Lie Groups

SO(2)

class inekf.SO2(*args, **kwargs)

Bases: inekf.lie_groups.LieGroup

2D rotational states, also known as the 2x2 special orthogonal group, SO(2).

See the C++ counterpart (InEKF::SO2) for documentation on constructing an object. Further, we have overloaded the [] operator to function as a python template. Example of this can be seen in Getting Started. Templates include:

Templates:

A Number of augmented Euclidean states. Can be -1 or “D” for dynamic. Defaults to 0.

SE(2)

class inekf.SE2(*args, **kwargs)

Bases: inekf.lie_groups.LieGroup

2D rigid body transformation, also known as the 3x3 special Euclidean group, SE(2).

See the C++ counterpart (InEKF::SE2) for documentation on constructing an object. Further, we have overloaded the [] operator to function as a python template. Example of this can be seen in Getting Started. Templates include:

Templates:

C Number of Euclideans columns to include. Can be -1 or “D” for dynamic. Defaults to 1.
A Number of augmented Euclidean states. Can be -1 or “D” for dynamic. Defaults to 0.

Methods:

`__getitem__`(idx)	Gets the ith positional column of the group.
`addCol`(x, sigma)	Adds a column to the matrix state.

__getitem__(idx)

Gets the ith positional column of the group.

Parameters: idx (float) – Index of column to get, from 0 to C-1.
Returns: np.ndarray

addCol(x, sigma)

Adds a column to the matrix state. Only usable if C = Eigen::Dynamic.

Parameters

x (np.ndarray) – Column to add in.
sigma (np.ndarray) – Covariance of element. Only used if state is uncertain.

SO(3)

class inekf.SO3(*args, **kwargs)

Bases: inekf.lie_groups.LieGroup

3D rotational states, also known as the 3x3 special orthogonal group, SO(3).

See the C++ counterpart (InEKF::SO3) for documentation on constructing an object. Further, we have overloaded the [] operator to function as a python template. Example of this can be seen in Getting Started. Templates include:

Templates:

A Number of augmented Euclidean states. Can be -1 or “D” for dynamic. Defaults to 0.

SE(3)

class inekf.SE3(*args, **kwargs)

Bases: inekf.lie_groups.LieGroup

3D rigid body transformation, also known as the 4x4 special Euclidean group, SE(3).

See the C++ counterpart (InEKF::SE3) for documentation on constructing an object. Further, we have overloaded the [] operator to function as a python template. Example of this can be seen in Getting Started. Templates include:

Templates:

C Number of Euclideans columns to include. Can be -1 or “D” for dynamic. Defaults to 1.
A Number of augmented Euclidean states. Can be -1 or “D” for dynamic. Defaults to 0.

Methods:

`__getitem__`(idx)	Gets the ith positional column of the group.
`addCol`(x, sigma)	Adds a column to the matrix state.

__getitem__(idx)

Gets the ith positional column of the group.

Parameters: idx (float) – Index of column to get, from 0 to C-1.
Returns: np.ndarray

addCol(x, sigma)

Adds a column to the matrix state. Only usable if C = Eigen::Dynamic.

Parameters

x (np.ndarray) – Column to add in.
sigma (np.ndarray) – Covariance of element. Only used if state is uncertain.

Lie Group Base

class inekf.LieGroup

Attributes:

`Ad`	Get adjoint of group element.
`R`	Gets rotational component of the state.
`aug`	Get additional Euclidean state of object.
`cov`	Get covariance of group element.
`inverse`	Invert group element.
`log`	Move this element from group -> algebra -> R^n
`mat`	Get actual group element.
`uncertain`	Returns whether object is uncertain, ie if it has a covariance.

Methods:

`Ad_`(g)	Compute the linear map Adjoint
`__invert__`()	Invert group element.
`__matmul__`(rhs)	Combine transformations.
`addAug`(a, sigma)	Adds an element to the augmented Euclidean state.
`exp`(xi)	Move an element from R^n -> algebra -> group
`log_`(g)	Move an element from group -> algebra -> R^n
`wedge`(xi)	Move element in R^n to the Lie algebra.

property Ad

Get adjoint of group element.

Returns: np.ndarray

static Ad_(g)

Compute the linear map Adjoint

Parameters: g (inekf.LieGroup) – Element of group
Returns: np.ndarray

property R

Gets rotational component of the state.

Returns: inekf.SO2

__invert__()

Invert group element. Drops augmented state and covariance.

Returns: inekf.LieGroup

__matmul__(rhs)

Combine transformations. Augmented states are summed.

Parameters: rhs (inekf.LieGroup) – Right hand element of multiplication.
Returns: inekf.LieGroup

addAug(a, sigma)

Adds an element to the augmented Euclidean state. Only usable if A = Eigen::Dynamic.

Parameters

x (float) – Variable to add.
sigma (float) – Covariance of element. Only used if state is uncertain.

property aug

Get additional Euclidean state of object.

Returns: np.ndarray

property cov

Get covariance of group element.

Returns: np.ndarray

static exp(xi)

Move an element from R^n -> algebra -> group

Parameters: xi (np.ndarray) – Tangent vector
Returns: inekf.LieGroup

property inverse

Invert group element. Augmented portion and covariance is dropped.

Returns: inekf.LieGroup

property log

Move this element from group -> algebra -> R^n

Returns: np.ndarray

static log_(g)

Move an element from group -> algebra -> R^n

Parameters: g (inekf.LieGroup) – Group element
Returns: np.ndarray

property mat

Get actual group element.

Returns: np.ndarray

property uncertain

Returns whether object is uncertain, ie if it has a covariance.

Returns: bool

static wedge(xi)

Move element in R^n to the Lie algebra.

Parameters: xi (np.ndarray) – Tangent vector
Returns: np.ndarray