Calculating a near time-optimal jerk-constrained trajectory along a specified smooth path

This article presents a near time-optimal and jerk-constrained trajectory planner. The presented work is an extension to the "proximate time-optimal algorithm" (Pardo-Castellote and Cannon, IEEE Int Conf Robot Autom 2:1539-1546, 1996), which is used to determine smooth and near time-optimal path-constrained trajectories, to problems where not only the velocity and the acceleration but also the jerk are explicitly constrained. It is shown that the constraint on the jerk translates into limits for the curvature of the phase-space velocity. As high-speed motion systems become more and more accurate, the trend goes clearly towards jerk-constrained trajectory calculation to avoid large deviations from the planned trajectory during the complete move. The proposed algorithm is nonperturbative and its calculation time is linear with respect to the length of the path.