newton.utils.transform_twist

newton.utils.transform_twist(t, x)

Transform a spatial twist between coordinate frames.

This routine applies the rigid-body twist transformation defined in Frank & Park, Modern Robotics (Definition 3.20, p. 100).

Given a spatial twist x = (v, ω) expressed in the source frame and a homogeneous transform t (source → destination), the returned twist x' = (v', ω') represents the same motion expressed in the destination frame:

\[\begin{split}x' = \begin{bmatrix} R & [p]_{\times} R \\ 0 & R \end{bmatrix} x\end{split}\]

where R and p are the rotation and translation components of t and [p]_x is the skew-symmetric matrix of p.

Parameters:

• t (transform) – The transform from the source frame to the destination frame.

• x (spatial_vector) – The spatial twist expressed in the source frame.

Returns:

The twist expressed in the destination frame.

Return type:

spatial_vector