Discontinuous energy shaping control of the Chaplygin sleigh

TL;DR

This paper introduces a discontinuous energy shaping control law for the nonholonomic Chaplygin sleigh, enabling set-point regulation despite the system's non-smooth stabilisation constraints.

Contribution

It presents a novel discontinuous control approach that achieves energy shaping and damping injection for the Chaplygin sleigh, overcoming limitations of smooth control laws.

Findings

The control law is robust against parameter variations.

It successfully stabilizes the system at a desired set point.

The approach circumvents Brockett's necessary condition for smooth stabilisation.

Abstract

In this paper we present an energy shaping control law for set-point regulation of the Chaplygin sleigh. It is well known that nonholonomic mechanical systems cannot be asymptotically stabilised using smooth control laws as they do no satisfy Brockett's necessary condition for smooth stabilisation. Here, we propose a discontinuous control law that can be seen as a potential energy shaping and damping injection controller. The proposed controller is shown to be robust against the parameters of both the inertia matrix and the damping structure of the open-loop system.