navlie.lib.states.MatrixLieGroupState

class navlie.lib.states.MatrixLieGroupState(value: ndarray, group: MatrixLieGroup, stamp: float | None = None, state_id: Any | None = None, direction='right')

Bases: State

The MatrixLieGroupState class. Although this class can technically be used directly, it is recommended to use one of the subclasses instead, such as SE2State or SO3State.

Parameters:

• value (np.ndarray) – Value of of the state. If the value has as many elements as the DOF of the group, then it is assumed to be a vector of exponential coordinates. Otherwise, the value must be a 2D numpy array representing a direct element of the group in matrix form.

• group (MatrixLieGroup) – A pymlg.MatrixLieGroup class, such as pymlg.SE2 or pymlg.SO3.

• stamp (float, optional) – timestamp, by default None

• state_id (Any, optional) – optional state ID, by default None

• direction (str, optional) –

  either “left” or “right”, by default “right”. Defines the perturbation \(\delta \mathbf{x}\) as either

  \[ \begin{align}\begin{aligned}\mathbf{X} = \mathbf{X} \exp(\delta \mathbf{x}^\wedge) ext{ (right)}\\\mathbf{X} = \exp(\delta \mathbf{x}^\wedge) \mathbf{X} ext{ (left)}\end{aligned}\end{align} \]

direction

group

value: ndarray

State value

Type:

Any

plus(dx: ndarray) → MatrixLieGroupState

A generic “addition” operation given a dx numpy array with as many elements as the dof of this state.

minus(x: MatrixLieGroupState) → ndarray

A generic “subtraction” operation given another State object of the same type, always returning a numpy array.

copy() → MatrixLieGroupState

Returns a copy of this State instance.

plus_jacobian(dx: ndarray) → ndarray

Jacobian of the plus operator. That is, using Lie derivative notation,

\[\mathbf{J} = \frac{D (\mathcal{X} \oplus \delta \mathbf{x})}{D \delta \mathbf{x}}\]

For Lie groups, this is known as the group Jacobian.

minus_jacobian(x: MatrixLieGroupState) → ndarray

Jacobian of the minus operator with respect to self.

\[\mathbf{J} = \frac{D (\mathcal{Y} \ominus \mathcal{X})}{D \mathcal{Y}}\]

That is, if dx = y.minus(x) then this is the Jacobian of dx with respect to y. For Lie groups, this is the inverse of the group Jacobian evaluated at dx = x1.minus(x2).

dot(other: MatrixLieGroupState) → MatrixLieGroupState

property attitude: ndarray

property position: ndarray

property velocity: ndarray

jacobian_from_blocks(**kwargs) → ndarray

dof

Degree of freedom of the state

Type:

int

minus_jacobian_fd(x: State, step_size=1e-08) → ndarray

Calculates the minus jacobian with finite difference.

plus_jacobian_fd(dx, step_size=1e-08) → ndarray

Calculates the plus jacobian with finite difference.

stamp

Timestamp

Type:

float

state_id

previous

navlie.lib.states

next

navlie.lib.states.MixtureState