Formulating the unicycle on the sphere path planning problem as a linear time-varying system

© 2025 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to s...

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Autores: Thomas, Federico|||0000-0001-9341-5528, Franch Bullich, Jaume|||0000-0002-6257-9113
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/446496
Acceso en línea:https://hdl.handle.net/2117/446496
https://dx.doi.org/10.1109/TRO.2025.3567525
Access Level:acceso abierto
Palabra clave:Automatic control
Dynamics, Rigid
System theory
Robots
Path planning
Kinematics
Finite element analysis
Time-varying systems
Standards
Automobiles
Angular velocity
Robot kinematics
Quaternions
Nonholonomic robots
Nonholonomic joints
Linear time-varying systems
Control automàtic
Dinàmica de cossos rígids
Sistemes de control
Classificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systems
Classificació AMS::70 Mechanics of particles and systems::70Q05 Control of mechanical systems
Classificació AMS::93 Systems Theory
Control::93C Control systems, guided systems
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
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spelling Formulating the unicycle on the sphere path planning problem as a linear time-varying systemThomas, Federico|||0000-0001-9341-5528Franch Bullich, Jaume|||0000-0002-6257-9113Automatic controlDynamics, RigidSystem theoryRobotsPath planningKinematicsFinite element analysisTime-varying systemsStandardsAutomobilesAngular velocityRobot kinematicsQuaternionsNonholonomic robotsNonholonomic jointsLinear time-varying systemsPath planningControl automàticDinàmica de cossos rígidsSistemes de controlClassificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systemsClassificació AMS::70 Mechanics of particles and systems::70Q05 Control of mechanical systemsClassificació AMS::93 Systems TheoryControl::93C Control systems, guided systemsÀrees temàtiques de la UPC::Informàtica::Automàtica i controlÀrees temàtiques de la UPC::Física::Física de l'estat sòlidÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa© 2025 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The kinematics, dynamics, and control of a unicycle moving without slipping on a plane has been extensively studied in the literature of nonholonomic mechanical systems. However, since planar motion can be seen as a limiting case of the motion on a sphere, we focus our analysis on the more general spherical case. This paper introduces a novel approach to path planning for a unicycle rolling on a sphere while satisfying the non-slipping constraint. Our method is based on a simple yet effective idea: first, we model the system as a linear time-varying dynamic system. Then, leveraging the fact that certain such systems can be integrated under specific algebraic conditions, we derive a closed-form expression for the control variables. This formulation includes three free parameters, which can be tuned to generate a path connecting any two configurations of the unicycle. Notably, our approach requires no prior knowledge of nonholonomic system analysis, making it accessible to a broader audience.Peer ReviewedInstitute of Electrical and Electronics Engineers (IEEE)20252025-01-0120252025-11-18journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/446496https://dx.doi.org/10.1109/TRO.2025.3567525reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-117509GB-I00 SINTESIS DE MOVIMIENTOS ROBOTICOS OPTIMAMENTE AGILES Y GRACILESopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4464962026-05-27T15:37:01Z
dc.title.none.fl_str_mv Formulating the unicycle on the sphere path planning problem as a linear time-varying system
title Formulating the unicycle on the sphere path planning problem as a linear time-varying system
spellingShingle Formulating the unicycle on the sphere path planning problem as a linear time-varying system
Thomas, Federico|||0000-0001-9341-5528
Automatic control
Dynamics, Rigid
System theory
Robots
Path planning
Kinematics
Finite element analysis
Time-varying systems
Standards
Automobiles
Angular velocity
Robot kinematics
Quaternions
Nonholonomic robots
Nonholonomic joints
Linear time-varying systems
Path planning
Control automàtic
Dinàmica de cossos rígids
Sistemes de control
Classificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systems
Classificació AMS::70 Mechanics of particles and systems::70Q05 Control of mechanical systems
Classificació AMS::93 Systems Theory
Control::93C Control systems, guided systems
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
title_short Formulating the unicycle on the sphere path planning problem as a linear time-varying system
title_full Formulating the unicycle on the sphere path planning problem as a linear time-varying system
title_fullStr Formulating the unicycle on the sphere path planning problem as a linear time-varying system
title_full_unstemmed Formulating the unicycle on the sphere path planning problem as a linear time-varying system
title_sort Formulating the unicycle on the sphere path planning problem as a linear time-varying system
dc.creator.none.fl_str_mv Thomas, Federico|||0000-0001-9341-5528
Franch Bullich, Jaume|||0000-0002-6257-9113
author Thomas, Federico|||0000-0001-9341-5528
author_facet Thomas, Federico|||0000-0001-9341-5528
Franch Bullich, Jaume|||0000-0002-6257-9113
author_role author
author2 Franch Bullich, Jaume|||0000-0002-6257-9113
author2_role author
dc.subject.none.fl_str_mv Automatic control
Dynamics, Rigid
System theory
Robots
Path planning
Kinematics
Finite element analysis
Time-varying systems
Standards
Automobiles
Angular velocity
Robot kinematics
Quaternions
Nonholonomic robots
Nonholonomic joints
Linear time-varying systems
Path planning
Control automàtic
Dinàmica de cossos rígids
Sistemes de control
Classificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systems
Classificació AMS::70 Mechanics of particles and systems::70Q05 Control of mechanical systems
Classificació AMS::93 Systems Theory
Control::93C Control systems, guided systems
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
topic Automatic control
Dynamics, Rigid
System theory
Robots
Path planning
Kinematics
Finite element analysis
Time-varying systems
Standards
Automobiles
Angular velocity
Robot kinematics
Quaternions
Nonholonomic robots
Nonholonomic joints
Linear time-varying systems
Path planning
Control automàtic
Dinàmica de cossos rígids
Sistemes de control
Classificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systems
Classificació AMS::70 Mechanics of particles and systems::70Q05 Control of mechanical systems
Classificació AMS::93 Systems Theory
Control::93C Control systems, guided systems
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
description © 2025 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-01-01
2025
2025-11-18
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/2117/446496
https://dx.doi.org/10.1109/TRO.2025.3567525
url https://hdl.handle.net/2117/446496
https://dx.doi.org/10.1109/TRO.2025.3567525
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-117509GB-I00 SINTESIS DE MOVIMIENTOS ROBOTICOS OPTIMAMENTE AGILES Y GRACILES
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 Institute of Electrical and Electronics Engineers (IEEE)
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers (IEEE)
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_ 1869404048723017728
score 15.812429

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