navlie.types.State

class navlie.types.State(value: Any, dof: int, stamp: float | None = None, state_id=None)

Bases: ABC

An abstract state \(\mathcal{X}\) is an object containing the following attributes:

• a value of some sort;

• a certain number of degrees of freedom (dof);

• plus and minus methods that generalize addition and subtracting to to this object.

Optionally, it is often useful to assign a timestamp (stamp) and a label (state_id) to differentiate state instances from others.

When implementing a new state type, you should inherit from this class as shown in the tutorial.

Note

The plus and minus must correspond to each other, in the sense that the following must hold:

\[\delta \mathbf{x} = (\mathcal{X} \oplus \delta \mathbf{x}) \ominus \mathcal{X}\]

for any state \(\mathcal{X}\) and any perturbation \(\delta \mathbf{x}\). In practice this can be tested with something along the lines of:

x = State(...) # some state object
dx = np.random.randn(x.dof)
dx_test = x.plus(dx).minus(x)
assert np.allclose(dx, dx_test)

value

State value

Type:

Any

dof

Degree of freedom of the state

Type:

int

stamp

Timestamp

Type:

float

state_id

abstract plus(dx: ndarray) → State

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

abstract minus(x: State) → ndarray

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

abstract copy() → State

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.

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

Calculates the plus jacobian with finite difference.

minus_jacobian(x: State) → 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).

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

Calculates the minus jacobian with finite difference.

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