Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates

In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae...

ver descrição completa

Detalhes bibliográficos
Autores: Bijalwan, Ashutosh|||0000-0002-4295-9493, Muñoz Romero, José|||0000-0002-0083-3673
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:dnet:upcommonspor::475e8f7b214e312dde12827c230c3457
Acesso em linha:https://hdl.handle.net/2117/462129
https://dx.doi.org/10.1016/j.cma.2023.116697
Access Level:acceso abierto
Palavra-chave:Strength of materials
Elastic solids
Calculus of variations
Mathematical optimization
Non-linear elasticity
Growth model
Soft robotics
Limbless locomotion
Optimal control
Adjoint method
Resistència de materials
Elasticitat
Càlcul de variacions
Optimització matemàtica
Classificació AMS::74 Mechanics of deformable solids::74B Elastic materials
Classificació AMS::49 Calculus of variations and optimal control
optimization::49M Methods of successive approximations
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
id ES_5dfd57df5aa7b2250620547f16c96dd0
oai_identifier_str oai:dnet:upcommonspor::475e8f7b214e312dde12827c230c3457
network_acronym_str ES
network_name_str España
repository_id_str
spelling Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substratesBijalwan, Ashutosh|||0000-0002-4295-9493Muñoz Romero, José|||0000-0002-0083-3673Strength of materialsElastic solidsCalculus of variationsMathematical optimizationNon-linear elasticityGrowth modelSoft roboticsLimbless locomotionOptimal controlAdjoint methodResistència de materialsElasticitatCàlcul de variacionsOptimització matemàticaClassificació AMS::74 Mechanics of deformable solids::74B Elastic materialsClassificació AMS::49 Calculus of variations and optimal controloptimization::49M Methods of successive approximationsÀrees temàtiques de la UPC::Física::Física de l'estat sòlidÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàticaIn nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae, and C. elegans. In this work, we developed a computationally efficient 3D Finite Element (FE) unified framework for the locomotion of limbless organisms on frictional substrates. Muscle activity is simulated with a multiplicative decomposition of the deformation gradient, which allows mimicking a broad range of locomotion patterns in 3D contractile elastic solids. We propose a two-field FE formulation based on positions and velocities. Governing partial differential equations are transformed into equivalent time-continuous differential–algebraic equations (DAEs). Next, the optimal locomotion strategies are studied in the framework of optimal control theory. We resort to adjoint-based methods and deduce the first-order optimality conditions, that yield a system of DAEs with two-point end conditions. Hidden symplectic structure is discussed, and Symplectic Euler time integration of optimality conditions are employed. The resulting discrete first-order optimality conditions form a non-linear programming problem that is solved efficiently with the Forward Backward Sweep Method. Finally, some numerical examples are provided to demonstrate the comprehensiveness of the proposed computational framework and investigate the energy-efficient optimal strategy out of distinct locomotion patterns adopted by limbless organisms.Peer ReviewedElsevier20242024-02-1520262026-05-18journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/462129https://dx.doi.org/10.1016/j.cma.2023.116697reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:dnet:upcommonspor::475e8f7b214e312dde12827c230c34572026-05-27T15:37:01Z
dc.title.none.fl_str_mv Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
title Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
spellingShingle Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
Bijalwan, Ashutosh|||0000-0002-4295-9493
Strength of materials
Elastic solids
Calculus of variations
Mathematical optimization
Non-linear elasticity
Growth model
Soft robotics
Limbless locomotion
Optimal control
Adjoint method
Resistència de materials
Elasticitat
Càlcul de variacions
Optimització matemàtica
Classificació AMS::74 Mechanics of deformable solids::74B Elastic materials
Classificació AMS::49 Calculus of variations and optimal control
optimization::49M Methods of successive approximations
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
title_short Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
title_full Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
title_fullStr Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
title_full_unstemmed Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
title_sort Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
dc.creator.none.fl_str_mv Bijalwan, Ashutosh|||0000-0002-4295-9493
Muñoz Romero, José|||0000-0002-0083-3673
author Bijalwan, Ashutosh|||0000-0002-4295-9493
author_facet Bijalwan, Ashutosh|||0000-0002-4295-9493
Muñoz Romero, José|||0000-0002-0083-3673
author_role author
author2 Muñoz Romero, José|||0000-0002-0083-3673
author2_role author
dc.subject.none.fl_str_mv Strength of materials
Elastic solids
Calculus of variations
Mathematical optimization
Non-linear elasticity
Growth model
Soft robotics
Limbless locomotion
Optimal control
Adjoint method
Resistència de materials
Elasticitat
Càlcul de variacions
Optimització matemàtica
Classificació AMS::74 Mechanics of deformable solids::74B Elastic materials
Classificació AMS::49 Calculus of variations and optimal control
optimization::49M Methods of successive approximations
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
topic Strength of materials
Elastic solids
Calculus of variations
Mathematical optimization
Non-linear elasticity
Growth model
Soft robotics
Limbless locomotion
Optimal control
Adjoint method
Resistència de materials
Elasticitat
Càlcul de variacions
Optimització matemàtica
Classificació AMS::74 Mechanics of deformable solids::74B Elastic materials
Classificació AMS::49 Calculus of variations and optimal control
optimization::49M Methods of successive approximations
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
description In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae, and C. elegans. In this work, we developed a computationally efficient 3D Finite Element (FE) unified framework for the locomotion of limbless organisms on frictional substrates. Muscle activity is simulated with a multiplicative decomposition of the deformation gradient, which allows mimicking a broad range of locomotion patterns in 3D contractile elastic solids. We propose a two-field FE formulation based on positions and velocities. Governing partial differential equations are transformed into equivalent time-continuous differential–algebraic equations (DAEs). Next, the optimal locomotion strategies are studied in the framework of optimal control theory. We resort to adjoint-based methods and deduce the first-order optimality conditions, that yield a system of DAEs with two-point end conditions. Hidden symplectic structure is discussed, and Symplectic Euler time integration of optimality conditions are employed. The resulting discrete first-order optimality conditions form a non-linear programming problem that is solved efficiently with the Forward Backward Sweep Method. Finally, some numerical examples are provided to demonstrate the comprehensiveness of the proposed computational framework and investigate the energy-efficient optimal strategy out of distinct locomotion patterns adopted by limbless organisms.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-02-15
2026
2026-05-18
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/462129
https://dx.doi.org/10.1016/j.cma.2023.116697
url https://hdl.handle.net/2117/462129
https://dx.doi.org/10.1016/j.cma.2023.116697
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
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869409071056027648
score 15.228081

Registos relacionados