{"id":"https://openalex.org/W2051877509","doi":"https://doi.org/10.1007/s10846-012-9679-4","title":"Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach","display_name":"Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach","publication_year":2012,"publication_date":"2012-05-17","ids":{"openalex":"https://openalex.org/W2051877509","doi":"https://doi.org/10.1007/s10846-012-9679-4","mag":"2051877509"},"language":"en","primary_location":{"id":"doi:10.1007/s10846-012-9679-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10846-012-9679-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10846-012-9679-4.pdf","source":{"id":"https://openalex.org/S91329792","display_name":"Journal of Intelligent & Robotic Systems","issn_l":"0921-0296","issn":["0921-0296","1573-0409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Robotic Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10846-012-9679-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051751849","display_name":"Joanna Karpi\u0144ska","orcid":null},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Joanna Karpi\u0144ska","raw_affiliation_strings":["Institute of Computer Engineering, Control and Robotics, Wroc\u0142aw University of Technology, ul. Janiszewskiego 11/17, 50\u2013372, Wroc\u0142aw, Poland","Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Wroclaw, Poland 50-372"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Engineering, Control and Robotics, Wroc\u0142aw University of Technology, ul. Janiszewskiego 11/17, 50\u2013372, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345"]},{"raw_affiliation_string":"Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Wroclaw, Poland 50-372","institution_ids":["https://openalex.org/I11923345"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036247461","display_name":"Krzysztof Tcho\u0144","orcid":"https://orcid.org/0000-0002-5691-9644"},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Tcho\u0144","raw_affiliation_strings":["Institute of Computer Engineering, Control and Robotics, Wroc\u0142aw University of Technology, ul. Janiszewskiego 11/17, 50\u2013372, Wroc\u0142aw, Poland","Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Wroclaw, Poland 50-372"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Engineering, Control and Robotics, Wroc\u0142aw University of Technology, ul. Janiszewskiego 11/17, 50\u2013372, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345"]},{"raw_affiliation_string":"Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Wroclaw, Poland 50-372","institution_ids":["https://openalex.org/I11923345"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077305204","display_name":"Mariusz Janiak","orcid":"https://orcid.org/0000-0002-5258-5296"},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mariusz Janiak","raw_affiliation_strings":["Institute of Computer Engineering, Control and Robotics, Wroc\u0142aw University of Technology, ul. Janiszewskiego 11/17, 50\u2013372, Wroc\u0142aw, Poland","Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Wroclaw, Poland 50-372"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Engineering, Control and Robotics, Wroc\u0142aw University of Technology, ul. Janiszewskiego 11/17, 50\u2013372, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345"]},{"raw_affiliation_string":"Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Wroclaw, Poland 50-372","institution_ids":["https://openalex.org/I11923345"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051751849"],"corresponding_institution_ids":["https://openalex.org/I11923345"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.6891,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.86552023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"68","issue":"3-4","first_page":"211","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11525","display_name":"Piezoelectric Actuators and Control","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.9017466306686401},{"id":"https://openalex.org/keywords/inverse-kinematics","display_name":"Inverse kinematics","score":0.7583605051040649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6369251608848572},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6173322200775146},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.5204315781593323},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.5094357132911682},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.46255767345428467},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3971266746520996},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3889314532279968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31262099742889404},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1985781490802765},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.08767762780189514},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05762818455696106}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.9017466306686401},{"id":"https://openalex.org/C17816587","wikidata":"https://www.wikidata.org/wiki/Q1501872","display_name":"Inverse kinematics","level":3,"score":0.7583605051040649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6369251608848572},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6173322200775146},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.5204315781593323},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.5094357132911682},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.46255767345428467},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3971266746520996},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3889314532279968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31262099742889404},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1985781490802765},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.08767762780189514},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05762818455696106}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10846-012-9679-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10846-012-9679-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10846-012-9679-4.pdf","source":{"id":"https://openalex.org/S91329792","display_name":"Journal of Intelligent & Robotic Systems","issn_l":"0921-0296","issn":["0921-0296","1573-0409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Robotic Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10846-012-9679-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10846-012-9679-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10846-012-9679-4.pdf","source":{"id":"https://openalex.org/S91329792","display_name":"Journal of Intelligent & Robotic Systems","issn_l":"0921-0296","issn":["0921-0296","1573-0409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Robotic Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2051877509.pdf","grobid_xml":"https://content.openalex.org/works/W2051877509.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W422604666","https://openalex.org/W653564841","https://openalex.org/W797792922","https://openalex.org/W1549194173","https://openalex.org/W1560270123","https://openalex.org/W1582076359","https://openalex.org/W1969911625","https://openalex.org/W1973295320","https://openalex.org/W2034190982","https://openalex.org/W2038533008","https://openalex.org/W2039927751","https://openalex.org/W2070133526","https://openalex.org/W2080642692","https://openalex.org/W2097677484","https://openalex.org/W2119109765","https://openalex.org/W2124817468","https://openalex.org/W2129644801","https://openalex.org/W2129995994","https://openalex.org/W2144629157"],"related_works":["https://openalex.org/W3126987580","https://openalex.org/W2156428778","https://openalex.org/W3021041098","https://openalex.org/W2573079680","https://openalex.org/W3127401300","https://openalex.org/W1991238271","https://openalex.org/W90735542","https://openalex.org/W1978469541","https://openalex.org/W1979286982","https://openalex.org/W68594487"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,19,22,27,41,55,65,74,93,110,117,127,130,136,152,156,166,174],"approximation":[4,20,94,111,121],"problem":[5,112],"of":[6,21,72,95,119,129,132,135,148,155],"Jacobian":[7,23,29,56,67,77,139],"inverse":[8,25,58,140,182],"kinematics":[9,141,153],"algorithms":[10,32,142],"for":[11,180],"redundant":[12],"robotic":[13],"manipulators.":[14],"Specifically,":[15],"we":[16],"focus":[17],"on":[18,92],"pseudo":[24,57],"by":[26,40,103,146],"extended":[28,66,76,138],"algorithm.":[30],"The":[31,51,81],"are":[33,79],"defined":[34],"as":[35,87,116],"certain":[36],"dynamic":[37],"systems":[38],"driven":[39],"task":[42],"space":[43],"error,":[44],"and":[45,90,124],"identified":[46],"with":[47,64],"vector":[48],"field":[49],"distributions.":[50],"distribution":[52,98],"corresponding":[53],"to":[54,86],"is":[59,68,84,163],"non-integrable,":[60],"while":[61,173],"that":[62,165],"associated":[63],"integrable.":[69],"Two":[70],"methods":[71,128],"devising":[73],"approximating":[75],"algorithm":[78],"examined.":[80],"first":[82],"method":[83,169,176],"referred":[85],"differential":[88,167],"geometric,":[89],"relies":[91],"a":[96,101,171,177],"non-integrable":[97],"(in":[99],"fact:":[100],"codistribution)":[102],"an":[104,108,120],"integrable":[105],"one.":[106],"As":[107],"alternative,":[109],"has":[113,143],"been":[114,144],"formulated":[115],"minimization":[118],"error":[122],"functional,":[123],"solved":[125],"using":[126],"calculus":[131],"variations.":[133],"Performance":[134],"obtained":[137],"compared":[145],"means":[147],"computer":[149],"simulations":[150],"involving":[151],"model":[154],"7":[157],"dof":[158],"industrial":[159],"manipulator":[160],"POLYCRANK.":[161],"It":[162],"concluded":[164],"geometric":[168],"offers":[170],"rapid,":[172],"variational":[175],"systematic":[178],"tool":[179],"solving":[181],"kinematic":[183],"problems.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
