First-State Contractive Model Predictive Control of Nonholonomic Mobile Robots

Abstract — In this paper, a first-state contractive (FSC) model predictive control (MPC) algorithm is developed for the trajec-tory tracking and point stabilization problems of nonholonomic mobile robots. Different from other stabilizing MPC methods, which address stability by adding terminal state penalties in the performance index and imposing constraints on the terminal state at the end of the prediction horizon, the proposed MPC algorithm guarantees its stability by adding a contractive constraint on the first state at the beginning of the prediction horizon. The resulting MPC scheme is denoted as first-state contractive MPC (FSC-MPC). In the absence of disturbances, it can be shown that the proposed algorithm is exponentially stable. Simulation results are provided to verify the effectiveness of the method. Moreover, it is shown that the FSC-MPC algorithm has simultaneous tracking and point stabilization capability. I