On quadratic stage costs for mobile robots in model predictive control

We consider nonholonomic mobile robots. Since the system is finite time controllable, it is stabilizable by a receding horizon control scheme with purely quadratic stage costs if an infinite optimization horizon is employed. However, due to the so called short-sightedness of model predictive control, these stability properties are not preserved if the control problem is only optimized on a truncated and, thus, finite prediction horizon — even if an arbitrarily large terminal weight is added. Hence, it is necessary to either incorporate structurally different terminal costs or use non-quadratic stage costs to appropriately penalize the deviation from the desired set point. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)