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arXiv · 2310.01849

On the Geometry of Virtual Nonlinear Nonholonomic Constraints

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

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Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch, Leonardo J. Colombo. 2023-10-03. On the Geometry of Virtual Nonlinear Nonholonomic Constraints. https://arxiv.org/abs/2310.01849

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