Reinforcement Learning-Based Fixed-Time Optimal Formation Control for Multiple Mobile Robots With Prescribed Performance

This study investigates reinforcement learning-based fixed-time optimal formation control for multiple nonholonomic mobile robots with prescribed performance constraints. First, the constrained formation error dynamics is established using a leader-follower approach. Meanwhile, a barrier function is employed to transform the constrained formation error dynamics into an unconstrained form. Then, an adaptive control technique and a critic-only reinforcement learning strategy are utilized to design a fixed-time optimal control law for the unconstrained error dynamics. Rigorous theoretical derivations demonstrate that the proposed control law guarantees that the constrained formation error converges to near zero within a fixed time, optimizing the performance index while satisfying the prescribed performance requirement. Finally, the feasibility of the proposed method is verified through simulations and experiments.