In recent years, safe reinforcement learning (RL) with the actor-critic structure has gained significant interest for continuous control tasks. However, achieving near-optimal control policies with safety and convergence guarantees remains challenging. Moreover, few works have focused on designing RL algorithms that handle time-varying safety constraints. This article proposes a safe RL algorithm for optimal control of nonlinear systems with time-varying state and control constraints. The algorithm's novelty lies in two key aspects. Firstly, the approach introduces a unique barrier force-based control policy structure to ensure control safety during learning. Secondly, a multistep policy evaluation mechanism is employed, enabling the prediction of policy safety risks under time-varying constraints and guiding safe updates. Theoretical results on learning convergence, stability, and robustness are proven. The proposed algorithm outperforms several state-of-the-art RL algorithms in the simulated Safety Gym environment. It is also applied to the real-world problem of integrated path following and collision avoidance for two intelligent vehicles - a differential-drive vehicle and an Ackermann-drive one. The experimental results demonstrate the impressive sim-to-real transfer capability of our approach, while showcasing satisfactory online control performance.

Distributed model predictive control (DMPC) concerns how to online control multiple robotic systems with constraints effectively. However, the nonlinearity, nonconvexity, and strong interconnections of dynamic system models and constraints can make the real-time and real-world DMPC implementations nontrivial. Reinforcement learning (RL) algorithms are promising for control policy design. However, how to ensure safety in terms of state constraints in RL remains a significant issue. This paper proposes a barrier function-based safe reinforcement learning algorithm for DMPC of nonlinear multi-robot systems under state constraints. The proposed approach is composed of several local learning-based MPC regulators. Each regulator, associated with a local system, learns and deploys the local control policy using a safe reinforcement learning algorithm in a distributed manner, i.e., with state information only among the neighbor agents. As a prominent feature of the proposed algorithm, we present a novel barrier-based policy structure to ensure safety, which has a clear mechanistic interpretation. Both simulated and real-world experiments on the formation control of mobile robots with collision avoidance show the effectiveness of the proposed safe reinforcement learning algorithm for DMPC.