Reinforcement Learning-Based PID Gain Optimization for Delta Parallel Robot Trajectory Tracking

In this study, a PID gain tuning approach using Deep Deterministic Policy Gradient (DDPG), a reinforcement learning (RL) algorithm, is proposed for trajectory tracking of delta parallel robots. Owing to their 3-degree-of-freedom (3-DOF) parallel kinematic structure, delta robots offer higher stiffness, precision, and speed capabilities than serial manipulators; they are therefore widely used in high-speed pick-and-place applications due to their low moving mass and the stiffness provided by the closed-chain mechanism. In this study, the proposed DDPG-PID approach is comparatively investigated against the conventional Ziegler–Nichols (ZN) and Cohen–Coon (CC) tuning methods; DDPG is designed to optimize the PID gains (K_p, K_i, K_d) within predefined bounds in a continuous action space. In simulations conducted on four different trajectories—circle, lemniscate, diamond, and star—RMSE, IAE, ISE, ITAE, and maximum error metrics are used for evaluation. According to the results, DDPG-PID achieves the lowest error on all trajectories, reducing RMSE by approximately 35–58% compared to ZN-PID and by approximately 79–82% compared to CC-PID; similarly, improvements are observed in IAE/ISE/ITAE and maximum error values. These findings indicate that DDPG-PID provides more stable and accurate tracking, particularly on complex trajectories involving sharp direction changes, and demonstrate that the proposed method offers a superior automatic PID tuning alternative to classical tuning rules for industrial parallel robot control applications.