tr2delta

Convert SE(3) homogeneous transform to differential motion

D = TR2DELTA(T0, T1) is the differential motion (6×1) corresponding to infinitessimal motion (in the T0 frame) from pose T0 to T1 which are homogeneous transformations (4×4) or SE3 objects.

The vector D=(dx, dy, dz, dRx, dRy, dRz) represents infinitessimal translation and rotation, and is an approximation to the instantaneous spatial velocity multiplied by time step.

D = TR2DELTA(T) as above but the motion is from the world frame to the SE3 pose T.

Notes

• D is only an approximation to the motion T, and assumes that T0 ~ T1 or T ~ eye(4,4).
• Can be considered as an approximation to the effect of spatial velocity over a a time interval, average spatial velocity multiplied by time.

Reference

• Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p67.

See also

delta2tr, skew, SE3.todelta

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