Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints

TL;DR

This paper develops a geometric control method to stabilize mechanical systems around virtual nonlinear nonholonomic constraints, ensuring exponential convergence and invariance, validated through simulations in multi-agent flocking and USV navigation.

Contribution

It introduces a novel control law for stabilizing systems on virtual nonholonomic manifolds, extending existing methods to velocity-dependent constraints.

Findings

Achieves exponential convergence to the virtual constraint manifold.

Ensures control invariance of the virtual constraints.

Validated effectiveness through simulations in multi-agent flocking and USV navigation.

Abstract

In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant through feedback control. Virtual nonholonomic constraints represent a specific class of virtual constraints that depend on the system's velocities in addition to its configurations. We derive a control law under which a mechanical control system achieves exponential convergence to the virtual constraint submanifold, and rendering it control-invariant. The proposed controller's performance is validated through simulation results in two distinct applications: flocking motion in multi-agent systems and the control of an unmanned surface vehicle (USV) navigating a stream.