Flexible manipulator trajectory tracking based on an improved adaptive particle swarm optimization algorithm with fuzzy PD control

Abstract. Trajectory planning for flexible manipulators is a critical area of research in robotics. A trajectory tracking controller can enhance the accuracy of the manipulator's path and reduce vibrations. However, current flexible manipulators remain largely in the research phase, with many studies revealing issues such as poor accuracy in dynamic modeling, weak tracking performance in controller design, and insufficient vibration suppression capabilities. To address these challenges and improve the trajectory tracking performance of the manipulator, this paper focused on vibration suppression and trajectory planning for a two-link flexible manipulator and proposed a novel control method that integrates a modified adaptive particle swarm optimization algorithm (MAPSO) with fuzzy proportional–derivative (PD) control to achieve effective trajectory tracking. Firstly, the dynamic equations of the two-link flexible manipulator system were derived using the assumed modal method in conjunction with Lagrangian dynamics. Next, a 3-5-3 hybrid polynomial algorithm based on MAPSO was proposed to optimize the trajectory of the manipulator. Simulation results demonstrated that the optimization algorithm significantly enhances efficiency. Specifically, the number of iterations required for the two joints was reduced by 33 % and 54 %, respectively, when compared to the original algorithm. Additionally, this optimization led to a total reduction in running time of 0.03 s. Subsequently, the MAPSO algorithm was utilized to enhance the fuzzy PD controller based on the previously obtained optimal trajectory, leading to the development of a trajectory tracking controller known as MAPSO-FuzzyPD. Simulation results indicated that the proposed algorithm significantly reduced the maximum starting torque for both joints. Specifically, the maximum starting torque of joint 1 was decreased by 61.3 % and 40.3 % when compared to PD control and fuzzy PD control, respectively. Additionally, the maximum starting torque of joint 2 was reduced by 57.9 % and 42.1 % in comparison to the same control methods. Finally, an experimental platform for the flexible manipulator was established, and the experimental results further validated the effectiveness and feasibility of the algorithm proposed in this paper concerning joint trajectory tracking.