Spatial vector

class SpatialVector(value)

Bases: BasePoseList

Spatial 6-vector abstract superclass

This class has two abstract subclasses, which each have concrete subclasses. Key characteristics:

• 6D vectors that represent velocity, acceleration, momentum and force of bodies in 3D.

• inherit list-like properties from SMUserList class

• support operators:

Operator	Operation
+	addition of spatial vectors of the same subclass
-	subtraction of spatial vectors of the same subclass
-	unary minus
*	see table below
^	cross product x or x*

Certain subtypes can be multiplied

Multiplicands		Product
left	right	type	operation
SE3, Twist3	SpatialVelocity	SpatialVelocity	adjoint product
SE3, Twist3	SpatialAcceleration	SpatialAcceleration	adjoint product
SE3, Twist3	SpatialMomentum	SpatialMomentum	adjoint transpose product
SE3, Twist3	SpatialForce	SpatialForce	adjoint transpose product
SpatialAcceleration	SpatialInertia	SpatialForce	matrix-vector product**
SpatialVelocity	SpatialInertia	SpatialMomentum	matrix-vector product**

** indicates commutative operator.

References:

• “Robot Dynamics Algorithms”, R. Featherstone, volume 22, Springer International Series in Engineering and Computer Science, Springer, 1987.

• “A beginner’s guide to 6-d vectors (part 1)”, R. Featherstone, IEEE Robotics Automation Magazine, 17(3):83-94, Sep. 2010.

• Online notes Methods:

Seealso:

SpatialM6(), SpatialF6(), SpatialVelocity(), SpatialAcceleration(), SpatialForce(), SpatialMomentum().

__add__(right)

Overloaded * operator (superclass method)

Returns:

sum of spatial vectors

Return type:

SpatialVector subclass instance

Raises:

• TypeError – attempting to add SpatialVectors of different subclass

• ValueErrror – attempting to add SpatialVectors with different numbers of values

v1 + v2 is a spatial vector of the same type as v1 and v2 whose value is the element-wise sum of v1 and v2. If both are arrays of spatial vectors V1 (1xN) and V2 (1xN) the result is an array (1xN).

Seealso:

__sub__()

__init__(value)

Create a new spatial vector (abstract superclass)

Parameters:

value – Value of the

• SpatialVector(vec) is a spatial vector constructed from the 6-element array-like vec

• SpatialVector([V1, V2, ... VN]) is a spatial vector array with N elements, constructed from the 6-element array-like values Vi

• SpatialVector(A) is a spatial vector array with N elements, constructed from the columns of the 6xN array A.

__neg__()

Overloaded unary - operator (superclass method)

Returns:

negative of spatial vector

Return type:

SpatialVector subclass instance

-v is a spatial vector of the same type as v whose value is the element-wise negative of v.

Seealso:

__sub__()

__sub__(right)

Overloaded - operator (superclass method)

Returns:

difference of spatial vectors

Return type:

SpatialVector subclass instance

Raises:

• TypeError – attempting to subtract SpatialVectors of different subclass

• ValueErrror – attempting to subtract SpatialVectors with different numbers of values

v1 - v2 is a spatial vector of the same type as v1 and v2 whose value is the element-wise difference of v1 and v2. If both are arrays of spatial vectors V1 (1xN) and V2 (1xN) the result is an array (1xN).

Seealso:

__add__(), __neg__()

isvalid(x, check)

Test if vector is valid spatial vector

Parameters:

• x (numpy.ndarray) – vector to test

• check (bool) – ignored

Returns:

True if the matrix has shape (6,).

Return type:

bool

property shape

Shape of the object’s interal matrix representation

Returns:

(6,)

Return type:

tuple