Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra

One of the most well-known applications of geometric algebra in engineering is providing a compact formulation of the kinematics of serial robotic manipulators. However, the use of geometric algebra in the field of robotics is still in its early stages, and there are still several open problems that...

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Detalhes bibliográficos
Autores: Marzabal Gatell, Arnau, Zaplana Agut, Isiah|||0000-0002-0862-3240
Formato: capítulo de livro
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:upcommons.upc.edu:2117/422216
Acesso em linha:https://hdl.handle.net/2117/422216
https://dx.doi.org/10.1007/978-3-031-70251-8_25
Access Level:acceso abierto
Palavra-chave:Inverse kinematics
Wrist offset
Conformal geometric algebra
Àrees temàtiques de la UPC::Informàtica::Robòtica
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spelling Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebraMarzabal Gatell, ArnauZaplana Agut, Isiah|||0000-0002-0862-3240Inverse kinematicsWrist offsetConformal geometric algebraÀrees temàtiques de la UPC::Informàtica::RobòticaOne of the most well-known applications of geometric algebra in engineering is providing a compact formulation of the kinematics of serial robotic manipulators. However, the use of geometric algebra in the field of robotics is still in its early stages, and there are still several open problems that can be addressed with this elegant and compact formulation. In this context, this work introduces a strategy based on conformal geometric algebra to solve the inverse kinematics problem for a class of 6DOF serial robots without a spherical wrist, for which it is known that the inverse kinematics problem generally does not have an analytical solution. To achieve this, a purely geometric strategy extending already existing contributions for the case where the robot has a spherical wrist is proposed. In particular, a point is assigned to each joint of the robot so that the problem reduces to computing the set of all possible joint positions for a given desired position and orientation of its end-effector. These points are found by defining and manipulating several geometric entities such as lines, planes, and spheres. Finally, validation with a real robot of the considered class is demonstrated both in simulation and experimentation.This work was partially supported by the European Commission’s Horizon Europe Framework Programme with the project Smarthandle (Resilient manufacturing lines based on smart handling systems) under Grant Agreement 101091792, and the Spanish Government through the project CaRo (Capacidades Intr´ınsecas para Robots Co-trabajadores) under Grant Agreement PID2020-114819GB-I00.Peer ReviewedSpringer20242024-01-0120252025-01-21book parthttp://purl.org/coar/resource_type/c_3248AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/2117/422216https://dx.doi.org/10.1007/978-3-031-70251-8_25reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/501100000780 HE 101091792 Resilient manufacturing lines based on smart handling systemsAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-114819GB-I00 CAPACIDADES INTRINSECAS PARA ROBOTS CO-TRABAJADORESopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4222162026-05-27T15:37:01Z
dc.title.none.fl_str_mv Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
title Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
spellingShingle Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
Marzabal Gatell, Arnau
Inverse kinematics
Wrist offset
Conformal geometric algebra
Àrees temàtiques de la UPC::Informàtica::Robòtica
title_short Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
title_full Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
title_fullStr Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
title_full_unstemmed Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
title_sort Closed-form inverse kinematics solutions for a class of serial robots without spherical wrist using conformal geometric algebra
dc.creator.none.fl_str_mv Marzabal Gatell, Arnau
Zaplana Agut, Isiah|||0000-0002-0862-3240
author Marzabal Gatell, Arnau
author_facet Marzabal Gatell, Arnau
Zaplana Agut, Isiah|||0000-0002-0862-3240
author_role author
author2 Zaplana Agut, Isiah|||0000-0002-0862-3240
author2_role author
dc.subject.none.fl_str_mv Inverse kinematics
Wrist offset
Conformal geometric algebra
Àrees temàtiques de la UPC::Informàtica::Robòtica
topic Inverse kinematics
Wrist offset
Conformal geometric algebra
Àrees temàtiques de la UPC::Informàtica::Robòtica
description One of the most well-known applications of geometric algebra in engineering is providing a compact formulation of the kinematics of serial robotic manipulators. However, the use of geometric algebra in the field of robotics is still in its early stages, and there are still several open problems that can be addressed with this elegant and compact formulation. In this context, this work introduces a strategy based on conformal geometric algebra to solve the inverse kinematics problem for a class of 6DOF serial robots without a spherical wrist, for which it is known that the inverse kinematics problem generally does not have an analytical solution. To achieve this, a purely geometric strategy extending already existing contributions for the case where the robot has a spherical wrist is proposed. In particular, a point is assigned to each joint of the robot so that the problem reduces to computing the set of all possible joint positions for a given desired position and orientation of its end-effector. These points are found by defining and manipulating several geometric entities such as lines, planes, and spheres. Finally, validation with a real robot of the considered class is demonstrated both in simulation and experimentation.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-01
2025
2025-01-21
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/422216
https://dx.doi.org/10.1007/978-3-031-70251-8_25
url https://hdl.handle.net/2117/422216
https://dx.doi.org/10.1007/978-3-031-70251-8_25
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/501100000780 HE 101091792 Resilient manufacturing lines based on smart handling systems
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-114819GB-I00 CAPACIDADES INTRINSECAS PARA ROBOTS CO-TRABAJADORES
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 Springer
publisher.none.fl_str_mv Springer
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
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