This is a partial port to Python/CasADi, with some modifications and additions, of the Spatial Math Toolbox for MATLAB. More...

Classes
class	Quaternion
	Quaternion class. More...

Functions
Callable	arrayify_args (Callable fun)
	Decorator that ensures all input arguments are casadi arrays (i.e. More...

cs.DM	I3 ()
	3-by-3 identity matrix. More...

cs.DM	I4 ()
	4-by-4 identity matrix. More...

CasADiArrayType	angvec2r (ArrayType theta, ArrayType v)
	Convert angle and vector orientation to a rotation matrix. More...

CasADiArrayType	r2t (ArrayType R)
	Convert rotation matrix to a homogeneous transform. More...

CasADiArrayType	rotx (ArrayType theta)
	SO(3) rotation about X axis. More...

CasADiArrayType	roty (ArrayType theta)
	SO(3) rotation about Y axis. More...

CasADiArrayType	rotz (ArrayType theta)
	SO(3) rotation about Z axis. More...

CasADiArrayType	rpy2r (ArrayType rpy, str opt="zyx")
	Roll-pitch-yaw angles to SO(3) rotation matrix. More...

CasADiArrayType	rt2tr (ArrayType R, ArrayType t)
	Convert rotation and translation to homogeneous transform. More...

CasADiArrayType	skew (ArrayType v)
	Create skew-symmetric matrix. More...

CasADiArrayType	t2r (ArrayType T)
	Rotational submatrix. More...

CasADiArrayType	invt (ArrayType T)
	Inverse of a homogeneous transformation matrix. More...

CasADiArrayType	transl (ArrayType T)
	SE(3) translational homogeneous transform. More...

CasADiArrayType	unit (ArrayType v)
	Unitize a vector. More...

Variables
	ArrayType = Union[cs.DM, cs.SX, List[float], Tuple[float], cs.np.ndarray, float, int]
	Accepted array types. More...

	CasADiArrayType = Union[cs.DM, cs.SX]
	CasADi array types typically returned by OpTaS methods. More...

	pi = cs.np.pi
	The number pi (i.e. More...

	eps = cs.np.finfo(float).eps
	The machine epsilon. More...

Detailed Description

This is a partial port to Python/CasADi, with some modifications and additions, of the Spatial Math Toolbox for MATLAB.

See the following. https://github.com/petercorke/spatialmath-matlab

Function Documentation

◆ angvec2r()

CasADiArrayType optas.spatialmath.angvec2r	(	ArrayType	theta,
		ArrayType	v
	)

Convert angle and vector orientation to a rotation matrix.

This method uses Rodrigue's formula.

Parameters

theta	Angle of rotation (radians).
v	Direction vector to rotate about.

Returns: Rotation matrix.

◆ arrayify_args()

Callable optas.spatialmath.arrayify_args ( Callable fun )

Decorator that ensures all input arguments are casadi arrays (i.e.

either DM or SX).

Parameters

fun	Callable function

Returns: Wrapper that ensures the input to the given function are casadi arrays.

◆ I3()

cs.DM optas.spatialmath.I3 ( )

3-by-3 identity matrix.

Returns: Identity matrix of order 3.

◆ I4()

cs.DM optas.spatialmath.I4 ( )

4-by-4 identity matrix.

Returns: Identity matrix of order 4.

◆ invt()

CasADiArrayType optas.spatialmath.invt ( ArrayType T )

Inverse of a homogeneous transformation matrix.

Parameters

T	Homogeneous transformation matrix.

Returns: Homogeneous transformation matrix such that Tinv @ T = I where I is the identity.

◆ r2t()

CasADiArrayType optas.spatialmath.r2t ( ArrayType R )

Convert rotation matrix to a homogeneous transform.

Parameters

R	A 3-by-3 rotation matrix.

Returns: Homogenous transformation with given rotation and zero translation.

◆ rotx()

CasADiArrayType optas.spatialmath.rotx ( ArrayType theta )

SO(3) rotation about X axis.

Parameters

theta Angle of rotation (radians).

Returns: A 3-by-3 rotation matrix.

◆ roty()

CasADiArrayType optas.spatialmath.roty ( ArrayType theta )

SO(3) rotation about Y axis.

Parameters

theta Angle of rotation (radians).

Returns: A 3-by-3 rotation matrix.

◆ rotz()

CasADiArrayType optas.spatialmath.rotz ( ArrayType theta )

SO(3) rotation about Z axis.

Parameters

theta Angle of rotation (radians).

Returns: A 3-by-3 rotation matrix.

◆ rpy2r()

CasADiArrayType optas.spatialmath.rpy2r	(	ArrayType	rpy,
		str	opt = `"zyx"`
	)

Roll-pitch-yaw angles to SO(3) rotation matrix.

Parameters

rpy	Roll-Pitch-Yaw angles in radians.
opt	Order option. Acceptable inputs: 'xyz' Rotations about X, Y, Z axes (for a robot gripper) 'zyx' Rotations about Z, Y, X axes (for a mobile robot, default) 'yxz' Rotations about Y, X, Z axes (for a camera) 'arm' Rotations about X, Y, Z axes (for a robot arm) 'vehicle' Rotations about Z, Y, X axes (for a mobile robot) 'camera' Rotations about Y, X, Z axes (for a camera)

Returns: A 3-by-3 rotation matrix.

◆ rt2tr()

CasADiArrayType optas.spatialmath.rt2tr	(	ArrayType	R,
		ArrayType	t
	)

Convert rotation and translation to homogeneous transform.

Parameters

R	A 3-by-3 rotation matrix.
t	A vector with 3 elements.

Returns: Homogeneous transformation matrix.

◆ skew()

CasADiArrayType optas.spatialmath.skew ( ArrayType v )

Create skew-symmetric matrix.

If V (1x1) then (order 2) S =

  | 0  -v |
  | v   0 |

and if V (1x3) then (order 3) S =

  |  0  -vz   vy |
  | vz    0  -vx |
  |-vy   vx    0 |

Parameters

v	The form of the skew-symmetric matrix, either a scalar or vector with 3 elements.

Returns: Skew-symmetric matrix of order 2 or 3.

◆ t2r()

CasADiArrayType optas.spatialmath.t2r ( ArrayType T )

Rotational submatrix.

Parameters

Homogenous transformation matrix.

Returns: A 3-by-3 rotation matrix.

◆ transl()

CasADiArrayType optas.spatialmath.transl ( ArrayType T )

SE(3) translational homogeneous transform.

Parameters

T	Homogeneous transformation matrix.

Returns: Translation part of the homogeneous transformation.

◆ unit()

CasADiArrayType optas.spatialmath.unit ( ArrayType v )

Unitize a vector.

Parameters

v	A vector of order 3.

Returns: A vector of order 3 with unit magnitude that is parralel to input vector.

Variable Documentation

◆ ArrayType

optas.spatialmath.ArrayType = Union[cs.DM, cs.SX, List[float], Tuple[float], cs.np.ndarray, float, int]

Accepted array types.

◆ CasADiArrayType

optas.spatialmath.CasADiArrayType = Union[cs.DM, cs.SX]

CasADi array types typically returned by OpTaS methods.

◆ eps

optas.spatialmath.eps = cs.np.finfo(float).eps

The machine epsilon.

◆ pi

optas.spatialmath.pi = cs.np.pi

The number pi (i.e.

3.141...).

Classes

Functions

Variables

Detailed Description

Function Documentation

◆ angvec2r()

◆ arrayify_args()

◆ I3()

◆ I4()

◆ invt()

◆ r2t()

◆ rotx()

◆ roty()

◆ rotz()

◆ rpy2r()

◆ rt2tr()

◆ skew()

◆ t2r()

◆ transl()

◆ unit()

Variable Documentation

◆ ArrayType

◆ CasADiArrayType

◆ eps

◆ pi