Variational integrators for underactuated mechanical control systems with symmetries

Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper...

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Detalhes bibliográficos
Autores: Colombo, Leonardo, Jiménez Alburquerque, Fernando, Martín de Diego, David
Formato: artículo
Fecha de publicación:2016
País:España
Recursos:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/31488
Acesso em linha:https://hdl.handle.net/20.500.14468/31488
Access Level:acceso abierto
Palavra-chave:12 Matemáticas
Variational integrators
higher-order mechanics
underactuated systems
optimal control
discrete variational calculus
constrained mechanics
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spelling Variational integrators for underactuated mechanical control systems with symmetriesColombo, LeonardoJiménez Alburquerque, FernandoMartín de Diego, David12 MatemáticasVariational integratorshigher-order mechanicsunderactuated systemsoptimal controldiscrete variational calculusconstrained mechanicsOptimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems when the configuration space is a trivial principal bundle and the construction of variational integrators for such mechanical control systems. An interesting family of geometric integrators can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators, being one of their main properties the preservation of geometric features as the symplecticity, momentum preservation and good behavior of the energy. We construct variational integrators for higher-order mechanical systems on trivial principal bundles and their extension for higher-order constrained systems, paying particular attention to the case of underactuated mechanical systems.American Institute of Mathematical Sciencese-Spacio UNED20262026-01-2020162016-05-0120162016-05-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14468/31488reponame:e-spacio. Repositorio Institucional de la UNEDinstname:Universidad Nacional de Educación a DistanciaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/deed.esoai:e-spacio.uned.es:20.500.14468/314882026-06-06T12:38:31Z
dc.title.none.fl_str_mv Variational integrators for underactuated mechanical control systems with symmetries
title Variational integrators for underactuated mechanical control systems with symmetries
spellingShingle Variational integrators for underactuated mechanical control systems with symmetries
Colombo, Leonardo
12 Matemáticas
Variational integrators
higher-order mechanics
underactuated systems
optimal control
discrete variational calculus
constrained mechanics
title_short Variational integrators for underactuated mechanical control systems with symmetries
title_full Variational integrators for underactuated mechanical control systems with symmetries
title_fullStr Variational integrators for underactuated mechanical control systems with symmetries
title_full_unstemmed Variational integrators for underactuated mechanical control systems with symmetries
title_sort Variational integrators for underactuated mechanical control systems with symmetries
dc.creator.none.fl_str_mv Colombo, Leonardo
Jiménez Alburquerque, Fernando
Martín de Diego, David
author Colombo, Leonardo
author_facet Colombo, Leonardo
Jiménez Alburquerque, Fernando
Martín de Diego, David
author_role author
author2 Jiménez Alburquerque, Fernando
Martín de Diego, David
author2_role author
author
dc.contributor.none.fl_str_mv e-Spacio UNED
dc.subject.none.fl_str_mv 12 Matemáticas
Variational integrators
higher-order mechanics
underactuated systems
optimal control
discrete variational calculus
constrained mechanics
topic 12 Matemáticas
Variational integrators
higher-order mechanics
underactuated systems
optimal control
discrete variational calculus
constrained mechanics
description Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems when the configuration space is a trivial principal bundle and the construction of variational integrators for such mechanical control systems. An interesting family of geometric integrators can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators, being one of their main properties the preservation of geometric features as the symplecticity, momentum preservation and good behavior of the energy. We construct variational integrators for higher-order mechanical systems on trivial principal bundles and their extension for higher-order constrained systems, paying particular attention to the case of underactuated mechanical systems.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-05-01
2016
2016-05-01
2026
2026-01-20
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14468/31488
url https://hdl.handle.net/20.500.14468/31488
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/deed.es
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
http://creativecommons.org/licenses/by/4.0/deed.es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:e-spacio. Repositorio Institucional de la UNED
instname:Universidad Nacional de Educación a Distancia
instname_str Universidad Nacional de Educación a Distancia
reponame_str e-spacio. Repositorio Institucional de la UNED
collection e-spacio. Repositorio Institucional de la UNED
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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