PREPRINT SUBMITTED TO IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1 Model Predictive Control of Nonholonomic Mobile Robots without Stabilizing Constraints and Costs*

Abstract—The problem of steering a nonholonomic mobile robot to a desired position and orientation is considered. In this paper, a model predictive control (MPC) scheme based on tailored non-quadratic stage cost is proposed to fulfil this control task. We rigorously prove asymptotic stability while neither stabilizing constraints nor costs are used. To this end, we first design suitable manoeuvres to construct bounds on the value function. Second, these bounds are exploited to determine a prediction horizon length such that asymptotic stability of the MPC closed-loop is guaranteed. Finally, numerical simulations are conducted to explain the necessity of having non-quadratic running costs. Index Terms—nonholonomic robots, model predictive control, asymptotic stability, prediction horizon, non-quadratic costs. I