Time-optimal multi-point trajectory generation for robotic manipulators with continuous jerk and constant average acceleration

Abstract

To meet the demands of high-speed and high-accuracy applications of robotic manipulators, this paper proposes a time-optimal multi-point trajectory planning method with continuous jerk and constant average acceleration. A piecewise sine jerk model is developed for jerk continuity throughout the entire motion profile. An equivalent transformation of this complex model into the simple trapezoidal velocity model is proposed, effectively reducing the computational complexity and ensuring the reliability of real-time planning. The introduction of a parameter, named the trajectory smoothness coefficient, allows for a convenient trade-off between the priorities of speed and smoothness. The adaptive computation algorithm for peak jerk results in a constant average acceleration along paths of any length, ensuring a consistent level of work efficiency regardless of the density of path control points. Through a comprehensive evaluation of the critical constraints for each potential profile type, the single joint’s time-optimal and multiple joints’ time-synchronized planning problems are solved with closed-form solutions. Furthermore, by designing a multi-joint multi-point velocity look-ahead strategy, time-optimal multi-point trajectory planning for robotic manipulators is realized. Simulation and experimental results on a manipulator demonstrate the effectiveness of the proposed approach in improving time efficiency.