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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Detalles Bibliográficos
Autores: Simoes, Alexandre Anahory, Stratoglou, Efstratios, Bloch, Anthony, Colombo, Leonardo J.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/369139
Acceso en línea:http://hdl.handle.net/10261/369139
Access Level:acceso abierto
Palabra clave:Underactuated mechanical systems
Affine connection control systems
Virtual constraints
Nonholonomic systems
Descripción
Sumario: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.