A port-Hamiltonian approach to the control of nonholonomic systems

TL;DR

This paper introduces a port-Hamiltonian framework for controlling nonholonomic systems, emphasizing the role of damping, and proposes a robust discontinuous control law demonstrated on a vehicle model.

Contribution

It presents a novel port-Hamiltonian modeling approach for nonholonomic systems that incorporates damping effects and introduces a robust control law based on a generalized chained structure.

Findings

Control law ensures asymptotic convergence to the origin

Method is robust against damping and inertial variations

Numerical validation on a car-like vehicle model

Abstract

In this paper a method of controlling nonholonomic systems within the port-Hamiltonian (pH) framework is presented. It is well known that nonholonomic systems can be represented as pH systems without Lagrange multipliers by considering a reduced momentum space. Here, we revisit the modelling of these systems for the purpose of identifying the role that physical damping plays. Using this representation, a geometric structure generalising the well known chained form is identified as \textit{chained structure}. A discontinuous control law is then proposed for pH systems with chained structure such that the configuration of the system asymptotically approaches the origin. The proposed control law is robust against the damping and inertial of the open-loop system. The results are then demonstrated numerically on a car-like vehicle.