Optimal control of underactuated mechanical systems: A geometric approach

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints.We study a regular case where it is possible to esta...

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Detalles Bibliográficos
Autores: Colombo, Leonardo, Martín De Diego, David, Zuccalli, Marcela
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2010
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/378183
Acceso en línea:http://hdl.handle.net/10261/378183
Access Level:acceso abierto
Palabra clave:Optimal Control
Lie Group
Integrable Variation
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spelling Optimal control of underactuated mechanical systems: A geometric approachColombo, LeonardoMartín De Diego, DavidZuccalli, MarcelaOptimal ControlLie GroupIntegrable VariationIn this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints.We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.This work has been partially supported by MEC Spain Grant No. MTM 2007-62478, project “Ingenio Mathematica” i-MATH Grant No. CSD 2006-00032 Consolider-Ingenio 2010 and Grant No. S-0505/ESP/0158 of the Comunidad de Madrid.Peer reviewedAmerican Institute of PhysicsMinisterio de Economía y Competitividad (España)Comunidad de MadridColombo, Leonardo [0000-0001-6493-6113]Martín De Diego, David [0000-0001-6762-8909]Zuccalli, Marcela [0000-0002-1590-8084]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252010info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/378183reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MEC//MTM2007-62478https://doi.org/10.1063/1.3456158Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3781832026-05-22T06:33:51Z
dc.title.none.fl_str_mv Optimal control of underactuated mechanical systems: A geometric approach
title Optimal control of underactuated mechanical systems: A geometric approach
spellingShingle Optimal control of underactuated mechanical systems: A geometric approach
Colombo, Leonardo
Optimal Control
Lie Group
Integrable Variation
title_short Optimal control of underactuated mechanical systems: A geometric approach
title_full Optimal control of underactuated mechanical systems: A geometric approach
title_fullStr Optimal control of underactuated mechanical systems: A geometric approach
title_full_unstemmed Optimal control of underactuated mechanical systems: A geometric approach
title_sort Optimal control of underactuated mechanical systems: A geometric approach
dc.creator.none.fl_str_mv Colombo, Leonardo
Martín De Diego, David
Zuccalli, Marcela
author Colombo, Leonardo
author_facet Colombo, Leonardo
Martín De Diego, David
Zuccalli, Marcela
author_role author
author2 Martín De Diego, David
Zuccalli, Marcela
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
Comunidad de Madrid
Colombo, Leonardo [0000-0001-6493-6113]
Martín De Diego, David [0000-0001-6762-8909]
Zuccalli, Marcela [0000-0002-1590-8084]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Optimal Control
Lie Group
Integrable Variation
topic Optimal Control
Lie Group
Integrable Variation
description In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints.We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.
publishDate 2010
dc.date.none.fl_str_mv 2010
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/378183
url http://hdl.handle.net/10261/378183
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/MEC//MTM2007-62478
https://doi.org/10.1063/1.3456158
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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