Simulating Nonholonomic Dynamics

TL;DR

This paper introduces novel geometric discretization schemes for nonholonomic systems, enhancing numerical accuracy and stability for robotic vehicle simulations through two integrator methods.

Contribution

It develops two new families of nonholonomic integrators, GNI and RDP, tailored to preserve geometric structure and improve simulation fidelity.

Findings

GNI and RDP integrators demonstrate improved numerical stability.

Methods are applicable to various robotic vehicle models.

Numerical experiments confirm effectiveness of the proposed schemes.

Abstract

This paper develops different discretization schemes for nonholonomic mechanical systems through a discrete geometric approach. The proposed methods are designed to account for the special geometric structure of the nonholonomic motion. Two different families of nonholonomic integrators are developed and examined numerically: the geometric nonholonomic integrator (GNI) and the reduced d'Alembert-Pontryagin integrator (RDP). As a result, the paper provides a general tool for engineering applications, i.e. for automatic derivation of numerically accurate and stable dynamics integration schemes applicable to a variety of robotic vehicle models.