| A singularity-robust trajectory
generator is presented that, 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 log 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 nonzero. 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.