On MPC without terminal conditions for dynamic non-holonomic robots

TL;DR

This paper demonstrates that MPC can ensure asymptotic stability for a differential-drive robot with actuator dynamics and state constraints without using terminal conditions, by combining barrier theory and cost controllability.

Contribution

It introduces a novel MPC approach that guarantees stability without terminal conditions for non-holonomic robots with actuator dynamics, using viability kernels and cost controllability.

Findings

Established asymptotic stability on convex sets without terminal conditions.

Derived bounds on prediction horizon length for stability.

Analyzed the viability kernel boundary and neighborhood of the origin.

Abstract

We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.