Optimal Formation Control for Mobile Robots Under Prescribed Performance Constraints via Reinforcement Learning

This study introduces an optimal control algorithm for the formation of mobile robots, addressing collision avoidance and adhering to specified performance constraints. The desired formation geometry is established within a leader-follower architecture, where each robot follows an intermediate leader while maintaining a desired distance. Limited communication range and collision avoidance are considered to ensure the safe operation of the formation system. Boundary functions defined as time-varying exponential functions are employed to manage transient performance of formation errors. To ensure transient and steady-state performance of formation errors, we propose a design technique of optimal formation control with prescribed performance. A reinforcement learning algorithm based on an actor-critic strategy is introduced to achieve optimal formation control and specified tracking accuracy simultaneously. Through stability analysis, it is demonstrated that the proposed optimal controller ensures the uniform ultimate stability of the formation system, while meeting the specified performance criteria. The effectiveness of the presented control algorithm is illustrated through experiment results.