Safe Reinforcement Learning for Constrained Optimal Control With Provable Guarantees: Applications to Motion Planning

This paper addresses the constrained infinite-horizon optimal control problem for autonomous vehicles operating in avoidance regions. A novel online adaptive safe reinforcement learning (RL) algorithm is presented to enable real-time generation of continuous and safe motion trajectories. Specifically, the framework utilizes a safety-certified learning approach, featuring a predefined-time convergent adaptive-critic network that rapidly learns the optimal policy under mild conditions, along with a control barrier function (CBF)-based safety filter to restore original constraints through forward invariance and prevent safety violations during the online exploration phase. Rigorous theoretical analysis establishes the safety, optimality, and convergence of the RL policy. Simulations demonstrate that the proposed scheme effectively generates safe, near-optimal trajectories for autonomous navigation tasks, with comparative evaluations highlighting its superiority in optimizing long-term performance over the prevailing motion planners with obstacle avoidance, while maintaining competitive execution time.