On the Geometry of Virtual Nonlinear Nonholonomic Constraints

TL;DR

This paper introduces a geometric framework for virtual nonlinear nonholonomic constraints, establishing their invariance and control law design, with applications demonstrated through examples and simulations.

Contribution

It presents a novel geometric approach to virtual nonlinear nonholonomic constraints, including existence and uniqueness results for control laws that preserve these constraints.

Findings

Control laws ensuring invariance of virtual constraints

Existence and uniqueness of such control laws

Simulation results demonstrating practical applications

Abstract

Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to 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 nonlinear nonholonomic constraints in a geometric framework which is a controlled invariant submanifold and we show the existence and uniqueness of a control law preserving this submanifold. We illustrate the theory with various examples and present simulation results for an application.