On trajectory design from motion primitives for near time-optimal transitions for systems with oscillating internal dynamics

Abstract: An efficient approach to compute near time-optimal trajectories for linear kinematic systems with oscillatory internal dynamics is presented. Thereby, kinematic constraints with respect to velocity, acceleration and jerk are taken into account. The trajectories are composed of several motion primitives, the most crucial of which is termed jerk segment. Within this contribution, the focus is put on the composition of the overall trajectories, assuming the required motion primitives to be readily available. Since the scheme considered is not time-optimal, even decreasing particular constraints can reduce the overall transition time, which is analysed in detail. This observation implies that replanning of the underlying jerk segments is required as an integral part of the motion planning scheme, further insight into which has been analysed in a complementary contribution. Although the proposed scheme is not time-optimal, it allows for significantly shorter transition times than established methods, such as zero-vibration shaping, while requiring significantly lower computational power than a fully time-optimal scheme.