Model Predictive Control without terminal constraints or costs for holonomic mobile robots

Abstract

We investigate Model Predictive Control (MPC) schemes without stabilizing constraints or costs for the set-point stabilization of holonomic mobile robots. Herein, we ensure closed-loop asymptotic stability using the concept of cost controllability. To this end, we derive a growth bound on the finite-horizon value function in terms of the running costs evaluated at the current state, which is then used to determine a stabilizing prediction horizon. In the discrete-time setting, we additionally show that asymptotic stability holds for the shortest possible prediction horizon. Moreover, we deduce a lower bound on the MPC performance on the infinite horizon. Theoretical results are verified by numerical simulations as well as laboratory experiments of stabilizing a holonomic mobile robot to a reference set point.