A Two-Stage Time-Optimal Trajectory Planning Algorithm with No Inverse Kinematics for Manipulator

This paper studies the time-optimal trajectory planning for manipulator. Conventional time-optimal trajectory planning utilizes the inverse solution, interpolation and intelligent optimization algorithms to search for the shortest time, making the process rather complex. To address this issue, we incorporate the kinematic equations and state transition equations into the existing Two-Stage algorithm used in unmanned aerial vehicles (UAVs), resulting in significantly improved computational speed and accuracy of the robotic arm's operation. The first stage predefines some resulting points related to path points and optimizes the robotic arm's kinematics and motion constraints as soft constraints to provide an initial solution for the second stage. In the second stage, based on the predetermined points of each trajectory segment provided by the first stage, the optimization problem is solved without the need for kinematic inverse solutions, in which the time intervals of each trajectory segment serve as optimization variables and the robotic arm's kinematics and motion constraints are used as hard constraints for optimization. Subsequently, the obtained joint points are interpolated using fifth-degree polynomials to form continuous joint trajectories. Comparative experiments with an improved particle swarm optimization algorithm verify that the proposed method exhibits higher optimization efficiency and achieves shorter optimized times.