Techreport,
Singularity-Robust Trajectory Generation for Robotic Manipulators
TR-98-01. Department of Computer Science, University of British Columbia, (April 1998)
Abstract
A singularity-robust trajectory generator is presented which, given
a prescribed manipulator path and corresponding kinematic solution,
computes a feasible trajectory in the presence of kinematic singularities.
The resulting trajectory is close to minimum time, subject to individual
bounds on joint velocities and accelerations, and follows the path
with precision. The algorithm has complexity O(M łog M), where
M is the number of robot joints, and works using ``coordinate pivoting'',
in which the path timing near singularities is controlled using the
fastest changing joint coordinate. This allows the handling of singular
situations, including linear self-motions (e.g., wrist singularities),
where the speed along the path is zero but some joint velocities
are non-zero. To compute the trajectory, knot points are inserted
along the path, dividing it into intervals, with the knot density
increasing near singularities. An appropriate path velocity is then
computed at each knot point, and the resulting knot-velocity sequence
is integrated to yield the path timing. Examples involving the PUMA
manipulator are shown.
