Virtual nonholonomic constraints: A geometric approach

Virtual constraints are relations imposed in a control system that become invariant via feedback instead of real 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...

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Bibliographic Details
Published in:Automatica (Oxford) 2023-09, Vol.155, p.111166, Article 111166
Main Authors: Simoes, Alexandre Anahory, Stratoglou, Efstratios, Bloch, Anthony, Colombo, Leonardo J.
Format: Article
Language:English
Subjects:
Affine connection control systems
Nonholonomic systems
Underactuated mechanical systems
Virtual constraints
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Summary:Virtual constraints are relations imposed in a control system that become invariant via feedback instead of real 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 nonholonomic constraints in a geometric framework. More precisely, it is a controlled invariant distribution associated with an affine connection mechanical control system. We show the existence and uniqueness of a control law defining a virtual nonholonomic constraint and we characterize the trajectories of the closed-loop system as solutions of a mechanical system associated with an induced constrained connection. Moreover, we characterize the dynamics for nonholonomic systems in terms of virtual nonholonomic constraints, i.e., we characterize when can we obtain nonholonomic dynamics from virtual nonholonomic constraints.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2023.111166