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

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 execu- tion 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. Note to Practitioners—In welding, assembly, and high-speed transport, robots must follow fixed paths quickly while minimiz- ing vibration, since excessive oscillations reduce accuracy and shorten component lifespan. Conventional trajectory planners seldom enforce jerk limits, leading to abrupt torque reversals and residual vibrations. This work introduces a method that simulta- neously accounts for torque and jerk constraints, enabling near time-optimal trajectories that remain smooth and dynamically stable. Experiments on a six-axis industrial robot demonstrate reduced vibration, faster post-motion settling, and improved compliance. A current limitation is the reliance on precise knowledge of dynamic limits, which may restrict deployment in uncertain environments. Future work will explore data-driven Received 4 September 2025; revised 20 November 2025; accepted 8 December 2025. Date of publication 11 December 2025; date of current version 12 January 2026. This article was recommended for publication by Associate Editor C. M. Abdissa and Editor H. Moon upon evaluation of the reviewers’ comments. This work was supported in part by the National Key Research and Development Program of China under Grant 2022YFB4700300, in part by the National Natural Science Foundation of China under Grant 52025054 and Grant 52435001, and in part by the Self-Planned Task of the State Key Laboratory of Robotics and Systems [Harbin Institute of Technology (HIT)] under Grant SKLRS2023KF18 and Grant SKLRS202401A01. (Corresponding authors: Tianjiao Zheng; Yanhe Zhu.) The authors are with the School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail: zhengtj@hit.edu.cn; yhzhu@hit.edu.cn). This article has supplementary downloadable material available at https://doi.org/10.1109/TASE.2025.3642937, provided by the authors. Digital Object Identifier 10.1109/TASE.2025.3642937 adaptation under real operating conditions to broaden industrial applicability.