Deep Reinforcement Learning-Based Motion Planning and PDE Control for Flexible Manipulators

This article presents a motion planning and control framework for flexible robotic manipulators, integrating deep reinforcement learning (DRL) with a nonlinear partial differential equation (PDE) controller. Unlike conventional approaches that focus solely on control, we demonstrate that the desired trajectory significantly influences endpoint vibrations. To address this, a DRL motion planner, trained using the soft actor-critic (SAC) algorithm, generates optimized trajectories that inherently minimize vibrations. The PDE nonlinear controller then computes the required torques to track the planned trajectory while ensuring closed-loop stability using Lyapunov analysis. The proposed methodology is validated through both simulations and real-world experiments, demonstrating superior vibration suppression and tracking accuracy compared to traditional methods. The results underscore the potential of combining learning-based motion planning with model-based control for enhancing the precision and stability of flexible robotic manipulators.