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arXiv · 2502.03902

Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints

Efstratios Stratoglou·Alexandre Anahory Simoes·Anthony Bloch·Leonardo Colombo
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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.

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Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo. 2025-02-06. Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints. https://arxiv.org/abs/2502.03902

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