Model Predictive Control for Leader-Follower Formation Control of Multiple Mobile Robots Using a Modified C/GMRES Method

This paper proposes a model predictive control (MPC) approach to address the leader-follower formation control problem of multiple mobile robots. To account for the proprietary dynamics of most commercial mobile robots that can significantly affect the system's control performance, we adopt an acceleration-level pseudo-dynamic control (ALPDC) framework for designing the controller. Furthermore, based on the communication topology of the robots, we design a distributed observer for each follower to estimate the state of the leader. By defining the formation tracking errors of the followers, we formulate the tracking problem as a standard MPC problem. To further enhance the real-time performance of MPC optimization, we propose an improved C/GMRES method based on the fixed-time stability theory. Simulation results demonstrate the effectiveness of the proposed strategy.