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, i.e., the time instants when the acceleration of any robot joint changes. When integrating parabolic trajectory generation into a motion planning pipeline, especially the one which involves a shortcutting procedure, the resulting trajectory usually contains a large number of switch points with a dense distribution. This high frequency acceleration switching intensifies joint motor wear as well as hamper 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 comparison with other methods. Note to Practitioners—A large number of industrial robots accept piecewise constant acceleration trajectories as inputs. Currently available procedures for planning such trajectories usually cause trajectories to have many switch points, the time instants when a robot joint changes its acceleration, concentrated in short time intervals. Switch points that are too close to each other might hamper the robot performance, in terms of execution time or tracking accuracy. To address this problem we develop an algorithm which plans piecewise constant acceleration trajectories by taking into account not only joint velocity and acceleration bounds but also 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. Although the constraint might result in longer trajectory durations, it significantly reduces the number of switch points. Comparisons with other methods show that our method produces higher quality trajectories. We also provide an opensource implementation in Python.