Time-optimal parabolic interpolation with velocity,acceleration, and minimum-switch-time constraints

Time-optimal trajectories with bounded velocities and accelerations are known to be parabolic, i.e. piecewise constant in acceleration. An important characteristic of this class of trajectories is the distribution of the switch points – the time instants when the acceleration of any robot joint changes. When integrating parabolic trajectory generation into a motion planning pipeline, especially one that involves a shortcutting procedure, resulting trajectories usually contain a large number of switch points with a dense distribution. This high frequency acceleration switching intensifies joint motor wear as well as hampers the robot performance. In this paper, we propose an algorithm for planning parabolic trajectories subject to both physical bounds, i.e. joint velocity and acceleration limits, and the minimum-switch-time constraint. The latter constraint ensures that the time duration between any two consecutive switch points is always greater than a given minimum value. Analytic derivations are given, as well as comparisons with other methods to demonstrate the efficiency of our approach.