Geometric stabilization of virtual linear nonholonomic constraints

TL;DR

This paper presents conditions and a control law ensuring exponential convergence of mechanical systems to virtual linear nonholonomic constraints, which depend on velocities and are invariant under feedback control.

Contribution

It introduces a novel control approach for stabilizing virtual linear nonholonomic constraints in mechanical systems, expanding the understanding of virtual constraint invariance.

Findings

Provided sufficient conditions for exponential convergence.

Developed a control law ensuring invariance of virtual constraints.

Enhanced stability analysis for velocity-dependent virtual constraints.

Abstract

In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic constraint that is control invariant via the same feedback control. Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Virtual nonholonomic constraints, similarly to mechanical nonholonomic constraints, are a class of virtual constraints that depend on velocities rather than only on the configurations of the system.