{"id":"https://openalex.org/W2134063392","doi":"https://doi.org/10.1177/0278364907078094","title":"Motion Planning for a Class of Planar Closed-chain Manipulators","display_name":"Motion Planning for a Class of Planar Closed-chain Manipulators","publication_year":2007,"publication_date":"2007-04-10","ids":{"openalex":"https://openalex.org/W2134063392","doi":"https://doi.org/10.1177/0278364907078094","mag":"2134063392"},"language":"en","primary_location":{"id":"doi:10.1177/0278364907078094","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0278364907078094","pdf_url":null,"source":{"id":"https://openalex.org/S73484101","display_name":"The International Journal of Robotics Research","issn_l":"0278-3649","issn":["0278-3649","1741-3176"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of Robotics Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079590419","display_name":"Nir Shvalb","orcid":"https://orcid.org/0000-0001-8246-3727"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]},{"id":"https://openalex.org/I4394709267","display_name":"Israel Institute","ror":"https://ror.org/00xfkzq83","country_code":null,"type":"nonprofit","lineage":["https://openalex.org/I4394709267"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"N. Shvalb","raw_affiliation_strings":["Department of ME, Technion-Israel Institute of Technology, Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ME, Technion-Israel Institute of Technology, Israel,","institution_ids":["https://openalex.org/I174306211","https://openalex.org/I4394709267"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110562045","display_name":"M. Shoham","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]},{"id":"https://openalex.org/I4394709267","display_name":"Israel Institute","ror":"https://ror.org/00xfkzq83","country_code":null,"type":"nonprofit","lineage":["https://openalex.org/I4394709267"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"M. Shoham","raw_affiliation_strings":["Department of ME, Technion-Israel Institute of Technology, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ME, Technion-Israel Institute of Technology, Israel","institution_ids":["https://openalex.org/I174306211","https://openalex.org/I4394709267"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085282379","display_name":"G. Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. Liu","raw_affiliation_strings":["Department of Computer Science, Stanford University, Stanford, CA, USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA, USA,","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032562243","display_name":"Jeff Trinkle","orcid":"https://orcid.org/0000-0002-9877-2003"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J.C. Trinkle","raw_affiliation_strings":["Department of Computer Science, Rensselaer Polytechnic Institute, USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rensselaer Polytechnic Institute, USA,","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032562243","https://openalex.org/A5079590419","https://openalex.org/A5085282379"],"corresponding_institution_ids":["https://openalex.org/I165799507","https://openalex.org/I174306211","https://openalex.org/I4394709267","https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":1.9429,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.8744483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"5","first_page":"457","last_page":"473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9993000030517578,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.8063890933990479},{"id":"https://openalex.org/keywords/motion-planning","display_name":"Motion planning","score":0.7676455974578857},{"id":"https://openalex.org/keywords/configuration-space","display_name":"Configuration space","score":0.5964553952217102},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5521103143692017},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5500789284706116},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.5189078450202942},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5074092745780945},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4993436336517334},{"id":"https://openalex.org/keywords/manipulator","display_name":"Manipulator (device)","score":0.49848365783691406},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.46393778920173645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45066678524017334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4446636736392975},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.2997884154319763},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2561274766921997},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2247685194015503},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20990383625030518},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16540515422821045}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.8063890933990479},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.7676455974578857},{"id":"https://openalex.org/C90738871","wikidata":"https://www.wikidata.org/wiki/Q41642869","display_name":"Configuration space","level":2,"score":0.5964553952217102},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5521103143692017},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5500789284706116},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5189078450202942},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5074092745780945},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4993436336517334},{"id":"https://openalex.org/C2781347998","wikidata":"https://www.wikidata.org/wiki/Q1587588","display_name":"Manipulator (device)","level":3,"score":0.49848365783691406},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.46393778920173645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45066678524017334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4446636736392975},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.2997884154319763},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2561274766921997},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2247685194015503},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20990383625030518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16540515422821045},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/0278364907078094","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0278364907078094","pdf_url":null,"source":{"id":"https://openalex.org/S73484101","display_name":"The International Journal of Robotics Research","issn_l":"0278-3649","issn":["0278-3649","1741-3176"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of Robotics Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.8100000023841858,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W35589853","https://openalex.org/W101508493","https://openalex.org/W111644038","https://openalex.org/W1493143088","https://openalex.org/W1495392417","https://openalex.org/W1509580513","https://openalex.org/W1516027685","https://openalex.org/W1520750594","https://openalex.org/W1520783297","https://openalex.org/W1531225991","https://openalex.org/W1763528081","https://openalex.org/W1847506590","https://openalex.org/W1863997888","https://openalex.org/W1995146364","https://openalex.org/W2005154889","https://openalex.org/W2033013465","https://openalex.org/W2036016432","https://openalex.org/W2047406013","https://openalex.org/W2048159974","https://openalex.org/W2056415051","https://openalex.org/W2058240764","https://openalex.org/W2063001312","https://openalex.org/W2066118009","https://openalex.org/W2093547815","https://openalex.org/W2096636360","https://openalex.org/W2107535513","https://openalex.org/W2110333200","https://openalex.org/W2125973284","https://openalex.org/W2127705885","https://openalex.org/W2128990851","https://openalex.org/W2141664020","https://openalex.org/W2142811920","https://openalex.org/W2150500908","https://openalex.org/W2156706225","https://openalex.org/W2156969101","https://openalex.org/W2158207287","https://openalex.org/W2159722616","https://openalex.org/W2160352419","https://openalex.org/W2163426622","https://openalex.org/W2170192219","https://openalex.org/W2171266831","https://openalex.org/W2198471588","https://openalex.org/W2341668857","https://openalex.org/W2600643276","https://openalex.org/W2623660146","https://openalex.org/W2966015659","https://openalex.org/W3104753760","https://openalex.org/W4385674282","https://openalex.org/W6629573421"],"related_works":["https://openalex.org/W2005695917","https://openalex.org/W2333571655","https://openalex.org/W3004930912","https://openalex.org/W2104320275","https://openalex.org/W2111158727","https://openalex.org/W1510039162","https://openalex.org/W2112736381","https://openalex.org/W2106317420","https://openalex.org/W2120794627","https://openalex.org/W2107702345"],"abstract_inverted_index":{"The":[0,39,76],"paper":[1],"reports":[2],"studies":[3],"on":[4],"the":[5,26,34,37,60,64,69,80,91,101],"motion":[6],"planning":[7,70],"problem":[8,71],"for":[9],"planar":[10,43],"star-shaped":[11],"manipulators.":[12],"These":[13],"manipulators":[14],"are":[15,103],"formed":[16],"by":[17],"joining":[18],"k":[19,47],"\u201clegs\u201d":[20],"to":[21,36,58],"a":[22,42,97],"common":[23],"point":[24],"(like":[25],"thorax":[27],"of":[28,63,79,94],"an":[29],"insect)":[30],"and":[31],"then":[32],"fixing":[33],"\u201cfeet\u201d":[35],"ground.":[38],"result":[40],"is":[41,56,82,90],"parallel":[44],"manipulator":[45],"with":[46],"-":[48],"1":[49],"independent":[50],"closed":[51],"loops.":[52],"A":[53],"topological":[54],"analysis":[55],"used":[57],"understand":[59],"global":[61],"structure":[62],"configuration":[65],"space":[66],"so":[67],"that":[68],"can":[72],"be":[73],"solved":[74],"exactly.":[75],"worst-case":[77],"complexity":[78],"algorithm":[81],"O(k":[83],"3":[84,86],"N":[85,89],"),":[87],"where":[88],"maximum":[92],"number":[93],"links":[95],"in":[96],"leg.":[98],"Examples":[99],"illustrating":[100],"method":[102],"given.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}