Optimal Time–Jerk Trajectory Planning for Manipulators Based on a Constrained Multi-Objective Dream Optimization Algorithm

A multi-objective optimal trajectory planning method is proposed for manipulators in this paper to enhance motion efficiency and to reduce component wear while ensuring motion smoothness. The trajectory is initially interpolated in the joint space by using quintic non-uniform B-splines with virtual points, achieving the C⁴ continuity of joint motion and satisfying dynamic, kinematic, geometric, synchronization, and boundary constraints. The interpolation reformulates the trajectory planning problem into an optimization problem, where the time intervals between desired adjacent waypoints serve as variables. Travelling time and the integral of the squared jerk along the entire trajectories comprise the multi-objective functions. A constrained multi-objective dream optimization algorithm is designed to solve the time–jerk optimal trajectory planning problem and generate Pareto solutions for optimized trajectories. Simulations conducted on 6-DOF manipulators validate the effectiveness and superiority of the proposed method in comparison with existing typical trajectory planning methods.