A Near-Time-Optimal Trajectory Planning under Torque and Jerk Constraints for Industrial Robots on Fixed Paths (I)

Abstract

Trajectory planning plays a pivotal role in robotic motion planning, particularly in achieving time-optimal motion under complex dynamic constraints. Although the Time-Optimal Path Parameterization (TOPP) algorithm effectively addresses trajectory generation under joint torque constraints, classical methods often overlook third-order constraints. As a result, the generated trajectories, while torque-feasible, exhibit excessive jerk and poor dynamic stability, which limits their practical applicability. To overcome these limitations, this paper proposes a trajectory planning framework that simultaneously enforces torque and jerk constraints. Building upon torque-constrained TOPP, the method integrates a shooting-based strategy to identify switching points through bidirectional integration under jerk constraints and employs a Sigmoid-based fusion scheme to eliminate integration errors and ensure smooth transitions. The proposed approach is experimentally validated on a six-degree-of-freedom industrial robot. Comparative evaluations with the TOPP-RA algorithm demonstrate that the method significantly reduces both high-frequency vibrations during high-speed execution and residual oscillations after motion termination. Feedback from torque rate measurements, vibration sensors, and laser tracker data confirms faster settling and improved compliance, making the approach well-suited for complex industrial scenarios.