Stabilization of Nonholonomic Robot Formations: A First-state Contractive Model Predictive Control Approach

Abstract

A model predictive control algorithm is developed for stabilizing a team of nonholonomic mobile robots navigating in formation within an obstacle-populated environment. In this scenario, the {\em leader} robot may need to execute abrupt maneuvers (i.e., sudden stops and backward motions) in order to avoid collisions and accomplish mission objectives. Moreover, follower robots should be capable of tracking their leaders maintaining desired relative distance and orientation. To this end, nonholonomic trajectory tracking and point stabilization should be combined in a suitable way. Most proposed control algorithms for nonholonomic robots do not have simultaneous tracking and point stabilization capability; therefore, they may perform poorly when the leader robot executes aggressive maneuvers. In this paper, we address this problem by applying model predictive control (MPC). Motivated by the contractive MPC scheme developed in [14], the proposed 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 control algorithm is stable and can achieve some practical formations without any special treatments. Simulation results are provided to verify the effectiveness of the method.