Virtual Affine Nonholonomic Constraints

TL;DR

This paper introduces virtual affine nonholonomic constraints within a geometric framework, providing a new way to impose invariant relations in control systems with nonholonomic properties.

Contribution

It formalizes the concept of virtual affine nonholonomic constraints and proves the existence and uniqueness of the control law that defines them.

Findings

Established the geometric framework for virtual affine nonholonomic constraints

Proved existence and uniqueness of the associated control law

Enhanced understanding of control invariants in nonholonomic systems

Abstract

Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the velocities. In this work, we introduce the notion of virtual affine nonholonomic constraints in a geometric framework. More precisely, it is a controlled invariant affine distribution associated with an affine connection mechanical control system. We show the existence and uniqueness of a control law defining a virtual affine nonholonomic constraint.