Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints
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.
Cite
@article{arxiv.2502.03902,
title = {Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints},
author = {Efstratios Stratoglou and Alexandre Anahory Simoes and Anthony Bloch and Leonardo Colombo},
journal= {arXiv preprint arXiv:2502.03902},
year = {2025}
}