Prescribed-Time Reinforcement Learning Fault-Tolerant Formation Control for Multiple Nonholonomic Robots: Theory and Experiment

In response to the dual challenges of limited energy and insufficient fault tolerance in nonholonomic robots (NRs), this article proposes a prescribed-time reinforcement learning (RL) fault-tolerant safety formation control strategy. The aim is to improve the operational efficiency and reliability of NRs. First, the normalized prescribed performance error with constraints is embedded into an obstacle function with performance indicators for optimization, ensuring that the robot completes the formation task in the prescribed-time while suppressing the adverse transient performance effects caused by actuator failures and RL. Then, a nonlinear filter with integrated adaptive compensation mechanism is designed, which can simplify the calculation process and compensate for filtering errors, significantly improving the tracking accuracy. Subsequently, an optimal fault-tolerant controller is designed in the framework of actor–critic, which decouples the optimal control and fault-tolerant control by introducing intermediate control signals, reducing the difficulty of applying RL in fault-tolerant control. Finally, Lyapunov theory is applied to prove that the closed-loop system signal is bounded, and the effectiveness of the algorithm is verified through simulations and experiments.