New Trajectory Planning Based on Bezier Curve Using Particle Swarm Optimization

Abstract

In this paper, a new trajectory planning based on Bezier curve is proposed to generate a smooth and time-optimal trajectory for point-to-point motions. The 10th-order Bezier curve is used to generate the path, and the trajectory with time is generated by time re-parameterization based on the fourth-order Bezier curve. The trajectory is determined by only two parameters. Then, using the accelerated particle swarm optimization method, the minimum execution time and two parameters under kinematic constraints (velocity, acceleration, and jerk) are determined to obtain the time-optimal trajectory. The obtained trajectory ensures that the velocity, acceleration, and jerk values at the beginning and end points are all zero and also guarantees the flexibility of the motion. The synchronization of all joints is also given for the effective actuator operation. The simulation of a 6-degree-of-freedom (DOF) robot manipulator shows the effectiveness of the proposed method to satisfy the optimal execution time. Also, the analysis using a mass-spring-damper system with a single-DOF shows well the characteristics for reducing residual vibration.

Received: 24 July 2025 | Revised: 30 September 2025 | Accepted: 10 April 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data available on request from the corresponding author upon reasonable request.

Author Contribution Statement

Chol Jun Han: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Supervision, Project administration. Kwang Rim Song: Software, Resources, Writing –review & editing. Sung-Gyu Pak: Formal analysis, Investigation, Visualization.