Path Seeking and Optimal Control for Mobile Robots: A Dual-Layer Reinforcement Learning Approach with Prescribed-Time Convergence

This paper proposes a Double-Layer Reinforcement Learning Control (DL-RLC) framework with prescribed-time convergence, aiming to enable mobile robots to achieve efficient trajectory tracking under restricted user commands or in nonideal environments. First, based on the [Formula: see text]-learning strategy and an improved least squares method, global path planning and continuous processing are realized, providing reliable path guidance for the robot. Then, at the control layer, a transformation function is introduced to embed the tracking error into the performance function for optimization, and a Hamilton–Jacobi–Bellman (HJB) equation is constructed. Based on this HJB equation, an actor–critic RLC strategy is employed to solve the HJB equation, and a prescribed-time optimal controller is designed, achieving dual optimization of control energy and control performance. This end-to-end control method greatly enhances the robot’s ability to cope with unknown challenges in nonideal environments while ensuring the real-time and robustness of the control system. Finally, the effectiveness of the proposed algorithm is verified through simulation experiments.