlinearity. The strictly positive real system can filter noise in the angular velocity measurement. With this control architecture the torques applied to the body are guaranteed to be below a predetermined value, thus preventing saturation of the actuators. The closed-loop equilibrium point corresponding to the desired attitude is shown to be asymptotically stable. Additionally, the control law does not require specific knowledge of the body’s inertia properties, and is therefore robust to such modelling errors.
On the Solution of Wahba’s Problem on SO(n)

Anton de Ruiter and James Richard Forbes

Journal of the Astronautical Sciences, 2015

Abs

Wahba’s problem is an important problem in both aerospace and robotics fields. It typically involves finding an optimal rotation to fit a series of vector measurements. In this paper, a rigorous analysis of the famous Wahba problem on SO(n) is presented. The entire set of solutions is obtained using both a singular value decomposition and matrix square-root method. Conditions for uniqueness of solutions are also obtained, correcting some errors in the existing literature. It is then shown that under a mild condition, Wahba’s problem can be recast as a convex optimization problem with linear matrix inequality constraints. This opens the door to a whole host of new possible solution methods for these types of Wahba problems.
An LMI-Based Solution to Wahba’s Problem

James Richard Forbes and Anton de Ruiter

AIAA Journal of Guidance, Control, and Dynamics, 2015

Abs

(No abstract.)

2014

Rolling Stability of a Power-Generating Tumbleweed Rover

Francois Robert Hogan, James Richard Forbes, and Timothy Barfoot

AIAA Journal of Spacecrafts and Rockets, 2014

Abs

In this paper, the rolling stability of a power-generating tumbleweed rover is investigated. The nonlinear equations of motion of the rover capture the nonholonomic nature of rolling without slipping, the external wind force, and energy dissipation due to rolling friction and power generation. To assess stability of the system as it rolls about a preferred axis of rotation, Lyapunov’s indirect method is employed. When the shell of the tumbleweed rover has a uniform mass distribution, Lyapunov’s indirect method predicts instability; when the inertia about a preferred axis of rotation is increased, Lyapunov’s indirect method predicts stability. Numerical simulation results of both the linearized and nonlinear equations of motion confirm both the instability and stability predictions of Lyapunov’s indirect method.
Dynamic Modelling and Noncollocated Control of a Flexible Planar Cable-Driven Manipulator

Ryan James Caverly and James Richard Forbes

IEEE Transactions on Robotics, 2014

Abs

This paper investigates the dynamic modeling and passivity-based control of a planar cable-actuated system. This system is modeled using a lumped-mass method that explicitly considers the change in cable stiffness and winch inertia that occurs when the cables are wound around their respective winches. In order to simplify the modeling process, each cable is modeled individually and then constrained to the other cables. Exploiting the fact that the payload is much more massive than the cables allows the definition of a modified output called the µ-tip rate. Coupling the µ-tip rate with a modified input realizes the definition of a passive input-output map. The two degrees of freedom of the system are controlled by four winches. This overactuation is simplified by employing a set of load-sharing parameters that effectively reduce four inputs to two. The performance and robustness of the controllers are evaluated in the simulation.
Do Unstable Systems Have Amplification and Phase Shift?

Khaled Aljanaideh, James Richard Forbes, and Dennis S. Bernstein

IEEE Control Systems Magazine, 2014

Abs

Control textbooks sometimes give the impression that amplification and phase shift are properties confined to asymptotically stable systems. For example, [1, p. 400] states that "Any system with a pole in the RHP is unstable; hence it would be impossible to determine its frequency response experimentally because the system would never reach a steady-state sinusoidal response for a sinusoidal input." This statement is correct in reference to an unstable plant operating in open loop but does not consider the case of an unstable plant operating inside a stabilized closed loop.
Continuous-Time Norm-Constrained Kalman Filtering

James Richard Forbes, Anton de Ruiter, and David Evan Zlotnik

Automatica, 2014

Abs

This paper considers continuous-time state estimation when part of the state estimate or the entire state estimate is norm-constrained. In the former case continuous-time state estimation is considered by posing a constrained optimization problem. The optimization problem can be broken up into two separate optimization problems, one which solves for the optimal observer gain associated with the unconstrained state estimates, while the other solves for the optimal observer gain associated with the constrained state estimates. The optimal constrained state estimate is found by projecting the time derivative of an unconstrained estimate onto the tangent space associated with the norm constraint. The special case where the entire state estimate is norm-constrained is briefly discussed. The utility of the filtering results developed are highlighted through a spacecraft attitude estimation example. Numerical simulation results are included. © 2014 Elsevier Ltd. All rights reserved.
Saturated Proportional Derivative Control of Flexible-Joint Manipulators

Ryan James Caverly, David Evan Zlotnik, Leila Jasmine Bridgeman, and 1 more author

Robotics and Computer Integrated Manufacturing, 2014

Abs

In this paper, the control of flexible-joint robotic manipulators while avoiding actuator saturation is investigated. Several proportional derivative controllers are developed, all of which disallow actuator saturation by guaranteeing that the applied torque is less than a specified maximum value. In particular, a Gibbs parameterization of the joint angles is included in the control laws, which allows for an increased control torque as compared to an Euler angle parameterization. An equilibrium point of the closed-loop system is proven to be asymptotically stable using the Lyapunov stability analysis. Moreover, the proposed control laws do not require any knowledge of the manipulator’s mass, stiffness, or dissipation properties, and as such, are robust to modelling errors. The proposed controllers are tested on a single-link flexible-joint manipulator experimentally and on a two-link flexible-joint manipulator in simulation, and are compared to the performance of controllers found in the literature.
Dynamic Modelling, Estimation, and Control for Precision Pointing of an Atmospheric Balloon Platform

David Evan Zlotnik and James Richard Forbes

Transactions of the Canadian Society for Mechanical Engineering, 2014

Invited Paper for Special Issue on Mechanisms, Machines and Mechatronics

Abs

In this paper we consider the dynamic modelling, estimation and control of an atmospheric balloon platform. The platform is modelled as a rigid body constrained to move with a three dimensional pendulum. We investigate the dynamics of the system and derive the equations of motion from first principles. A nonlinear estimator that evolves on the special orthogonal group, denoted SO(3), is implemented and used in conjunction with a proportional derivative (PD) compensator to control the yaw angle of the platform. In addition, a continuous-time Gaussian process disturbance model is used to simulate the effects of disturbances on the platform. A simulation is conducted, and the results demonstrate successful estimation and yaw control.
Saturated Proportional Derivative Control of a Single-Link Flexible-Joint Manipulator

Ryan James Caverly, David Evan Zlotnik, and James Richard Forbes

Transactions of the Canadian Society for Mechanical Engineering, 2014

Invited Paper for Special Issue on Mechanisms, Machines and Mechatronics

Abs

This paper considers the control of a single-link flexible-joint robot manipulator subject to actuator saturation. Alternative controllers are proposed and compared to one found in literature. In particular, a controller with proportional and derivative components is guaranteed to provide a total torque less than a chosen value, thereby disallowing actuator saturation. It is shown that an equilibrium point of the closed-loop system is asymptotically stable. Additionally, it is shown that the controllers are robust to modelling errors. Finally, this paper presents simulation results demonstrating the performance of the proposed control architecture.
General Identities for Parameterizations of SO(3) with Applications

Anton de Ruiter and James Richard Forbes

ASME Journal of Applied Mechanics, 2014

Abs

Rotation matrices, which are three-by-three orthonormal matrices with determinant equal to plus one, constitute the special orthogonal group of rigid-body rotations, denoted SO(3). Owing to the three-by-three nature of rotation matrices plus their orthonormality constraint, parameterizations are often used in favor of rotation matrices for computations and derivations. For example, Euler angles and Rodrigues parameters are common three-parameter unconstrained parameterizations, while unit-length quaternions are a popular four-parameter constrained parameterization. In this paper various identities associated with the parameterization of SO(3) are considered. In particular, we present six identities, three related to unconstrained parameterizations and three related to constrained parameterizations. We also discuss rotation matrix perturbations. The utility of these identities is highlighted when deriving the motion equations of a rigid body using Lagrange’s equation. We also use them to examine some issues associated with spacecraft attitude determination.
Norm-Constrained Consider Kalman Filtering

Stephen Alexander Chee and James Richard Forbes

AIAA Journal of Guidance, Control, and Dynamics, 2014

Abs

(No abstract.)
Identities for Deriving Equations of Motion Using Constrained Attitude Parameterizations

James Richard Forbes

AIAA Journal of Guidance, Control, and Dynamics, 2014

Abs

(No abstract.)
Conic-Sector-Based Control to Circumvent Passivity Violations

Leila Jasmine Bridgeman and James Richard Forbes

International Journal of Control, 2014

Abs

In order to ensure input-output stability for plants experiencing passivity violations, this paper explores the use of the conic sector theorem for both stability analysis and controller design. Given a previously designed controller and a plant that has experienced a (partially unknown) passivity violation, a novel conic bound selection procedure is presented. This procedure can be used to assess input-output stability of the violated plant and original controller via the conic sector theorem. Should input-output stability not be ensured, two original controller synthesis methods are suggested: one is designed to mimic the controller, and the other is inspired by strictly positive real controller synthesis. Both methods guarantee input-output stability by selecting controllers within appropriate conic sectors, and involve only the evaluation of readily solvable linear matrix inequalities and algebraic Riccati equations. Along with details on computational considerations, numerical simulations are provided, demonstrating the effectiveness of the proposed methods.

2013

Adaptive Approaches to Nonlinear State Estimation for Mobile Robot Localization: An Experimental Comparison

James Richard Forbes

Transactions of the Institute of Measurement and Control, Dec 2013

Abs

We compare the state estimation performance of various nonlinear filters using experimental data. The experiment, a mobile robot driving on a planar surface, provides noisy odometry and laser rangefinder measurements, while groundtruth is provided by an accurate motion capture system. We investigate the localization accuracy of standard extended Kalman and sigma point filters, and compare their performance with adaptive extended Kalman and adaptive sigma point filters. The adaptive filters update the noise covariance matrices based on the measurements available at a given time step (without using groundtruth data). The groundtruth data is used to assess the performance of each filter. Our results show that the adaptive schemes outperform the equivalent traditional formulations, however, they are slightly more difficult to implement and tune.
Passivity-Based Attitude Control on the Special Orthogonal Group of Rigid-Body Rotations

James Richard Forbes

AIAA Journal of Guidance, Control, and Dynamics, 2013

Abs

Set-point regulation and tracking control of a rigid body is considered. The rigid body, which could be a spacecraft, underwater vehicle, or unmanned aerial vehicle, is equipped with various sensors, including those that provide unit-length vector measurements. At no point is the rotation matrix associated with the rigid-body’s orientation parameterized. The control algorithms developed in this paper are posed directly on the special orthogonal group of rigid-body rotations SO⁡(3). The set-point controller presented is composed of a proportional control term and an angular velocity control term. The proportional control term is a function of the vector measurements and a set of desired vector measurements that are used to compute the orientation error of the rigid body. Passive systems theory is used to motivate the use of a strictly positive real angular velocity controller. The set-point regulator is robust to modeling errors associated with the mass distribution of the body. Tracking control is also considered. To ensure robust tracking control, an adaptive scheme is developed in which the controller is composed of feedback and feedforward terms. The feedback term is composed of a proportional term and a strictly-positive-real-based angular velocity term, similar to the set-point regulator. The feedforward term is a function of an estimate of the spacecraft mass distribution. The synthesis of strictly positive real controllers to be used within the set-point and tracking controllers is discussed. Numerical simulation results that demonstrate successful set-point regulation and tracking control are presented.
Investigation of Active Vibration Suppression of a Flexible Satellite Using Magnetic Attitude Control

Everett J Findlay, Anton de Ruiter, James Richard Forbes, and 3 more authors

AIAA Journal of Guidance, Control, and Dynamics, 2013

Abs

(No abstract.)
Synthesis of Optimal Finite Frequency Controllers Able to Accommodate Passivity Violations

James Richard Forbes and Christopher John Damaren

IEEE Transactions on Control Systems Technology, 2013

Abs

In this paper, we explore the relationship between the hybrid passivity/finite-gain systems framework and the generalized Kalman-Yakubovich-Popov (GKYP) lemma. In particular, we investigate how to optimally design finite-frequency (FF) controllers that possess strictly positive real (SPR) properties over a low-frequency range and bounded real (BR) properties over a high-frequency range. Such FF SPR/BR controllers will be used to control systems that have experienced a passivity violation. We first review the hybrid passive/finite-gain systems framework and how linear time-invariant hybrid passive/finitegain systems relate to systems with low-frequency FF positive real (PR) or SPR properties, and high-frequency FF BR properties as characterized by the GKYP lemma. Optimal design of FF SPR/BR controllers is considered next. A convex optimization problem constrained by a set of linear matrix inequalities is posed where constraints are imposed using various forms of the GKYP lemma, yielding optimal FF SPR/BR controllers. The FF SPR/BR controllers are optimal in that they approximate the traditional H 2 control solution. Finally, FF SPR/BR controllers are used within a gain-scheduling architecture to control a two-link flexible manipulator. Experimental results successfully demonstrate closed-loop stability and good closed-loop performance.
Dual Approaches to Strictly Positive Real Controller Synthesis with a H_2 Performance Using Linear Matrix Inequalities

James Richard Forbes

International Journal of Robust and Nonlinear Control, 2013

Abs

The synthesis of controllers that minimize a H_2 performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state-feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed-loop H_2-norm is minimized and the controller is SPR. The first method retools the standard H_2 control problem by using a common Lyapunov matrix variable to satisfy both the H_2 criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the H_2 performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented.
Overcoming Passivity Violations: Closed-Loop Stability, Controller Design, and Controller Scheduling

James Richard Forbes and Christopher John Damaren

IET Control Theory and Applications, 2013

Abs DOI

Control of systems that have had their passive input-output map partially violated is the motivation of this study. The hybrid passivity/finite-gain systems framework is specifically well suited to systems that have experienced a passivity violation. The focus of this study is the extension and application of the hybrid passivity/finite-gain systems framework to a multi-input multi-output (MIMO) control problem. Calculation of the hybrid passivity/finite-gain parameters in a linear time-invariant (LTI) MIMO context is considered. Additionally, we show that a set of hybrid very strictly passive/finite-gain (VSP/finitegain) controllers gain-scheduled in a particular way also possesses hybrid VSP/finite-gain properties. To synthesise hybrid VSP/finite-gain controllers a frequency-weighted optimal control scheme is used to parameterise controllers that are then constrained and optimised within a numerical optimisation framework. The theoretical contributions of this work are validated experimentally using a two-link flexible manipulator apparatus. Results highlight the utility of the hybrid passivity/finite-gain framework, the scheduling scheme and controller design method.

2012

Single-Link Flexible Manipulator Control Accommodating Passivity Violations: Theory and Experiments

James Richard Forbes and Christopher John Damaren

IEEE Transactions on Control Systems Technology, May 2012

Nominated for “Outstanding Paper Award"

Abs DOI

The robust control of a system which is nominally passive, but experiences a passivity violation is considered in this paper. Specifically, we utilize the hybrid passivity and finite gain stability theorem to robustly control a single-link flexible manipulator experiment. This system is nominally passive, but passivity is destroyed by, for example, sensor dynamics. The hybrid theorem is specifically applicable to such a scenario. We review and develop further the hybrid passivity and finite gain stability theorem in a linear time-invariant, single-input-single-output context. Calculation of the various passivity and finite gain parameters that classify a system as hybrid is discussed. In the interest of developing a hybrid controller that is optimal in some sense, we pose a numerical optimization problem which is constrained by the hybrid passivity and finite gain stability theorem. The numerical optimization objective function seeks to have a hybrid controller mimic a nominal 2 controller. Experimental results successfully demonstrate tip-based feedback control of a single-link flexible manipulator.

2011

Design of Optimal Strictly Positive Real Controllers Using Numerical Optimization for the Control of Flexible Robotic Systems

James Richard Forbes and Christopher John Damaren

Journal of the Franklin Institute, 2011

Abs DOI

The design of optimal strictly positive real (SPR) controllers using numerical optimization is considered. We focus on how to parameterize the SPR controllers being optimized and the effect of parameterization. Minimization of the closed-loop H2 -norm is the optimization objective function. Various single-input single-output and multi-input multi-output controller parameterizations using transfer functions/matrices and state-space equations are considered. Depending on the controller form, constraints are enforced (i) using simple inequalities guaranteeing SPRness, (ii) in the frequency domain or, (iii) by implementing the Kalman-Yakubovich-Popov Lemma. None of the parameterizations we consider foster an observerbased controller structure. Simulated control of a single-link and a two-link flexible manipulators demonstrates the effectiveness of our proposed controller optimization formulations. & 2011 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Linear Time-Varying Passivity-Based Attitude Control Employing Magnetic and Mechanical Actuation

James Richard Forbes and Christopher John Damaren

AIAA Journal of Guidance, Control, and Dynamics, 2011

Abs DOI

Spacecraft attitude control using both magnetic and mechanical actuation is considered. Attitude control is composed of quaternion-based proportional control and passivity-based rate (angular velocity) control. A passivity-based scheme is adopted in order to guarantee robust closed-loop stability. Motivated by the nearly periodic nature of the Earth’s magnetic field, a linear time-varying input strictly passive system is used within the rate control. Conditions that ensure a linear time-varying system is input strictly passive are given and are used in conjunction with the linear quadratic regulator formulation to design and synthesize the rate control. The attitude control formulation ensures that as time goes to infinity the spacecraft attitude and angular velocity go to zero. Simulation results are included that highlight the robust nature of the closed loop subject to both orbit and spacecraft model uncertainty.
Pose Estimation Using Linearized Rotations and Quaternion Algebra

Timothy Barfoot, James Richard Forbes, and P. T. Furgale

Acta Astronautica, 2011

Abs

In this paper we revisit the topic of how to formulate error terms for estimation problems that involve rotational state variables. We present a first-principles linearization approach that yields multiplicative error terms for unit-length quaternion representations of rotations, as well as for canonical rotation matrices. Quaternion algebra is employed throughout our derivations. We show the utility of our approach through two examples: (i) linearizing a sun sensor measurement error term, and (ii) weighted-least-squares point-cloud alignment.

2010

Dynamic Modeling and Stability Analysis of a Power-Generating Tumbleweed Rover

James Richard Forbes, Timothy Barfoot, and Christopher John Damaren

Multibody System Dynamics, 2010

Abs

This paper introduces a novel tumbleweed rover design that employs a pendulum-generator system to harvest electrical power from the wind. First, the dynamics of this multibody system are developed, including the internal pendulum dynamics, resistance (damping) provided by the electrical generators, external wind force, and rolling constraints between the sphere and the ground. Second, the stability of the system (without wind) is studied and it is shown that it is stable in the sense of Lyapunov. Finally, simulation results are provided that verify the system will roll stably downwind while generating power.
A Hybrid Passivity and Finite Gain Stability Theorem: Stability and Control of Systems Possessing Passivity Violations

James Richard Forbes and Christopher John Damaren

IET Control Theory and Applications, 2010

Abs

The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal lowpass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input-output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.
Design of Gain-Scheduled Strictly Positive Real Controllers Using Numerical Optimization for Flexible Robotic Systems

James Richard Forbes and Christopher John Damaren

ASME Journal of Dynamic Systems, Measurement, and Control, 2010

Abs DOI

The design of gain-scheduled strictly positive real (SPR) controllers using numerical optimization is considered. Our motivation is robust, yet accurate motion control of flexible robotic systems via the passivity theorem. It is proven that a family of very strictly passive compensators scheduled via time- or state-dependent scheduling signals is also very strictly passive. Two optimization problems are posed; we first present a simple method to optimize the linear SPR controllers, which compose the gain-scheduled controller. Second, we formulate the optimization problem associated with the gain-scheduled controller itself. Restricting our investigation to time-dependent scheduling signals, the signals are parameterized, and the optimization objective function seeks to find the form of the scheduling signals, which minimizes a combination of the manipulator tip tracking error and the control effort. A numerical example employing a two-link flexible manipulator is used to demonstrate the effectiveness of the optimal gain-scheduling algorithm. The closed-loop system performance is improved, and it is shown that the optimal scheduling signals are not necessarily linear.
Geometric Approach to Spacecraft Attitude Control Using Magnetic and Mechanical Actuation

James Richard Forbes and Christopher John Damaren

AIAA Journal of Guidance, Control, and Dynamics, 2010

Abs

(No abstract.)

Conference Papers

2026

ECC
dkpy: Robust Control with Structured Uncertainty in Python

Timothy Everett Adams, Steven Dahdah, and James Richard Forbes

In European Control Conference (ECC), Jul 2026

Abs Bib PDF Code

Models used for control design are, to some degree, uncertain. Model uncertainty must be accounted for to ensure the robustness of the closed-loop system. μ-analysis and μ-synthesis methods allow for the analysis and design of controllers subject to structured uncertainties. Moreover, these tools can be applied to robust performance problems as they are fundamentally robust control problems with structured uncertainty. The contribution of this paper is dkpy, an open-source Python package for performing robust controller analysis and synthesis for systems subject to structured uncertainty. dkpy also provides tools for performing model uncertainty characterization using data from a set of perturbed systems. The open-source project can be found at https://github.com/decargroup/dkpy.
@inproceedings{adamsDkpyRobustControl2026, title = {dkpy: {{Robust Control}} with {{Structured Uncertainty}} in {{Python}}}, booktitle = {{{European Control Conference}} ({{ECC}})}, author = {Adams, Timothy Everett and Dahdah, Steven and Forbes, James Richard}, year = {2026}, month = jul, pages = {2760--2767}, issn = {2996-8895}, url = {https://ieeexplore.ieee.org/document/11625412}, urldate = {2026-08-11}, eventtitle = {2026 {{European Control Conference}} ({{ECC}})}, selected = true, bibtex_show = true }
KILO-EKF: Koopman-Inspired Learned Observations Extended Kalman Filter

Zi Cong Guo^*, James Richard Forbes, and Timothy Barfoot

Conference on Intelligent Robots and Systems, Pittsburgh, PA, September 27 - October 1, 2026

Abs arXiv

We present the Koopman-Inspired Learned Observations Extended Kalman Filter (KILO-EKF), which combines a standard EKF prediction step with a correction step based on a Koopman-inspired measurement model learned from data. By lifting measurements into a feature space where they are linear in the state, KILO-EKF enables flexible modeling of complex or poorly calibrated sensors while retaining the structure and efficiency of recursive filtering. The resulting linear-Gaussian measurement model is learned in closed form from ground truth training data, without iterative optimization or reliance on an explicit parametric sensor model. At inference, KILO-EKF performs a standard EKF update using Jacobians obtained via the learned lifting. We validate the approach on a real-world quadrotor localization task using an IMU, ultra-wideband (UWB) sensors, and a downward-facing laser. We compare against multiple EKF baselines with varying levels of sensor calibration. KILO-EKF achieves better accuracy and consistency compared to data-calibrated baselines, and significantly outperforms EKFs that rely on imperfect geometric models, while maintaining real-time inference and fast training. These results demonstrate the effectiveness of Koopman-inspired measurement learning as a scalable alternative to traditional model-based calibration.
Observability and Consistency Analysis for Visual-Inertial Navigation with Anchored Feature Parameterizations

Mitchell Cohen^*, Vassili Korotkine, and James Richard Forbes

Conference on Intelligent Robots and Systems, Pittsburgh, PA, September 27 - October 1, 2026

Abs arXiv

This paper presents an analysis of the observability and consistency properties of filtering-based visual-inertial navigation systems (VINS) that utilize anchored feature representations. The unobservable subspace of VINS with anchored landmark parameterizations is shown to be independent of the estimated landmark state, which leads to improved estimator consistency properties without any additional modifications. However, the unobservable subspace is still found to depend on the estimated navigation state, necessitating additional consistency-enforcing techniques. Two methods to improve the consistency of VINS with anchored feature representations are presented. Simulation results showcase that all estimators employing anchored feature paramterizations exhibit improved consistency properties compared to algorithms that estimate features resolved in a global reference frame, especially in scenarios where feature initialization may be poor. Real-world experiments on the TUM-VI dataset showcase that the use of anchored feature representations alone can yield comparable performance to consistency-improved estimators employing a global feature representation, demonstrating the benefit of using anchored feature parameterizations for VINS.
Continuous-Time Estimation of Deformation and Dynamic Parameters for Cosserat Rods under Free Vibration

Samuel Herschmann^*, James Richard Forbes, Christoffer Sloth, and 2 more authors

IFAC World Congress, Busan, Republic of Korea, August 23-28, 2026

Abs

Accurate modelling of flexible robotic structures is essential for achieving precise control in many engineering applications. Parameter estimation for nonlinear flexible systems becomes particularly challenging when measurements of dynamic deformation are limited and the system’s initial states are unknown. This paper introduces a continuous-time parameter and deformation trajectory estimation method for robotic payloads modelled as Cosserat rods, using temporal and spatial basis functions. The method enables identification of parameters that enter the dynamics nonlinearly from limited measurements. Simulation and experimental validation on a flexible manipulator payload equipped with a tip-mounted IMU demonstrate accurate reconstruction of both deformation and wrench responses, highlighting strong performance under limited sensing conditions.
ECC
Power Hardware-in-the-loop Interfacing via ℋ∞ Model Matching

Jonathan Eid, Ashley Meagher, Dmitry Rimorov, and 3 more authors

In 2026 European Control Conference (ECC), Jul 2026

Abs Bib

This paper presents an ℋ∞ model matching control approach to the problem of power hardware-in-the-loop (PHIL) interfacing. The objective is to interconnect a grid simulation and a physical device via an interface in a way that is stable and accurate. Conventional approaches include the ideal transformer method (ITM) and its impedance-based variants, which trade accuracy for stability, as well as some ℋ∞ control-based approaches, which do not make use of all the available information in their optimization for accuracy. Designing for transparency, as opposed to accuracy as existing approaches do, would achieve both stability and accuracy, while making use of all the dynamical information present in the idealized interconnection of the grid and device. The approach proposed in this paper employs model matching to formulate the PHIL problem as an ℋ∞ control problem using transparency as the explicit frequency-domain control objective. The approach is experimentally validated in a real-time resistive-load PHIL setup, and is found to achieve accuracy levels that are comparable or superior to those of an ITM-based interface.
@inproceedings{eid2026power, author = {Eid, Jonathan and Meagher, Ashley and Rimorov, Dmitry and Bonala, Anil Kumar and Thike, Rajendra and Forbes, James Richard}, booktitle = {{2026 European Control Conference (ECC)}}, title = {{Power Hardware-in-the-loop Interfacing via ℋ∞ Model Matching}}, year = {2026}, pages = {2184-2189}, url = {https://ieeexplore.ieee.org/document/11625593}, urldate = {2026-08-17}, month = jul, issn = {2996-8895}, eventtitle = {{2026 European Control Conference (ECC)}}, selected = true, bibtex_show = true }
Output Feedback Controller Synthesis with Finite Frequency Positive Realness Constraint

Dmitry Rimorov^* and James Richard Forbes

European Control Conference (ECC), Reykjavik, Iceland, July 7-10, 2026

Abs

The paper addresses the problem of multiobjective controller synthesis with a finite frequency positive realness constraint. The challenge is particularly relevant in practical applications, where positive realness is sought to ensure robust stability, but enforcing it over an entire frequency range is either not possible or severely limits the performance. This paper proposes a design methodology that allows imposing finite frequency positive realness constraint via the Generalized KYP Lemma. The novelty lies in reducing the conservatism of the Generalized KYP Lemma synthesis based on the Projection Lemma. It is achieved by coupling the extended formulation of the KYP Lemma with the multiplier expansion of the Generalized KYP Lemma and applying iterative convex overbounding to the resulting problem with bilinear matrix inequality constraint. A heuristic for choosing the multiplier coefficients is equally proposed. A numerical example demonstrates the effectiveness of the proposed approach.
dkpy: Robust Control with Structured Uncertainty in Python

Timothy Everett Adams^*, Steven Dahdah, and James Richard Forbes

European Control Conference (ECC), Reykjavik, Iceland, July 7-10, 2026

Abs arXiv Code

Models used for control design are, to some degree, uncertain. Model uncertainty must be accounted for to ensure the robustness of the closed-loop system. µ-analysis and µ-synthesis methods allow for the analysis and design of controllers subject to structured uncertainties. Moreover, these tools can be applied to robust performance problems as they are fundamentally robust control problems with structured uncertainty. The contribution of this paper is dkpy, an opensource Python package for performing robust controller analysis and synthesis for systems subject to structured uncertainty. dkpy also provides tools for performing model uncertainty characterization using data from a set of perturbed systems. The open-source project can be found at https://github.com/decargroup/dkpy.
Measurement-Based Robust Stability Assessment of Interconnections Using Impedance Models

Dmitry Rimorov^*, James Richard Forbes, and Richard Gagnon

2026 IEEE Power and Energy Society General Meeting, Montreal, QC, July 19-23, 2026

Abs

Impedance model-based stability assessment is a popular approach for interconnection studies and is often complementary to full-scale simulation studies. It can be of great utility when only frequency response measurements are available. Given that the stability assessment must be done for various operating points and network conditions, it is of great importance to develop tools that give the most information about relevant stability margins and robustness metrics, especially when there are few measurements available. The paper applies the structured singular value analysis methodology for robust stability assessment of converter-based generation interconnection to electric grids. It is shown that in some important cases the associated uncertainty models can be refined to provide tight bounds on robust stability metrics. The proposed approach is demonstrated for a case of wind-park interconnection to a series-compensated grid to analyze subsynchronous control interactions. The results confirm the practical utility of the described methodology.
Observability-Informed Optimal Sensor Placement for Soft Robots

Samuel Smocot^*, James Richard Forbes, and Audrey Sedal

9th IEEE-RAS International Conference on Soft Robotics (RoboSoft 2026), Kanazawa, Japan, April 7-11, 2026

Abs

This paper presents the application and experimental evaluation of a systematic method for optimal sensor placement in soft robots. Existing methods either lack generalizability across different soft robot morphologies or do not account for system dynamics. The applied method uses convex optimization to find the optimal sensor configuration that maximizes an observability Gramian-based metric. The framework is experimentally evaluated using position and strain measurements on a soft continuum arm. Kalman filter state estimates using optimal sensor placements yield lower reconstruction error than a baseline across all sinusoidal input trials, with improvements on the order of millimeters. This case study shows that linear control theory tools can guide optimal sensor placement in soft robots, suggesting an interpretable approach to sensor placement that may extend to other morphologies.
Evaluation of Data-driven Kinematic Models for Autonomous Control of Continuum Robotic In-situ Bioprinters

Swen Groen^*, David Brenken, Samuel Smocot, and 3 more authors

9th IEEE-RAS International Conference on Soft Robotics (RoboSoft 2026), Kanazawa, Japan, April 7-11, 2026

Abs

Minimally invasive in-situ bioprinting involves the direct deposition of hydrogels within the body to reconstruct tissue defects. These bioprinters use soft robotic printheads to extrude hydrogels through a hollow channel and nozzle. The accurate control of the nozzle tip position is critical for safety and shape fidelity. Due to a lack of sensing integration, existing control strategies are limited to feedforward models and are design-specific, thereby increasing development cost and complexity. This present study systematically compared three different data-driven modeling strategies for autonomous control of a cable-driven continuum in-situ bioprinter: 1) Polynomial regression, 2) Gaussian process regression, and 3) a neural network. Submillimeter accuracy was achieved for both the Gaussian process and the neural network in static measurements. The Polynomial regression model had a 1.67 mm accuracy. Dynamic trajectory tracking indicated that the performance of the neural network was comparable to that of the polynomial regression model and lower than that of the Gaussian process. Printing of different shaped constructs yielded minor visual deviations across all models from the target shapes. These results support the feasibility of real-time autonomous control for minimally invasive in-situ bioprinters and indicate the advantages of the different models during the design process of novel printing strategies.
Koopman Representation of Nonlinear Virtual Environments in Kinesthetic Haptic Systems

Yanting Zhou^*, Jozsef Kovecses, and James Richard Forbes

International Conference on Robotics and Automation, Vienna, Austria, June 1-5, 2026

Abs

Rendering haptic feedback with nonlinear virtual environments (VEs) is important in many applications that require highly accurate force feedback. This paper considers the use of the Koopman operator to represent a nonlinear VE interacting with a haptic system. Simulation and experimental results demonstrated that the proposed method provides an effective representation of the nonlinear dynamics of a Duffing-oscillator VE. A multi-user study further confirmed this conclusion. In addition, a closed-loop (CL) stability analysis is performed leveraging the Koopman representation of the nonlinear VE to assess stability of the overall haptic system. This alternative way of representing nonlinear VEs enables a convenient CL stability analysis that is less conservative than traditional passivity-based methods. Since a linear combination of all lifted states is used to represent the nonlinearity, such representation is also more robust to uncertainties in the modeling of the haptic device than a traditional nonlinear model.

2025

Input-Output Stability of Gradient Descent: A Discrete-Time Passivity-Based Approach

Sepehr Moalemi^* and James Richard Forbes

American Control Conference, Denver, CO, USA, July 8-10, 2025

Abs arXiv

This paper presents a discrete-time passivitybased analysis of the gradient descent method for a class of functions with sector-bounded gradients. Using a loop transformation, it is shown that the gradient descent method can be interpreted as a passive controller in negative feedback with a very strictly passive system. The passivity theorem is then used to guarantee input-output stability, as well as the global convergence, of the gradient descent method. Furthermore, provided that the lower and upper sector bounds are not equal, the input-output stability of the gradient descent method is guaranteed using the weak passivity theorem for a larger choice of step size. Finally, to demonstrate the utility of this passivitybased analysis, a new variation of the gradient descent method with variable step size is proposed by gain-scheduling the input and output of the gradient.
An SE(3) Noise Model for Range-Azimuth-Elevation Sensors

Thomas Hitchcox and James Richard Forbes

Conference on Robots and Vision (CRV), Calgary, AB, May 26-29, 2025

Presented by A. Del Castillo Bernal*

Abs arXiv

Scan matching is a widely used technique in state estimation. Point-cloud alignment, one of the most popular methods for scan matching, is a weighted least-squares problem in which the weights are determined from the inverse covariance of the measured points. An inaccurate representation of the covariance will affect the weighting of the least-squares problem. For example, if ellipsoidal covariance bounds are used to approximate the curved, “banana-shaped” noise characteristics of many scanning sensors, the weighting in the least-squares problem may be overconfident. Additionally, sensor-to-vehicle extrinsic uncertainty and odometry uncertainty during submap formation are two sources of uncertainty that are often overlooked in scan matching applications, also likely contributing to overconfidence on the scan matching estimate. This paper attempts to address these issues by developing a model for range-azimuth-elevation sensors on matrix Lie groups. The model allows for the seamless incorporation of extrinsic and odometry uncertainty. Illustrative results are shown both for a simulated example and for a real point-cloud submap collected with an underwater laser scanner.
Marginalizing and Conditioning Gaussians onto Linear Approximations of Smooth Manifolds with Applications in Robotics

Zi Cong Guo^*, James Richard Forbes, and Timothy Barfoot

International Conference on Robotics and Automation, Atlanta, GA, May 19-23, 2025

ICRA 2025 Best Paper Award.

Abs arXiv

We present closed-form expressions for marginalizing and conditioning Gaussians onto linear manifolds, and demonstrate how to apply these expressions to smooth nonlinear manifolds through linearization. Although marginalization and conditioning onto axis-aligned manifolds are well-established procedures, doing so onto non-axis-aligned manifolds is not as well understood. We demonstrate the utility of our expressions through three applications: 1) approximation of the projected normal distribution, where the quality of our linearized approximation increases as problem nonlinearity decreases; 2) covariance extraction in Koopman SLAM, where our covariances are shown to be consistent on a real-world dataset; and 3) covariance extraction in constrained GTSAM, where our covariances are shown to be consistent in simulation.

2024

Optimal Robot Formations: Balancing Range-Based Observability and User-Defined Configurations

Syed Shabbir Ahmed^*, Mohammed Ayman Shalaby, Jerome Le Ny, and 1 more author

Conference on Intelligent Robots and Systems, Abu Dhabi, UAE, October 14-18, 2024

Abs arXiv

This paper introduces a set of customizable and novel cost functions that enable the user to easily specify desirable robot formations, such as a "high-coverage" infrastructure inspection formation, while maintaining high relative pose estimation accuracy. The overall cost function balances the need for the robots to be close together for good ranging-based relative localization accuracy and the need for the robots to achieve specific tasks, such as minimizing the time taken to inspect a given area. The formations found by minimizing the aggregated cost function are evaluated in a coverage path planning task in simulation and experiment, where the robots localize themselves and unknown landmarks using a simultaneous localization and mapping algorithm based on the extended Kalman filter. Compared to an optimal formation that maximizes ranging-based relative localization accuracy, these formations significantly reduce the time to cover a given area with minimal impact on relative pose estimation accuracy.
Gaussian-Sum Filter for Range-based 3D Relative Pose Estimation in the Presence of Ambiguities

Syed Shabbir Ahmed^*, Mohammed Ayman Shalaby, Charles Champagne Cossette, and 2 more authors

Conference on Control Technology and Applications, Newcastle upon Tyne, UK, August 21-23, 2024

Abs arXiv

Multi-robot systems must have the ability to accurately estimate relative states between robots in order to perform collaborative tasks, possibly with no external aiding. Three-dimensional relative pose estimation using range measurements oftentimes suffers from a finite number of nonunique solutions, or ambiguities. This paper: 1) identifies and accurately estimates all possible ambiguities in 2D; 2) treats them as components of a Gaussian mixture model; and 3) presents a computationally-efficient estimator, in the form of a Gaussian-sum filter (GSF), to realize range-based relative pose estimation in an infrastructure-free, 3D, setup. This estimator is evaluated in simulation and experiment and is shown to avoid divergence to local minima induced by the ambiguous poses. Furthermore, the proposed GSF outperforms an extended Kalman filter, demonstrates similar performance to the computationally-demanding particle filter, and is shown to be consistent.
Passivity-Based Gain-Scheduled Control with Scheduling Matrices

Sepehr Moalemi^* and James Richard Forbes

Conference on Control Technology and Applications, Newcastle upon Tyne, UK, August 21-23, 2024

Abs arXiv Code

This paper considers gain-scheduling of very strictly passive (VSP) subcontrollers using scheduling matrices. The use of scheduling matrices, over scalar scheduling signals, realizes greater design freedom, which in turn can improve closed-loop performance. The form and properties of the scheduling matrices such that the overall gain-scheduled controller is VSP are explicitly discussed. The proposed gainscheduled VSP controller is used to control a rigid two-link robot subject to model uncertainty where robust input-output stability is assured via the passivity theorem. Numerical simulation results highlight the greater design freedom, resulting in improved performance, when scheduling matrices are used over scalar scheduled signals.
Synthesizing Control Laws from Data using Sum-of-Squares Optimization

Jason Bramburger, Steven Dahdah^*, and James Richard Forbes

Conference on Control Technology and Applications, Newcastle upon Tyne, UK, August 21-23, 2024

Abs arXiv

The control Lyapunov function (CLF) approach to nonlinear control design is well established. Moreover, when the plant is control affine and polynomial, sum-of-squares (SOS) optimization can be used to find a polynomial controller as a solution to a semidefinite program. This letter considers the use of data-driven methods to design a polynomial controller by leveraging Koopman operator theory, CLFs, and SOS optimization. First, Extended Dynamic Mode Decomposition (EDMD) is used to approximate the Lie derivative of a given CLF candidate with polynomial lifting functions. Then, the polynomial Koopman model of the Lie derivative is used to synthesize a polynomial controller via SOS optimization. The result is a data-driven method that skips the intermediary process of system identification and can be applied widely to control problems. The proposed approach is used to successfully synthesize a controller to stabilize an inverted pendulum on a cart.

2023

navlie: A Python Package for State Estimation on Lie Groups

Charles Champagne Cossette, Mitchell Cohen, Vassili Korotkine, and 3 more authors

Conference on Intelligent Robots and Systems, Detroit, MI, October 1-5, 2023

Abs arXiv Code

The ability to rapidly test a variety of algorithms for an arbitrary state estimation task is valuable in the prototyping phase of navigation systems. Lie group theory is now mainstream in the robotics community, and hence estimation prototyping tools should allow state definitions that belong to manifolds. A new package, called navlie, provides a framework that allows a user to model a large class of problems by implementing a set of classes complying with a generic interface. Once accomplished, navlie provides a variety of on-manifold estimation algorithms that can run directly on these classes. The package also provides a built-in library of common models, as well as many useful utilities. The open-source project can be found at: https://github.com/decargroup/navlie.
Magnetic Navigation using Attitude-Invariant Magnetic Field Information for Loop Closure Detection

Natalia Pavlasek^*, Charles Champagne Cossette, and James Richard Forbes

Conference on Intelligent Robots and Systems, Detroit, MI, October 1-5, 2023

Abs arXiv

Indoor magnetic fields are a combination of Earth’s magnetic field and disruptions induced by ferromag-netic objects, such as steel structural components in buildings. As a result of these disruptions, pervasive in indoor spaces, mag-netic field data is often omitted from navigation algorithms in indoor environments. This paper leverages the spatially-varying disruptions to Earth’s magnetic field to extract positional information for use in indoor navigation algorithms. The algorithm uses a rate gyro and an array of four magnetometers to estimate the robot’s pose. Additionally, the magnetometer array is used to compute attitude-invariant measurements associated with the magnetic field and its gradient. These measurements are used to detect loop closure points. Experimental results indicate that the proposed approach can estimate the pose of a ground robot in an indoor environment within meter accuracy.
Performance Evaluation of 3D Keypoint Detectors and Descriptors on Coloured Point Clouds in Subsea Environments

Kyungmin Jung^*, Thomas Hitchcox, and James Richard Forbes

International Conference on Robotics and Automation, London, UK, May 29 - June 2, 2023

Abs arXiv

The recent development of high-precision subsea optical scanners allows for 3D keypoint detectors and feature descriptors to be leveraged on point cloud scans from subsea environments. However, the literature lacks a comprehensive survey to identify the best combination of detectors and descriptors to be used in these challenging and novel environments. This paper aims to identify the best detector/descriptor pair using a challenging field dataset collected using a commercial underwater laser scanner. Furthermore, studies have shown that incorporating texture information to extend geometric features adds robustness to feature matching on synthetic datasets. This paper also proposes a novel method of fusing images with underwater laser scans to produce coloured point clouds, which are used to study the effectiveness of 6D point cloud descriptors.
Calibration and Uncertainty Characterization for Ultra-Wideband Two-Way-Ranging Measurements

Mohammed Ayman Shalaby^*, Charles Champagne Cossette, James Richard Forbes, and 1 more author

International Conference on Robotics and Automation, London, UK, May 29 - June 2, 2023

Abs arXiv

Ultra-Wideband (UWB) systems are becoming increasingly popular for indoor localization, where range measurements are obtained by measuring the time-of-flight of radio signals. However, the range measurements typically suffer from a systematic error or bias that must be corrected for high-accuracy localization. In this paper, a ranging protocol is proposed alongside a robust and scalable antenna-delay calibration procedure to accurately and efficiently calibrate antenna delays for many UWB tags. Additionally, the bias and uncertainty of the measurements are modelled as a function of the received-signal power. The full calibration procedure is presented using experimental training data of 3 aerial robots fitted with 2 UWB tags each, and then evaluated on 2 test experiments. A localization problem is then formulated on the experimental test data, and the calibrated measurements and their modelled uncertainty are fed into an extended Kalman filter (EKF). The proposed calibration is shown to yield an average of 46% improvement in localization accuracy. Lastly, the paper is accompanied by an opensource UWB-calibration Python library, which can be found at https://github.com/decargroup/uwb calibration.

2022

Optimal Multi-robot Formations for Relative Pose Estimation Using Range Measurements

Charles Champagne Cossette^*, Mohammed Ayman Shalaby, David Saussié, and 2 more authors

Conference on Intelligent Robots and Systems, Kyoto, Japan, October 23-27, 2022

Abs arXiv

In multi-robot missions, relative position and attitude information between robots is valuable for a variety of tasks such as mapping, planning, and formation control. In this paper, the problem of estimating relative poses from a set of inter-robot range measurements is investigated. Specifically, it is shown that the estimation accuracy is highly dependent on the true relative poses themselves, which prompts the desire to find multi-robot formations that provide the best estimation performance. By direct maximization of Fischer information, it is shown in simulation and experiment that large improvements in estimation accuracy can be obtained by optimizing the formation geometry of a team of robots.

2021

Map-Aided Train Navigation with IMU Measurements

Marc-Antoine Lavoie^* and James Richard Forbes

Conference on Intelligent Robots and Systems, Prague, Czech Republic (online), September 27 - October 1, 2021

Abs

Autonomous train navigation using only a lowcost MEMS IMU and a track map is considered in this paper. The approach is designed for urban rail or subway environments where GNSS measurements are unreliable or unavailable, and is intended as a baseline against which more complex sensor fusion approaches can be compared to ensure the consistency of the estimates. The estimator exploits the track motion constraint and information about position and velocity derived from centripetal acceleration and angular velocity measurements to improve the dead-reckoning solution and keep error and uncertainty bounded. In experimental validation over a 6 km run of a subway train during commuter service, the proposed approach had a maximum error of 6.0 m, validating the approach as an independent estimator.
Localization with Directional Coordinates

Charles Champagne Cossette^*, Mohammed Ayman Shalaby, David Saussié, and 1 more author

Conference on Intelligent Robots and Systems, Prague, Czech Republic (online), September 27 - October 1, 2021

Abs arXiv

A coordinate system is proposed that replaces the usual three-dimensional Cartesian x, y, z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and, unlike spherical coordinates, the proposed coordinates do not suffer from the same kinematic singularities and angle wraparound. When compared to Cartesian coordinates, the proposed coordinate system results in a significantly enhanced ability to represent the true distribution of robot positions, ultimately leading to large improvements in state estimation consistency.
Invariant Extended Kalman Filtering Using Two Position Receivers for Extended Pose Estimation

Natalia Pavlasek^*, Alex Walsh, and James Richard Forbes

International Conference on Robotics and Automation, Xi’an, China, May 30 - June 5, 2021

Abs arXiv

This paper considers the use of two position receivers and an inertial measurement unit (IMU) to estimate the position, velocity, and attitude of a rigid body, collectively called extended pose. The measurement model consisting of the position of one receiver and the relative position between the two receivers is left invariant, enabling the use of the invariant extended Kalman filter (IEKF) framework. The IEKF possesses various advantages over the standard multiplicative extended Kalman filter, such as state-estimate-independent Jacobians. Monte Carlo simulations demonstrate that the two-receiver IEKF approach yields improved estimates over a two-receiver multiplicative extended Kalman filter (MEKF) and a singlereceiver IEKF approach. An experiment further validates the proposed approach, confirming that the two-receiver IEKF has improved performance over the other filters considered.
Deep Koopman Representation for Control over Images (DKRCI)

Philippe Laferriere^*, Samuel Laferriere, Steven Dahdah, and 2 more authors

18th Conference on Robots and Vision, Burnaby, BC,, May 26 - 28, 2021

Abs

The Koopman operator provides a means to represent nonlinear systems as infinite dimensional linear systems in a lifted state space. This enables the application of linear control techniques to nonlinear systems. However, the choice of a finite number of lifting functions, or Koopman observables, is still an unresolved problem. Deep learning techniques have recently been used to jointly learn these lifting function along with the Koopman operator. However, these methods require knowledge of the system’s state space. In this paper, we present a method to learn a Koopman representation directly from images and control inputs. We then demonstrate our deep learning architecture on a cart-pole system with external inputs.

2020

A Point Cloud Registration Pipeline using Gaussian Process Regression for Bathymetric SLAM

Thomas Hitchcox^* and James Richard Forbes

Conference on Intelligent Robots and Systems, Las Vegas, NV, October 25-29, 2020

Abs

Point cloud registration is a means of achieving loop closure correction within a simultaneous localization and mapping (SLAM) algorithm. Data association is a critical component in point cloud registration, and can be very challenging in feature-depleted environments such as seabed. This paper presents a point cloud registration pipeline for performing loop closure correction in feature-depleted subsea environments using data collected from an optical scanner. The pipeline uses Gaussian process regression to extract keypoint sets, and a weighted network alignment algorithm to propose point correspondences. A variant of the iterative closest point (ICP) registration algorithm is used to perform fine alignment, with point correspondences informed by the mappings determined following the network alignment step. The developed registration pipeline is deployed with success on a challenging section of field data containing topography that cannot be resolved using conventional imaging sonar.
TWOLATE: Total Registration of Point-Clouds Using a Weighted Optimal Linear Attitude and Translation Estimator

Duowen Qian^*, Guillaume Charland-Arcand, and James Richard Forbes

Conference on Control Technology and Applications, Montreal, QC, August 24-26, 2020

Abs

A novel point-cloud registration method that can register points to points, points to planes, and points to lines simultaneously, and in a weighted fashion, is presented. The backbone of the proposed point-cloud registration method is a weighted version of the Optimal Linear Attitude and Translation Estimator (OLATE) called weighted OLATE (WOLATE). The first contribution of this work is the derivation of WOLATE versions of point-to-point, point-to-plane, and point-to-line, all of which take the form of weighted linear least-squares problems. This allows each WOLATE variant to be combined into one large weighted linear least-squares problem. Formulation of this combined registration algorithm, called Total Registration using WOLATE (TWOLATE), is the second contribution of this work. TWOLATE is embedded into a LIDAR odometry pipeline, and is shown to have similar performance relative to state-of-the-art methods, the third contribution of this work.
System Identification and H∞ Control of a Fatigue Structural Testing Rig

Robyn Fortune^*, Christopher André Beltempo, and James Richard Forbes

Conference on Control Technology and Applications, Montreal, QC, August 24-26, 2020

Abs

This paper considers system identification and H∞ control of a load-controlled fatigue structural test rig. The test rig is comprised of an aluminum-composite structure and hydraulic actuators that apply desired loads. Fatigue tests must be performed using closed-loop control in order to avoid damaging the test article. Therefore, three closed-loop system identification methods are considered, the direct method, indirect method, and dual-Youla method. The best identified models in terms of variance accounted for are then used to design two degree-offreedom H∞ controllers. Reduced-order versions of the H∞ controllers are implemented on the test rig and used to track a load profile. The system identification and H∞ controller synthesis methods are presented, along with identification and tracking results.
Cartesian Elastodynamics Model of a Full-Mobility PKM with Flexible Links

Qi Sun^*, Jorge Angeles, and James Richard Forbes

New Trends in Mechanism and Machine Science. EuCoMeS 2020. Mechanisms and Machine Science, 2020

Abs

(No abstract.)
Dynamics Modeling and Validation of a 3-PRR Planar Parallel Robot

Qi Sun^*, Jorge Angeles, and James Richard Forbes

Canadian Society for Mechanical Engineering International Congress, Charlottetown, PEI, June 21-24, 2020

Abs

(No abstract.)

2019

DReCon: Data-Driven Responsive Control of Physics-Based Characters

Kevin Bergemin^*, Daniel Holden, Simon Clavet, and 1 more author

SIGGRAPH Asia, Brisbane, Australia, November 18-21, 2019

Abs

Interactive control of self-balancing, physically simulated humanoids is a long standing problem in the ield of real-time character animation. While physical simulation guarantees realistic interactions in the virtual world, simulated characters can appear unnatural if they perform unusual movements in order to maintain balance. Therefore, obtaining a high level of responsiveness to user control, runtime performance, and diversity has often been overlooked in exchange for motion quality. Recent work in the ield of deep reinforcement learning has shown that training physically simulated characters to follow motion capture clips can yield high quality tracking results. We propose a two-step approach for building responsive simulated character controllers from unstructured motion capture data. First, meaningful features from the data such as movement direction, heading direction, speed, and locomotion style, are interactively speciied and drive a kinematic character controller implemented using motion matching. Second, reinforcement learning is used to train a simulated character controller that is general enough to track the entire distribution of motion that can be generated by the kinematic controller. Our design emphasizes responsiveness to user input, visual quality, and low runtime cost for application in video-games.
Periodic Tracking Control Using Gain-Scheduled Fourier Series-Based Internal Models

Dylan Caverly, Ryan James Caverly^*, and James Richard Forbes

ASME Dynamic Systems and Control Conference, Park City, UT, October 9-11, 2019

Abs

This paper presents a gain-scheduled controller composed of a number of positive real controllers that contain internal models of reference command signals. Using the internal model principle as inspiration, and the Passivity Theorem to assure input-output closed-loop stability, the proposed controller is designed to realize tracking while maintaining input-output stability of the closed-loop system. The gain-scheduled nature of the internal models allows for a number of internal models to be simultaneously implemented. In particular, by expressing a periodic reference command as a Fourier series, the first few Fourier modes can be included as internal models in the controllers to be gain-scheduled, which reduces steady-state tracking error. An example involving tracking the outlet temperature of a heat exchanger is presented, where the first nine Fourier modes of the reference signal are used as internal models to reduce tracking error.
An Invariant Extended H∞ Filter

Marc-Antoine Lavoie^*, Jonathan Arsenault, and James Richard Forbes

Conference on Decision and Control, Nice, France, December 11-13, 2019

Invited session 1 on “multi-sensor fusion techniques for state estimation in navigation"

Abs

This paper presents an invariant extended H∞ filter for position and attitude estimation on the matrix Lie group SE (2). Extended H∞ filtering results are adapted to work directly within a matrix Lie group framework in an analogous way to how the invariant extended Kalman filter (IEKF) adapts the standard extended Kalman filter (EKF) to work within a matrix Lie group framework. The principal advantage of the invariant extended H∞ filter over the extended H∞ filter is that the linearization of the state and measurement models is independent of the current state estimate, leading to state-independent Jacobians at any linearization point. Moreover, for the SE (2) problem considered, the invariant extended H∞ filter realizes a substantially lower minimum performance bound γ than the standard extended H∞ filter.
System Identification and Feedforward Control of a Fatigue Structural Testing Rig: The Single Actuator Case

Robyn Fortune^*, Christopher André Beltempo, and James Richard Forbes

21th IFAC Symposium on Automatic Control in Aerospace (ACA 2019), Cranfield UK, August 27-30, 2019

Abs

This paper considers single-input-single-output (SISO) system identification of a fatigue test rig. The test rig consists of an aluminum-composite structure and four hydraulic actuators that are independently actuated. Because the test rig cannot be run in an open-loop manner, three different closed-loop system identification methods are considered. Specifically, direct, indirect, and dual-Youla closed-loop system identification methods are considered. The models obtained via system identification are used to generate inversion-based feedforward controllers of varying order. The feedforward controllers are implemented on the test rig in combination with a proportional-integral (PI) feedback controller, and together the feedforward and feedback controllers are used to track a random load profile. System identification and tracking results are presented.
Invariant Sliding Window Filtering for Attitude and Bias Estimation

Alex Walsh^*, Jonathan Arsenault, and James Richard Forbes

American Control Conference, Philadelphia, PA, USA, July 10-12, 2019

Abs

This paper considers sliding window filtering in an invariant framework for estimation of attitude and rate gyro bias in a matrix Lie group formulation. The multiplicative extended Kalman filter (MEKF) and invariant extended Kalman filter (IEKF), variants of the extended Kalman filter well suited to estimation on matrix Lie groups, are discussed. The sliding window formulation of both the MEKF and IEKF is presented, leading to the sliding window filter (SWF), the invariant SWF (ISWF), and the imperfect ISWF for systems that are not group affine. Simulation results for an attitude and heading reference system with bias are presented, comparing the ISWF to the traditional SWF, MEKF, and IEKF.
Relative Constrained SLAM for Robot Navigation

Duowen Qian^*, Shatil Rahman, and James Richard Forbes

American Control Conference, Philadelphia, PA, USA, July 10-12, 2019

Abs

This paper presents a relative-constrained SLAM formulation where partial a priori landmark information is built into the SLAM problem. Incorporating a priori relative constraints is motivated by the desire to avoid drawbacks of global constraints and to reduce uncertainty in the overall map and pose estimates. First, a Relative Deterministic-Constrained SLAM (RDC-SLAM) method is presented, where a Lagrange multiplier term is added to the cost function of the standard graph-based SLAM method, realizing a new deterministicconstrained least squares solution. Next, this method is extended to incorporate probabilistic constraints and is solved using chance-constrained optimization for a more robust least square solution, leading to Relative Probabilistic-Constrained SLAM (RPC-SLAM). Both RDC-SLAM and RPC-SLAM are tested within a Monte-Carlo framework using a 2D dataset. It is shown that the RPC-SLAM framework outperforms the other methods considered when landmark initialization is poor. landmarks is generally available or easily obtainable. For example, an autonomous vehicle navigating in a city center will observe certain landmarks such as traffic-light poles, stop signs, buildings, etc. When the robot “sees” a landmark that is a known distance relative to another, the location of the other landmark can be inferred, and as such, the position error and uncertainty of both the map and pose of the robot can be reduced. However, there is often inherent uncertainty present in such constraints. The contribution of this paper is the derivation of a novel Constrained SLAM formulation that not only integrates relative node-to-node constraints as a priori information into the SLAM problem formulation, but also explicitly incorporates uncertainty in these constraints, leading to a more robust algorithm.
Synthesis of Strictly Negative Imaginary Controllers Using a H∞ Performance Index

Ken Lee^* and James Richard Forbes

American Control Conference, Philadelphia, PA, USA, July 10-12, 2019

Abs

Negative imaginary (NI) systems are those characterized by a negative imaginary frequency response. A NI system connected in a positive feedback interconnection with a strictly negative imaginary (SNI) controller is internally stable if and only if a DC gain condition is satisfied. This can be interpreted as a robust stability result in situations where plant uncertainty does not destroy the NI nature of the plant nor the DC gain condition. Motivated by a desire to realize improved closed-loop performance, this paper considers the design of H∞-optimal SNI controllers. The proposed synthesis method makes use of convex optimization and linear matrix inequality (LMI) tools. Another contribution of this paper is pointing out how to realize tip position control, rather than joint position control, of a flexible manipulator within a NI framework. Numerical simulation results are included.
Nonlinear Attitude and Bias Observer Design with a Gibbs-Inspired Cost Function Using Direct Vector Measurements

David Evan Zlotnik and James Richard Forbes^*

American Control Conference, Philadelphia, PA, USA, July 10-12, 2019

Abs

This paper considers the problem of rigid-body attitude and rate-gyro bias estimation. Available measurements include a biased rate-gyro measurement and two or more linearly independent vector measurements. The gradient-based observer design methodology for Lie groups is employed to derive a provably convergent attitude observer. The observer propagates the state estimate along the gradient descent direction of a proposed attitude error function. The use of the proposed attitude error function, which is inspired by previous cost functions using the Gibbs parameterization, results in an innovation term that aggressively drives the attitude error to zero, leading to fast convergence of the observer. The innovation term can be constructed directly from the vector measurements. Numerical results are included that demonstrate the desirable convergence properties of the observer compared to previous results.
H∞-Optimal Strictly Positive Real Parallel Feedforward Control

Ryan James Caverly^* and James Richard Forbes

American Control Conference, Philadelphia, PA, USA, July 10-12, 2019

Abs

This paper presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system strictly positive real (SPR) in an H∞-optimal fashion. The parallel feedforward controller is designed in such a manner that when the output of the system is added to the output of the parallel feedforward controller, the transfer matrix from the system input to the new output is SPR. In order to ensure that the difference between the new output and the original system output is small, the maximum singular value of a static parallel feedforward controller or the weighted H∞ norm of a dynamic parallel feedforward controller is minimized. The proposed synthesis methods are convex optimization problems that make use of linear matrix inequality and equality constraints. The controllers are implemented numerically on a flexible-joint robotic manipulator and compared to a parallel feedforward controller from the literature. It is shown in closed-loop simulation that a significant improvement in tracking error is achieved with one of the proposed dynamic parallel feedforward controller synthesis methods.
Elastodynamics of a Parallel Schonflies-Motion Generator

Zuyu Yin^*, Bruno Belzile, Jorge Angeles, and 1 more author

2019 CCToMM M3 Symposium, Montreal, QC, May 16-17, 2019

Abs

(No abstract.)
Modeling and Control of a Passively-Coupled Tilt-Rotor Vertical Takeoff and Landing Aircraft

Romain Chiappinelli^*, Mitchell Cohen, Martin Doff-Sotta, and 3 more authors

International Conference on Robotics and Automation, Montreal, QC, May 20-24, 2019

Abs

This paper presents the modeling and control of a passively-coupled tilt-rotor vertical takeoff and landing aircraft. The aircraft consists of a quadrotor frame attached to a fixedwing aircraft by an unactuated hinged mechanism. The platform is capable of smooth transitions from hover to forward flight without the use of tilting actuators. The transition from hover to forward flight is made possible by differential thrust between the fore and aft propellers of the quadrotor frame. In this paper, the coupled dynamics between the quadrotor frame and the aircraft frame are modeled as a constrained multi-body system. The equations of motion are established using a constrained Lagrangian approach and the model developed is used to build a realistic simulation environment for control design purpose. A cascaded control architecture based on P/PID controllers is proposed to achieve inner-loop attitude, height and forward velocity control. Simulated and experimental results are obtained with a close match for hover, transitions, forward flight, and banked turn maneuvers.

2018

H∞-Optimal Parallel Feedforward Control using Minimum Gain

Ryan James Caverly^* and James Richard Forbes

IEEE Conference on Decision and Control, Miami Beach, FL, December 17-19, 2018

Abs

This letter presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system minimum phase by augmenting its output. The system output is perturbed the least amount possible by minimizing the gain of the parallel feedforward controller while ensuring the augmented system is minimum phase. This is done by minimizing the maximum singular value of a static parallel feedforward controller or the weighted H∞ norm of a dynamic parallel feedforward controller. Static and dynamic parallel feedforward controllers are synthesized using direct and indirect methods that involve bilinear matrix inequality constraints and are solved iteratively using linear matrix inequalities. The direct method enforces a minimum gain constraint directly on the augmented system, while the indirect method solves for an asymptotically stabilizing negative feedback controller that is inverted to obtain the parallel feedforward controller. Numerical examples are provided to demonstrate the effectiveness of the proposed controller synthesis methods.
Linearly Combining Sensor Measurements Optimally to Enforce an SPR Transfer Matrix

Ryan James Caverly and James Richard Forbes^*

IEEE Conference on Control Technology and Applications, Copenhagen, Denmark, August 21-24, 2018

Abs

This paper presents methods to combine measurements of a linear time-invariant system in such a manner that the new system obtained is strictly positive real (SPR). In particular, this paper focuses on how to best combine measurements in a linear fashion by minimizing the difference in an H_2 or H∞ sense between the new system and a given desired system. The methods proposed to linearly combine sensor measurements rely on linear matrix inequalities (LMIs), which lead to tractable synthesis procedures. Numerical examples involving noncolocated elastic mechanical systems are provided that illustrate the effectiveness of the proposed techniques when used for output tracking control.
Riemann Sphere Interpretation of the Passivity, Small Gain, and Conic Sector Theorems

Ken Lee, Alex Walsh, and James Richard Forbes^*

IEEE Conference on Control Technology and Applications, Copenhagen, Denmark, August 21-24, 2018

Abs

One way to visualize the frequency response of a single-input single-output transfer function is to use the Nyquist plot. This plot gives insight into system properties, such as gain and phase properties, that are not immediately evident when looking at the transfer function itself. The Nyquist plot can also be used to assess closed-loop stability via the Nyquist stability criterion. There are well-known Nyquist interpretations of passive, finite gain, and conic system properties, as well as Nyquist interpretations of the passivity, small gain, and conic sector theorems. This paper provides Riemann sphere interpretations of passive, finite gain, and conic system properties, as well as Riemann sphere interpretations of the passivity, small gain, and conic sector theorems. These Riemann sphere interpretations provide control systems engineers with yet another tool to glean insight into plant and controller properties, closed-loop stability, performance, and robustness.
A Linear- and Linear-Matrix-Inequality-Constrained Extended Kalman Filter

Robin Aucoin^*, Stephen Alexander Chee, and James Richard Forbes

American Control Conference, Milwaukee, WI, USA, June 27-29, 2018

Abs

This study proposes a method for state estimation of nonlinear systems that incorporates linear- and linear-matrixinequalities as constraints on the state estimate. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. In this formulation, additional state-estimate constraints are incorporated into the optimization problem as linear- and linearmatrix-inequality constraints. This methodology is applied in the multiplicative extended Kalman filter (MEKF) framework for three-dimensional position and attitude estimation, and is validated on a simulation of a mobile robot translating and rotating in a constrained domain space. Results are presented and compared to those for the unconstrained MEKF.
Iterative H_2-Conic Controller Synthesis

Leila Jasmine Bridgeman^* and James Richard Forbes

American Control Conference, Milwaukee, WI, USA, June 27-29, 2018

Abs

The Conic Sector Theorem is a versatile input-output stability result that can be used to ensure closed-loop, input-output stability where better-known results, such as the Passivity and Small Gain Theorems, cannot. This paper proposes a linear-matrix-inequality-based approach to the synthesis of conic controllers that minimizes an upper bound on the closed-loop H_2-norm. The upper bound is iteratively improved, providing controllers that successively decrease an upper bound on the closed-loop H_2-norm. This provides a valuable tool for robust and optimal control by combining the utility of conic sectors and the Conic Sector Theorem with H_2-optimal control. The effectiveness of this method is compared to an existing conic controller synthesis method in a numerical example.
Elastostatics of a Full-Mobility PKM with Flexible Links

Qi Sun^*, Jorge Angeles, and James Richard Forbes

ROMANSY 22 - Robot Design, Dynamics and Control, Rennes, France, June 25-38, 2018

Abs

The subject of this paper is the elastostatics of a novel three-limb, full-mobility parallel-kinematics machine (PKM) with flexible links, dubbed the SDelta robot. Due to the inherent flexibility of the light-weight limb rods under fast operations, they are modeled as identical linearly elastic beams. The moving platform of the PKM is assumed to be elastically attached to the base platform via a six-dof generalized spring. Because of the symmetric design of the SDelta robot, the constant generalized stiffness matrix becomes isotropic. Moreover, the posture-dependent Cartesian stiffness matrix is derived. Based on the preliminary design of a prototype at the desktop scale, its stiffness matrix is numerically evaluated.
Zero Shaping of Nonminimum Phase Aircraft Dynamics

Ryan James Caverly^* and James Richard Forbes

AIAA Science and Technology Forum and Exposition 2018, Gaylord Palms, Kissimmee, FL, USA, January 9–12, 2018

Abs

In this paper, two controller synthesis methods are proposed that ensure that the closedloop transfer matrix from the process disturbance acting on an aircraft to the performance output of the aircraft has only minimum phase blocking and transmission zeros. The first method employs a parallel feedforward controller, while the second method uses a static output feedback controller and relies on the concept of minimum gain. Both methods make use of linear matrix inequalities for controller synthesis. The proposed controller synthesis methods are applied to nonminimum phase linearized longitudinal and lateral-directional aircraft dynamics, and their performance is compared in simulation.

2017

Sigma Point Kalman Filtering on Matrix Lie Groups

James Richard Forbes^* and David Evan Zlotnik

3rd conference on Geometric Science of Information (GSI 2017), Société Mathématique de France, Paris, France, November 7–9, 2017

J.R. Forbes is an invited speaker as part of “Geometric Robotics" session.

Abs

This paper considers sigma point Kalman filtering on matrix Lie groups. Sigma points that are elements of a matrix Lie group are generated using the matrix exponential. Computing the mean and covariance using the sigma points via weighted averaging and effective use of the matrix natural logarithm, respectively, is discussed. The specific details of estimating landmark locations, and the position and attitude of a vehicle relative to the estimated landmark locations, is considered.
Trimetric Imaging of the Martian Ionosphere using a CubeSat Constellation

Edgar Bering^*, Laila Andersson, Ji Chen, and 13 more authors

AIAA SPACE and Astronautics Forum and Exposition, Orlando, FL, USA, September 12-14, 2017

Abs

(No abtract.)
Norm- and Linear-Inequality-Constrained State Estimation: An LMI Approach

Stephen Alexander Chee^*, Leila Jasmine Bridgeman, and James Richard Forbes

IEEE Conference on Control Technology and Applications, Kohala Coast, HI, USA, August 27–30, 2017

Abs

This paper proposes a method for state estimation that incorporates norm- and linear-inequality constraints using Linear Matrix Inequalities (LMIs). This is accomplished by adopting a prediction-correction filter form and calculating the observer gain matrix by solving a convex optimization problem with LMI constraints where the state constraints are expressed as LMIs. The state constraints considered in this study include norm and linear inequalities. Simulation results are included to assess the performance of the proposed filter in a scenario involving a mobile robot moving within a constrained area taking range and bearing measurements of known landmarks. The filter’s performance is compared with a traditional EKF.
Modelling of Flexible Cable-Driven Parallel Robots using a Rayleigh-Ritz Approach

Harsh Atul Godbole^*, Ryan James Caverly, and James Richard Forbes

Third International Conference on Cable-Driven Parallel Robots, Quebec City, QC, August 2-4, 2017

Abs

This paper investigates the use of the Rayleigh-Ritz method to model single degree-of-freedom flexible cable-driven parallel robots (CDPRs) using a set of time-dependent basis functions to discretize cables of varying length. An energy-based model simplification is proposed to further facilitate reduction in the computational load when performing numerical simulations involving the proposed model. Open-loop system responses are used to compare the effect of the energy-based model simplification. Frequency responses are used to compare the influence of the number of basis functions used and to provide a comparison to a lumped-mass model.
Nyquist Interpretation of the Large Gain Theorem

Ryan James Caverly and James Richard Forbes^*

20th IFAC World Congress, Toulouse, France, July 9–14, 2017

Abs

This paper presents a proof of the Large Gain Theorem using the Nyquist Stability Criterion. The minimum gain constraint stipulated by the Large Gain Theorem guarantees the open-loop transfer function encircles the point (-1,0) exactly P times in the counterclockwise direction, where P is the number of open-loop open right-half plane poles. This guarantees asymptotic stability of the feedback system, even in the presence of an unstable open-loop transfer function. The Nyquist interpretation of the Large Gain Theorem is compared to Nyquist interpretations of the Large Gain and Passivity Theorems. Applications of the Large Gain Theorem are discussed and numerical examples illustrating the concept of minimum gain and the Large Gain Theorem are presented.
Conic Controller Synthesis that Minimizes an Upper Bound on the Closed-Loop H_2-Norm

Leila Jasmine Bridgeman^* and James Richard Forbes

American Control Conference, Seattle, WA, USA, May 24-26, 2017

Abs

The Conic Sector Theorem is a versatile inputoutput stability result that can be used to ensure closed-loop, input-output stability where better-known results, such as the Passivity and Small Gain Theorems, cannot. This paper proposes a linear-matrix-inequality-based approach to the synthesis of conic controllers that minimizes an upper bound on the closed-loop H_2-norm. The upper bound is iteratively improved, providing controllers that successively decrease an upper bound on the closed-loop H_2-norm. This provides a valuable tool for robust and optimal control by combining the utility of conic sectors and the Conic Sector Theorem with H_2-optimal control. The effectiveness of this method is compared to an existing conic controller synthesis method in a numerical example.
Regional Pole and Zero Placement with Static Output Feedback via the Modified Minimum Gain Lemma

Ryan James Caverly^* and James Richard Forbes

American Control Conference, Seattle, WA, USA, May 24-26, 2017

Abs

This paper presents static output feedback controller synthesis methods that place closed-loop poles, blocking zeros, and transmission zeros within regions of the complex plane. In particular, closed-loop poles are placed within linear matrix inequality (LMI) regions of the complex plane, while closed-loop blocking and transmission zeros are placed in the open left-half plane (OLHP), and are thus minimum phase. An LMI formulation of the Modified Minimum Gain Lemma is used to ensure that the closed-loop system is minimum phase by forcing a nonzero minimum gain constraint. Two controller synthesis methods are presented, including Method 1, which places the closed-loop poles in the OLHP, and Method 2, which places closed-loop poles in the OLHP and closed-loop poles within a specified LMI region of the complex plane. Numerical examples are provided for both controller synthesis methods, with comparisons to controllers in the literature.
Constrained Extremum-Seeking Guidance Using a Constrained Kalman Filter

Alex Walsh^*, John Jack Ryan, and James Richard Forbes

American Control Conference, Seattle, WA, USA, May 24-26, 2017

Abs

A constrained extremum-seeking guidance algorithm using a constrained Kalman filter is presented. The Kalman filter estimates the gradient such that the performance variables determined by the extremum-seeking algorithm satisfy linear constraints. A simple linear example is first presented to demonstrate constrained extremum-seeking. Then, the extremum-seeking guidance law is applied to the formation flight of two aircraft. Simulation results demonstrate effective extremum seeking subject to linear constraints.
Gust-Load Alleviation of a Flexible Aircraft using a Disturbance Observer

Ryan James Caverly^*, James Richard Forbes, Brian Danowsky, and 1 more author

AIAA Science and Technology Forum and Exposition 2017, Gaylord Texan, Grapevine, TX, USA, January 9–13, 2017

Abs

In this paper, a disturbance observer is designed for the gust-load alleviation of a flexible high-altitude long-endurance (HALE) aircraft. A nonlinear dynamic model of a HALE vehicle is considered with a primary flight controller based on nonlinear dynamic inversion. Individual disturbance estimating filters (DEF) are designed to estimate and mitigate the effect of disturbances using sensor/actuator pairs of the aircraft. The individual DEFs are single-input single-output (SISO) disturbance observers for gust-load alleviation (DOGLAs) that are then combined together into a decoupled multi-input multi-output (D-MIMO) DOGLA. The D-MIMO DOGLA contains SISO DOGLAs dedicated to canceling out the effect of wind gusts on the body roll, pitch, and yaw rates of the aircraft, as well as on the deflection of the flexible wings. Numerical simulation results with the nonlinear flexible HALE aircraft model demonstrate that the D-MIMO DOGLA successfully mitigates the effect of wind gust loads on the aircraft in multiple flight profiles.
Norm-Constrained Forward-Backward Smoothing

Stephen Alexander Chee^* and James Richard Forbes

AIAA Science and Technology Forum and Exposition 2017, Gaylord Texan, Grapevine, TX, USA, January 9–13, 2017

Abs

This paper derives a discrete-time forward-backward fixed-interval smoother that enforces a norm-constraint on the entire state estimate or part of the state estimate. This is accomplished by modifying the optimization problem in which the forward-time filter and backward-time filter results are combined using Lagrange multipliers to enforce the constraint on the state estimates. This smoother is then applied to a nonlinear spacecraft attitude estimation problem as both a batch estimator and a sliding-window estimator. Numerical simulation results demonstrate the effectiveness of the proposed smoother.

2016

Exteroceptive Measurement Filtering Embedded within an SO(3)-Based Attitude Estimator

David Evan Zlotnik^* and James Richard Forbes

55^th Conference on Decision and Control, Las Vagas, NV, USA, December 12-14, 2016

Abs

A nonlinear deterministic attitude estimator is developed. The estimator evolves directly on the special orthogonal group of rigid-body rotations. Similar estimators in the literature are characterized by constant estimator gains that amplify noise across all frequencies. The proposed method accounts for undesirable noise in exteroceptive measurements by incorporating a strictly positive real (SPR) filter in the estimator structure. By tuning the “embedded” SPR filter over a frequency bandwidth undesirable noise corrupting exteroceptive measurements may be rejected. Rate-gyro bias estimation is also considered. The proposed attitude estimator is shown to asymptotically converge to the desired equilibrium point (i.e., when the estimated attitude and bias are equal to their true counterparts), provided a restriction on the set of initial conditions is satisfied. Moreover, exponential convergence is shown in a certain region about the desired equilibrium point. The proposed method is demonstrated in simulation.
Nonlinear Dynamic Inversion of a Flexible Aircraft

Ryan James Caverly^*, Anouck Girard, Ilya Kolmanovsky, and 1 more author

20th IFAC Symposium on Automatic Control in Aerospace (ACA 2016), Sherbrooke, Quebec, Canada, August 21-15, 2016

Abs

This paper investigates the use of dynamic inversion for the attitude control of a flexible aircraft. Input-output feedback linearization-based dynamic inversion is used to linearize the angular velocity and forward translational velocity equations of motion. A proportional-integral-derivative (PID) controller based on the direction cosine matrix (DCM) that describes the attitude of the aircraft is used, in addition to a proportional-integral (PI) controller to maintain a desired airspeed. Numerical simulations are performed using the proposed dynamic inversion controller, as well as more practical implementations of the controller that include saturated control inputs and no knowledge of the aircraft’s flexible states. In simulation, the practical controllers successfully stabilize a flexible aircraft with reasonable control surface deflections.
Gravity-Gradient-Stabilized Spacecraft Attitude Estimation Using Rate-Gyroscope Measurements

Stephen Alexander Chee^*, James Richard Forbes, and Dennis S. Bernstein

American Control Conference, Boston, MA, USA, July 6-8, 2016

Abs

This paper considers attitude estimation of a gravity-gradient-stabilized spacecraft. In particular, an observability analysis based on the linearized equations of motion, as well as numerical simulations, show that it is possible to estimate attitude using only a rate gyroscope. The ability to estimate the attitude using only a rate gyroscope reduces the need for additional sensing hardware such as sun sensors and horizon sensors. These savings allow for more mass, volume, and power resources to be devoted to scientific payloads, communications, and other operations, which in the context of Earth orbiting microsatellites and nanosatellites, is highly desirable.
Control Bandwidth Recovery of Flexible Pointing Systems

David Evan Zlotnik^*, James Richard Forbes, and Jack Aldrich

American Control Conference, Boston, MA, USA, July 6-8, 2016

Abs

Instrument pointing control systems mounted on spacecraft are inherently bandwidth-limited (due to lightlydamped flexible modes of the spacecraft) compared to the same system mounted to a rigid body (such as the ground). This work is concerned with the recovery of control bandwidth for spacebased pointing systems via the application of µ-tip control, a passivity-based control methodology. First, the equations of motion of a pointing system are derived. Then, using a “massive payload assumption” a passive input-output map is established between a modified output, called the µ-tip rate, and a modified control input. Bandwidth recovery is confirmed by investigating the frequency response of the linearized system. Simulation results that demonstrate the performance of the developed control algorithm are presented.
Robust Controller Design using the Large Gain Theorem: The Full-State Feedback Case

Ryan James Caverly^* and James Richard Forbes

American Control Conference, Boston, MA, USA, July 6-8, 2016

Awarded “Best Paper" in session

Abs

This paper presents full-state feedback controller synthesis methods that are robust to inverse additive uncertainty via the Large Gain Theorem. In particular, the controller synthesis methods can account for unstable uncertainties. Controllers are designed to either maximize robustness or maximize performance while satisfying a linear matrix inequality (LMI) that enforces a sufficient condition on the minimum gain of the closed-loop system. The Large Gain Theorem is used to prove the robust input-output stability of the system subject to inverse additive uncertainty. A numerical example is provided to illustrate the proposed controller design methods.
Flexible Kiteplane Modeling and Control with an Unsteady Aerodynamic Model

Ryan James Caverly^* and James Richard Forbes

American Control Conference, Boston, MA, USA, July 6-8, 2016

Abs

This paper considers dynamic modeling and control of a flexible kiteplane used for wind-energy harvesting. Each component of the kiteplane is modeled separately and is then constrained to the other components using the nullspace method. The flexible wings are modeled as thin plates with bending and torsional stiffness. An unsteady aerodynamic model is included to increase the fidelity of the simulation under transient conditions. A proportional-integral-derivative (PID) attitude control law is implemented that uses the direction cosine matrix (DCM) directly and proportional-integral (PI) control is used to track a desired tether reel-in rate. Numerical simulation of the closed-loop system demonstrate the kiteplane’s ability to harvest wind energy.
MarsCAT: Mars Array of ionospheric Research Satellites using the CubeSat Ambipolar Thruster

Edgar Bering^*, L. S. Pinsky, Liming Li, and 11 more authors

AIAA Science and Technology Forum and Exposition 2016, San Diego, CA, USA, January 4–8, 2016

Abs

(No abstract)
Norm-constrained Unscented Kalman Filter with Application to High Area-to-Mass Ratio Space-Debris Tracking

Stephen Alexander Chee^* and James Richard Forbes

AIAA Science and Technology Forum and Exposition 2016, San Diego, CA, USA, January 4–8, 2016

Abs

In this paper a norm-constrained unscented Kalman filter that enforces a state normconstraint is presented. This filter is an extension of the norm-constrained Kalman filter presented by Zanetti et al. The proposed norm-constrained Kalman Filter is used to estimate the pose of a High Area-to-Mass Ratio (HAMR) space-debris object. In much of the literature, the pose and other properties of space-debris objects are estimated assuming that the debris object being observed is a cuboid or some other convex multifaceted object. However, the literature also makes the case that a portion of the HAMR objects found near the Geosynchronous orbit (GEO) belt are fragments of multi-layered insulation (MLI) blankets that have separated from their parent satellites. These objects are slender and are appropriately modeled as thin plates. In this paper, simulated estimation results are presented demonstrating that the tumbling motion of these plate-like objects cannot be reasonably captured by light curve observations from a single observation site. However, by combining together measurements from multiple observation sites, estimation of these tumbling motions is possible. This observation further motivates the development of projects like DARPA’s OrbitOutlook program to add more diverse locations for sensors and implement a central database to collect this data.

2015

Trajectory Tracking of a Pendulum-Driven Spherical Robot

Francois Robert Hogan^* and James Richard Forbes

ASME 2015 Dynamic Systems and Control Conference, Columbus, OH, USA, October 28-30, 2015

Abs

In this paper, a controller is designed to achieve tracking of a pendulum-driven spherical robot about a desired trajectory in the presence of model uncertainty and external disturbances. A methodology is proposed to design a feedforward controller for the spherical robot by approximating the desired trajectory using circles as basis functions. A linear state-feedback controller is used to drive the perturbations from the desired trajectory to zero. Numerical simulations show that the controller realizes tracking of the desired trajectory with perturbed initial conditions.
Dynamic Modeling of a Flexible Rolling Sphere

Francois Robert Hogan^*, James Richard Forbes, and Alex Walsh

Proc. 11^th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Boston, MA, USA, August 2-5, 2015

Abs

The motion equations of a rolling flexible spherical shell are derived using a Lagrangian formulation. The motion equations developed capture the nonholonomic nature of the flexible sphere rolling without slip on a flat surface. The free vibrations of the spherical shell are modeled using the Rayleigh-Ritz discretization method. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the spherical shell on its trajectory.
A Nonlinear Attitude Estimator with Desirable Convergence Properties

David Evan Zlotnik^* and James Richard Forbes

European Control Conference, Linz, Austria, July 15-17, 2015

Abs

A nonlinear attitude estimator is considered in this paper. The estimator shares several properties with estimators previously considered including ease of implementation and guaranteed asymptotic stability. The proposed algorithm is based on Poisson’s equation and propagates the attitude estimate using measurements taken by typical low-cost sensing systems. Rate gyro bias estimation is also considered. The estimator structure is derived using an alternate attitude error function, which results in desirable convergence properties. These properties are demonstrated in simulation where the proposed attitude estimator is shown to achieve a faster convergence rate than an attitude estimator considered in the literature.
Strictly Positive Real and Conic System Syntheses Using Observers

Leila Jasmine Bridgeman^*, Mohamed Najih, and James Richard Forbes

American Control Conference, Chicago, IL, USA, July 1-3, 2015

Abs

This paper studies how linear time-invariant systems may be transformed into strictly positive real or interior conic systems using observers. The transformation into a strictly positive real system is achieved for a broader class of systems than in previous work, including those that are uncontrollable or unobservable. The transformation into an interior conic system using an observer is a novel contribution. Both methods are illustrated in a numerical example.
Control of a Planar Wind Energy Harvesting Kite with Flexible Cables

Alex Walsh^* and James Richard Forbes

American Control Conference, Chicago, IL, USA, July 1-3, 2015

Special session on Dynamics and Control of Airborne Wind Energy Systems

Abs

This paper considers modeling and control of a planar kite system with flexible cables used to harvest energy from high-altitude winds. The kite is tethered to flexible cables at its leading and trailing edges. The flexible cables are reeled in and out by ground-based winches. The change in winch inertia and cable stiffness as the cable is reeled in and out is also explicitly modeled. The equations of motion of the flexible kite system are derived using Lagrange’s equation. A specific form of PD control is used control the system as it harvests energy from the wind.
Maintaining Positive Cable Tensions During Operation of a Single Degree of Freedom Flexible Cable-Driven Parallel Manipulator

Ryan James Caverly^* and James Richard Forbes

American Control Conference, Chicago, IL, USA, July 1-3, 2015

Awarded “Best Paper" in session

Abs

This paper investigates the control of a single degree of freedom flexible cable-driven parallel manipulator (CDPM) with a focus on maintaining positive cable tensions. A control architecture that uses a particular saturation prevention function is used to force the control torques to remain within limits that maintain positive cable tensions. The maximum and minimum allowable control torque limits are calculated by solving a linear programming problem on an element-wise inequality involving the equations of motion of the system. It is shown that the controller is input strictly passive and the closedloop system is input-output stable. Numerical simulation results compare the performance of the proposed controller to that of an existing controller from the literature.
Conic-Sector-Based Control in the Presence of Delay

Leila Jasmine Bridgeman^* and James Richard Forbes

12th IFAC Workshop on Time Delay Systems (TDS 2015), Ann Arbor, MI, USA, June 28-30, 2015

Abs

Linear matrix inequality conditions implying interior conic bounds are developed for stable linear time-invariant systems with unknown input delay. Combined with the Conic Sector Theorem, these bounds enable the design of controllers ensuring closed-loop input-output stability that is robust with respect to input delay uncertainty. These contributions are used in a numerical example to design a nearly-optimal controller, which, for moderate delays, achieves improved performance relative to an H_2-optimal controller designed for the nominally undelayed system. Moreover, the nearly-optimal controller has guaranteed input-output-stability for all delays, while in simulation the H_2-optimal controller is observed to destabilize the closed-loop when adequately large delays are present.

2014

Design of Biaxial Navigation-grade MEMS Accelerometers

Xiaowei Shan^*, Ting Zou, James Richard Forbes, and 1 more author

ASME 2014 International Mechanical Engineering Congress & Exposition, Montreal, QC, November 14-20, 2014

Abs

The focus of this paper is the design of a biaxial MEMS accelerometer for navigation applications. First, a survey is conducted to outline the commercial landscape of navigation-grade and MEMS accelerometers. The survey shows a potential market for navigation-grade accelerometers at the MEMS scale. Based on the specifications for navigation applications, the design targets are derived for the proposed biaxial MEMS accelerometers, including the common concerns of natural frequency ratios and bandwidth, as well as the important parameters for MEMS devices, such as hinge width, proof-mass size and mobility range. In light of the design targets, the ideal frequency matrix of the biaxial accelerometer system is derived based on the concept of generalized spring, in connection with the design targets. The stiffness values required are estimated herein. For further structural optimization, the parametric entries of the frequency-ratio matrix act as the objectives to be maximized for the lowest offaxis sensitivity of the proposed accelerometer. A suitable architecture for MEMS biaxial accelerometers is proposed thereafter. Address all correspondence to this author. This architecture not only provides high compliance and structural isotropy for the in-plane translation, but also allows for direct measurement of the proof-mass motion. The proposed architecture is then optimized for the highest frequency ratio between the non-sensitive and sensitive axes, with regard to the design parameters and constraints. The optimization results of the proposed accelerometer demonstrate navigation-grade mechanical performance.
Rotation-Matrix-Based Attitude Control Without Angular Velocity Measurements

David Evan Zlotnik^* and James Richard Forbes

American Control Conference, Portland, OR, USA, June 4-6, 2014

Abs

Rigid-body attitude control without angular velocity measurements is considered. The error rotation matrix describing the attitude error is used directly within the control algorithm. A controller composed of a proportional control term and an angular velocity control term is first considered. The proportional control term is a function of the error rotation matrix, while the angular velocity control term is realized by a strictly positive real system. Asymptotic stability of a desired closed-loop equilibrium point is shown, and a derivative free implementation of the controller is identified for use when angular velocity measurements are not available. Numerical simulation results demonstrate successful set-point regulation and noise mitigation.
Spacecraft Constrained Attitude Control using Positively Invariant Constraint Admissible Sets on SO(3) \times \mathbbR^3

Avishai Weiss^*, Frederick Leve, Morgan Baldwin, and 2 more authors

American Control Conference, Portland, OR, USA, June 4-6, 2014

Abs

This paper presents a constrained attitude control approach for performing spacecraft reorientation maneuvers that maintain specified body vectors within inclusion zones and out of exclusion zones, while respecting control authority limits. The controller uses a supervisory switching strategy with an inner-loop Lyapunov SO(3)-based controller and an outer-loop set-point guidance. A virtual net of orientation equilibria covering SO(3) is introduced, and positively invariant constraint admissible sets on SO(3) x R^3 of the inner loop controller are constructed to determine if equilibria are connected by a feasible trajectory. Optimization procedures to maximize the size of the positively-invariant sets are discussed. Graph search is used in the outer-loop to compute the set-point sequence leading from an initial orientation to a final orientation that rigorously enforces constraints. The proposed methodology reduces the search space of possible attitude maneuver solutions, and has computational and implementation simplicity. Numerical simulation results are reported to illustrate the performance of the proposed constrained attitude control methodology.
The Minimum Gain Lemma

Leila Jasmine Bridgeman^* and James Richard Forbes

American Control Conference, Portland, OR, USA, June 4-6, 2014

Abs

The question of how to establish closed-loop stability for systems involving unstable plants remains a difficult problem in control engineering. Although the notion of minimum gain and the corresponding Large Gain Theorem are designed specifically to tackle this issue, they are not yet widely used. This paper aims to facilitate the practical application of minimum gain and the Large Gain Theorem. An altered definition of minimum gain broadens the applicability of the Large Gain Theorem and the novel Minimum Gain Lemma provides linear matrix inequality conditions that imply and are often equivalent to a minimum gain for unstable linear time invariant systems. Both results play crucial roles in establishing a stability result that is robust with respect to reasonable changes in parameters for a numerical example involving an unstable plant.
Conic-Sector-Based Synthesis: Theory and Experiments

Leila Jasmine Bridgeman^*, Ryan James Caverly, and James Richard Forbes

American Control Conference, Portland, OR, USA, June 4-6, 2014

Awarded “Best Paper" in session

Abs

The Passivity Theorem is a popular input-output stability analysis tool. However, passivity violations, which are often due to sensor and actuator dynamics, may cause instabilities, necessitating the adoption of alternative stability results. This paper presents experimental results employing controllers that ensure stability via the Conic Sector Theorem. A new conic sector controller synthesis method mimicking an H_2-optimal controller is presented and compared to an existing conic sector controller synthesis method, and an H_2 controller itself. The conic controllers are found to yield increased robustness and improved performance in the presence of passivity violations.

2013

Passivity-Based Adaptive Attitude Control with Gravity-Gradient Torque Compensation

Julian Pierre Stellini, James Richard Forbes^*, and Christopher John Damaren

AIAA Guidance, Navigation, and Control Conference, Boston, MA, USA, August 19-22, 2013

Abs

Passivity-based adaptive attitude control in the presence of a gravity-gradient disturbance torque is considered. Traditional passivity-based adaptive attitude control adaptively estimates the spacecraft inertia matrix. To guarantee closed-loop stability via the passivity theorem, the system inputs (the disturbances) must be L2 functions. Unfortunately, the gravity-gradient disturbance torque is not an L2 disturbance. To this end, we propose a modification to the traditional passivitybased adaptive attitude control architecture where the gravity-gradient disturbance torque is incorporated into the control and adaptation laws directly. This is possible because the gravity-gradient torque is a linear function of the spacecraft inertia matrix. We show that our modified passivity-based adaptive attitude control method is guaranteed to stabilize the closed-loop system via the passivity theorem. A numerical example is included.
Conic-Sector-Based Control to Circumvent Passivity Violations

Leila Jasmine Bridgeman^* and James Richard Forbes

American Control Conference, Washington, DC, USA, June 17-19, 2013

Abs

This paper explores the use of the Conic Sector Theorem for both stability analysis and controller design. Ensuring input-output stability of plants experiencing passivity violations is the motivation behind this work. Given a previously designed controller and plant that has experienced a (partially unknown) passivity violation, a novel sector bound selection procedure is presented. This procedure can be used to assess input-output stability of the violated plant and original controller via the Conic Sector Theorem. Should input-output stability not be ensured, two original controller synthesis methods are suggested: one is designed to mimic the H_2 controller, and the other is inspired by strictly positive real controller synthesis. Both methods guarantee input-output stability by selecting controllers within appropriate conic sectors, and involve only the evaluation of readily solvable linear matrix inequalities and algebraic Riccati inequalities. A numerical simulation is provided as a proof of concept.
Dynamic Modelling, Estimation, and Control for Precision Pointing of an Atmospheric Balloon Platform

David Evan Zlotnik^* and James Richard Forbes

2013 CCToMM M3 Symposium, Montreal, QC, May 30-31, 2013

Abs

In this paper we consider the dynamic modelling, estimation and control of an atmospheric balloon platform. The platform is modelled as a rigid body constrained to move with a three dimensional pendulum. We investigate the dynamics of the system and derive the equations of motion from first principles. A nonlinear estimator that evolves on the special orthogonal group, denoted SO(3), is implemented and used in conjunction with a proportional derivative (PD) compensator to control the yaw angle of the platform. In addition, a continuous-time Gaussian process disturbance model is used to simulate the effects of disturbances on the platform. A simulation is conducted, and the results demonstrate successful estimation and yaw control.
Saturated Proportional Derivative Control of a Single-Link Flexible-Joint Manipulator

Ryan James Caverly^*, David Evan Zlotnik, and James Richard Forbes

2013 CCToMM M3 Symposium, Montreal, QC, May 30-31, 2013

Abs

This paper considers the control of a single-link flexible-joint robot manipulator subject to actuator saturation. Alternative controllers are proposed and compared to one found in literature. In particular, a controller with proportional and derivative components is guaranteed to provide a total torque less than a chosen value, thereby disallowing actuator saturation. It is shown that an equilibrium point of the closed-loop system is asymptotically stable. Additionally, it is shown that the controllers are robust to modelling errors. Finally, this paper presents simulation results demonstrating the performance of the proposed control architecture.
Sequential Pose Estimation Using Linearized Rotation Matrices for Consumer Devices

Timothy Drews^*, Paul Kry, James Richard Forbes, and 1 more author

Conference on Computer and Robot Vision (CRV 2013), Regina, SK, May 28-31, 2013

Timothy Drews awarded “Best Student Paper” award

Abs

We present a new formulation for pose estimation using an extended Kalman filter that takes advantage of the Lie group structure of rotations. Using the exponential map along with linearized rotations for updates and errors permits a graceful filter formulation that avoids the awkward representation of Euler angles and the required norm constraint for quaternions. We demonstrate this approach with an implementation that uses sensors commonly found in consumer tablets and mobile phones: a camera and gyroscope, which we use to estimate attitude, position, and gyroscope bias. We use gyroscope measurements for prediction, and vision-based measurements for correction. We show results and discuss the performance of our pose estimation method using ground truth data obtained via a motion capture system.

2012

Nonlinear Optimal Control of a Holonomic Airship

Yin Yang, Inna Sharf, and James Richard Forbes^*

AIAA Guidance, Navigation, and Control Conference, Minneapolis, MN, USA, August 13-16, 2012

Awarded “Best Presentation” in Control in Aerospace Robotics 1 session

Abs

A full-state feedback controller is proposed to meet the requirements of an indoor holonomic airship. The airship is a custom-designed spherical blimp actuated by six propellers arranged symmetrically, enabling independent translational and rotational motion. A continuous trajectory-tracking controller is developed to follow arbitrary reference trajectories using a finite-horizon continuous linear quadratic regulator (CLQR). The controller is implemented and tested on the airship while tracking a rectangular trajectory in a laboratory environment. With minimal computational cost, the CLQR controller achieves significant improvements in overshoot and attitude tracking error compared to a standard proportional-derivative controller. To provide state estimates for feedback control, an unscented Kalman filter fuses measurements from a Vicon motion-capture system and an onboard inertial measurement unit. The filter is integrated with the CLQR controller to form a dynamic output-feedback control system, which is evaluated on the same rectangular trajectory. The use of sensor fusion and state estimation results in a significant reduction in actuator effort.

2011

Synthesis of Optimal Finite Frequency Controllers for Flexible Robotic Manipulator Control

James Richard Forbes^* and Christopher John Damaren

AIAA Guidance, Navigation, and Control Conference, Portland, OR, USA, August 8-11, 2011

Awarded “Best Presentation” in Optimal Control session

Abs

This paper presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system strictly positive real (SPR) in an H optimal fashion. The parallel feedforward controller is designed in such a manner that when the output of the system is added to the output of the parallel feedforward controller, the transfer matrix from the system input to the new output is SPR. In order to ensure that the difference between the new output and the original system output is small, the maximum singular value of a static parallel feedforward controller or the weighted H norm of a dynamic parallel feedforward controller is minimized. The proposed synthesis methods are convex optimization problems that make use of linear matrix inequality and equality constraints. The controllers are implemented numerically on a flexible-joint robotic manipulator and compared to a parallel feedforward controller from the literature. It is shown in closedloop simulation that a significant improvement in tracking error is achieved with one of the proposed dynamic parallel feedforward controller synthesis methods.
Investigation of Active Vibration Suppression of a Flexible Satellite Using Magnetic Attitude Control

Everett J. Findlay^*, James Richard Forbes, Hugh H. T. Liu, and 3 more authors

AIAA Guidance, Navigation, and Control Conference, Portland, OR, USA, August 8-11, 2011

Abs

The problem of attitude control of a flexible, momentum-biased satellite, using three magnetic torque rods and a single reaction wheel, is investigated. Four controllers are compared under various initial conditions. An LQR approach is used to design both time- invariant and periodic controllers where either the satellite is assumed to be rigid, or the unmeasurable flexible states are actively controlled using an observer to estimate the states. The controllers are compared via simulation. The periodic controllers show no increase in performance over their time-invariant counterparts while the controllers which actively controlled the flexible states perform better than their rigid counterparts.

2010

Extended Kalman Filter and Sigma Point Filter Approaches to Adaptive Filtering

James Richard Forbes^*

AIAA Guidance, Navigation, and Control Conference, Toronto, ON, August 2-5, 2010

AIAA GNC 2010 Graduate Student Paper Competition Finalist

Abs
Linear Time-Varying Passivity-Based Attitude Control Employing Magnetic and Mechanical Actuation

James Richard Forbes^* and Christopher John Damaren

AIAA Guidance, Navigation, and Control Conference, Toronto, ON, August 2-5, 2010

Abs
Passive Linear Time-Varying Systems: State-Space Realizations, Stability in Feedback, and Controller Synthesis

James Richard Forbes^* and Christopher John Damaren

American Control Conference, Baltimore, MD, USA, June 30 - July 2, 2010

Abs

In this paper we consider linear time-varying passive systems. We state various theorems, which rely on the state-space matrices of the system, that identify when a linear-time varying system is purely passive, input strictly passive, output strictly passive, or input-state strictly passive which is a nonstandard notion of passivity defined in this paper. Two of our theorems resemble the Kalman-YakubovichPopov Lemma, one applicable to time-varying systems with a feedthrough matrix and the other for linear time-varying systems without one. The negative feedback interconnection of various systems is considered. We show that an output strictly passive system negatively interconnected with an input-state strictly passive system is globally asymptotically stable. We also show that both linear time-varying input-state and output strictly passive systems when connected in negative feedback with a sector bounded, memoryless nonlinearity are also globally asymptotically stable. The optimal design of a time-varying output strictly passive controller is also considered. We present an example: the position and velocity control of a time-varying mass controlled via a dynamic time-varying compensator and a sector bounded, memoryless nonlinearity.

2009

Robust Control of a Vibrating Beam Using the Hybrid Passivity and Finite Gain Stability Theorem

James Richard Forbes^* and Christopher John Damaren

AIAA Guidance, Navigation, and Control Conference, Chicago, IL, USA, August 10-13, AIAA-2009-5787, 2009

Abs

Our motivation is robust control of systems which are nominally passive, but experience a passivity violation. In particular, we consider the robust control of a two dimensional flexible beam equipped with a double-gimbaled control moment gyro used for actuation. First we present definitions related to the hybrid passivity and finite gain stability theorem. Calculation of the passivity and finite gain parameters (in a LTI, MIMO context) used to ensure the stability of two hybrid systems within a negative feedback loop is presented. After developing the plant dynamics it is shown that the plant in nominally passive, but including the gimbal motor dynamics induces a passivity violation. Using a numerical optimization strategy and guided by the hybrid passivity and finite gain stability theorem, controllers which are guaranteed to robustly stabilize the closed-loop are optimally found. The controller parameterization, optimization objective function, and optimization constraints are discussed.

2008

Design of Gain-Scheduled SPR Controllers Using Numerical Optimization

James Richard Forbes^* and Christopher John Damaren

AIAA Guidance, Navigation, and Control Conference, Honolulu, HI, USA, August 18-21, AIAA-2008-7312, 2008

Abs

The design of gain-scheduled strictly positive real (SPR) controllers using numerical optimization is considered. The thrust of this investigation is robust, yet accurate motion control of flexible robotic systems via the passivity theorem. Two optimization problems are posed; we first present a simple method to optimize the N linear SPR controllers which make up the gain-scheduled controller. Second, we formulate the optimization problem associated with the gain-scheduled controller itself. Using passivity concepts, it is proven that a family of very strictly passive compensators scheduled via time- or statedependent scheduling signals is also very strictly passive. Restricting our investigation to time-dependent scheduling signals, the signals are parameterized, and the optimization objective function seeks to find the form of the scheduling signals which minimizes a combination of the manipulator tip tracking error and the control effort. A numerical example employing a two-link flexible manipulator is used to demonstrate the effectiveness of the optimal gain-scheduling algorithm.