{"id":"https://openalex.org/W2086790315","doi":"https://doi.org/10.1109/tac.2009.2037480","title":"Differential Flatness of a Class of $n$-DOF Planar Manipulators Driven by 1 or 2 Actuators","display_name":"Differential Flatness of a Class of $n$-DOF Planar Manipulators Driven by 1 or 2 Actuators","publication_year":2010,"publication_date":"2010-01-12","ids":{"openalex":"https://openalex.org/W2086790315","doi":"https://doi.org/10.1109/tac.2009.2037480","mag":"2086790315"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2009.2037480","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2037480","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2117/7799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020730717","display_name":"Jaume Franch","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. Franch","raw_affiliation_strings":["Department of Applied Mathematics, Universitat Politecnica de Catalunya, Barcelona, Spain","Dept. of Appl. Math. 4, Univ. Politec. de Catalunya, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Universitat Politecnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Dept. of Appl. Math. 4, Univ. Politec. de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066608996","display_name":"Sunil K. Agrawal","orcid":"https://orcid.org/0000-0002-4008-1437"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S.K. Agrawal","raw_affiliation_strings":["Mechanical Engineering Department, University of Delaware, Newark, DE, USA","Mech. Eng. Dept., Univ. of Delaware, Newark, DE, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Department, University of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]},{"raw_affiliation_string":"Mech. Eng. Dept., Univ. of Delaware, Newark, DE, USA#TAB#","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103015212","display_name":"Vivek Sangwan","orcid":"https://orcid.org/0000-0003-4610-0966"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"V. Sangwan","raw_affiliation_strings":["Department of Mechanical Engineering, University of Delaware, Newark, DE, USA","Dept. of Mech. Eng., Univ. of Delaware, Newark, DE, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]},{"raw_affiliation_string":"Dept. of Mech. Eng., Univ. of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7767,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.95689727,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"55","issue":"2","first_page":"548","last_page":"554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9977999925613403,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9977999925613403,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9976000189781189,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9973999857902527,"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/actuator","display_name":"Actuator","score":0.6488004326820374},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6155614256858826},{"id":"https://openalex.org/keywords/flatness","display_name":"Flatness (cosmology)","score":0.608939528465271},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.601448655128479},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5898448824882507},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45152655243873596},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4176808297634125},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36036044359207153},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3536642789840698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.323703408241272},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26979392766952515},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.23633015155792236},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14106053113937378},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11555925011634827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08236953616142273},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07239830493927002}],"concepts":[{"id":"https://openalex.org/C172707124","wikidata":"https://www.wikidata.org/wiki/Q423488","display_name":"Actuator","level":2,"score":0.6488004326820374},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6155614256858826},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.608939528465271},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.601448655128479},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5898448824882507},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45152655243873596},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4176808297634125},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36036044359207153},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3536642789840698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.323703408241272},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26979392766952515},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.23633015155792236},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14106053113937378},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11555925011634827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08236953616142273},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07239830493927002},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2009.2037480","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2037480","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:dnet:upcommonspor::e98d8fd319b3a978ea477fe30c42052a","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/7799","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/7799","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/7799","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:repository.hanyang.ac.kr:20.500.11754/86981","is_oa":false,"landing_page_url":"http://repository.hanyang.ac.kr/handle/20.500.11754/86981","pdf_url":null,"source":{"id":"https://openalex.org/S4306401328","display_name":"The Royal Society of Chemistry\u2019s Journals, Books and Databases (The Royal Society of Chemistry)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2751430930","host_organization_name":"Royal Society of Chemistry","host_organization_lineage":["https://openalex.org/I2751430930"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:dnet:upcommonspor::e98d8fd319b3a978ea477fe30c42052a","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/7799","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W48920821","https://openalex.org/W160955151","https://openalex.org/W1964373008","https://openalex.org/W1971902590","https://openalex.org/W1981733589","https://openalex.org/W2056295510","https://openalex.org/W2059234421","https://openalex.org/W2065297540","https://openalex.org/W2094004401","https://openalex.org/W2112396687","https://openalex.org/W2665063868","https://openalex.org/W6664423988","https://openalex.org/W6674369579"],"related_works":["https://openalex.org/W2789295429","https://openalex.org/W2743501974","https://openalex.org/W2540573954","https://openalex.org/W2782313579","https://openalex.org/W2066314436","https://openalex.org/W2588834286","https://openalex.org/W2510927817","https://openalex.org/W2325727422","https://openalex.org/W2003275872","https://openalex.org/W2140790411"],"abstract_inverted_index":{"A":[0],"fully":[1],"actuated":[2],"system":[3,12],"can":[4,41,51],"execute":[5],"any":[6],"joint":[7,17,137],"trajectory.":[8],"However,":[9],"if":[10,124],"a":[11,79,87],"is":[13,126],"under-actuated,":[14],"not":[15],"all":[16],"trajectories":[18],"are":[19,33],"attainable.":[20],"The":[21],"authors":[22],"have":[23],"actively":[24],"pursued":[25],"novel":[26],"designs":[27],"of":[28,73,81,111,132],"under-actuated":[29,83],"robotic":[30],"arms":[31],"which":[32],"both":[34],"controllable":[35],"and":[36],"feedback":[37],"linearizable.":[38],"These":[39],"robots":[40,85],"perform":[42],"point-to-point":[43],"motions":[44],"in":[45],"the":[46,67,71,103],"state":[47],"space,":[48],"but":[49,91],"potentially":[50],"be":[52],"designed":[53,127],"to":[54],"work":[55],"with":[56,60],"fewer":[57],"actuators,":[58],"hence":[59],"lower":[61],"cost.":[62],"With":[63],"this":[64],"same":[65],"spirit,":[66],"technical":[68,100],"note":[69,101],"investigates":[70],"property":[72],"<i":[74,107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[75,108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">differential":[76],"flatness</i>":[77],"for":[78],"class":[80],"planar":[82,120],"open-chain":[84],"having":[86],"specific":[88],"inertia":[89],"distribution,":[90],"driven":[92],"by":[93],"only":[94],"one":[95,112],"or":[96,113],"two":[97,114],"actuators.":[98],"This":[99],"addresses":[102],"following":[104],"theoretical":[105],"question:":[106],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">what":[109],"placement":[110],"actuators":[115],"will":[116],"make":[117],"an":[118],"n-DOF":[119],"robot":[121],"differentially":[122],"flat":[123],"it":[125],"so":[128],"that":[129],"its":[130],"center":[131],"mass":[133],"always":[134],"lies":[135],"at":[136],"2?</i>":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}