Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917914811039744 |
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| author | Stratoglou, Efstratios Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo |
| author_facet | Stratoglou, Efstratios Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_03902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints Stratoglou, Efstratios Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo Systems and Control Dynamical Systems Optimization and Control 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. |
| title | Geometric Stabilization of Virtual Nonlinear Nonholonomic Constraints |
| topic | Systems and Control Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2502.03902 |