{"id":"https://openalex.org/W2021599527","doi":"https://doi.org/10.1177/027836499101000305","title":"Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions","display_name":"Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions","publication_year":1991,"publication_date":"1991-06-01","ids":{"openalex":"https://openalex.org/W2021599527","doi":"https://doi.org/10.1177/027836499101000305","mag":"2021599527"},"language":"en","primary_location":{"id":"doi:10.1177/027836499101000305","is_oa":false,"landing_page_url":"https://doi.org/10.1177/027836499101000305","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/A5017816005","display_name":"J.C.K. Chou","orcid":null},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jack C. K. Chou","raw_affiliation_strings":["Computer Aided Design and Systems Analysis Laboratory Erik Jonsson School of Engineering and Computer Science University of Texas at Dallas Richardson, Texas 75083-0688"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Aided Design and Systems Analysis Laboratory Erik Jonsson School of Engineering and Computer Science University of Texas at Dallas Richardson, Texas 75083-0688","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039318050","display_name":"Mohamed S. Kamel","orcid":"https://orcid.org/0000-0001-6173-8082"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"M. Kamel","raw_affiliation_strings":["Pattern Analysis and Machine Intelligence Laboratory Department of Systems Design Engineering Institute for Computer Research University of Waterloo Waterloo, Ontario, Canada N2L 3G 1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pattern Analysis and Machine Intelligence Laboratory Department of Systems Design Engineering Institute for Computer Research University of Waterloo Waterloo, Ontario, Canada N2L 3G 1","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017816005"],"corresponding_institution_ids":["https://openalex.org/I162577319"],"apc_list":null,"apc_paid":null,"fwci":7.7103,"has_fulltext":false,"cited_by_count":260,"citation_normalized_percentile":{"value":0.97383194,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"10","issue":"3","first_page":"240","last_page":"254"},"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9979000091552734,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9930999875068665,"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/overdetermined-system","display_name":"Overdetermined system","score":0.9143743515014648},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.8843190670013428},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.6839944124221802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6300462484359741},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.6237068176269531},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5892284512519836},{"id":"https://openalex.org/keywords/euler-angles","display_name":"Euler angles","score":0.5132081508636475},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.49735239148139954},{"id":"https://openalex.org/keywords/moore\u2013penrose-pseudoinverse","display_name":"Moore\u2013Penrose pseudoinverse","score":0.48136597871780396},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.46304255723953247},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4360054135322571},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.43080461025238037},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4148778021335602},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3659725785255432},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36268526315689087},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.3100811839103699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26318255066871643},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2111838161945343},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19119492173194885},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18335431814193726}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.9143743515014648},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8843190670013428},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.6839944124221802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6300462484359741},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.6237068176269531},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5892284512519836},{"id":"https://openalex.org/C146160929","wikidata":"https://www.wikidata.org/wiki/Q751290","display_name":"Euler angles","level":2,"score":0.5132081508636475},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.49735239148139954},{"id":"https://openalex.org/C21556879","wikidata":"https://www.wikidata.org/wiki/Q43219517","display_name":"Moore\u2013Penrose pseudoinverse","level":3,"score":0.48136597871780396},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.46304255723953247},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4360054135322571},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.43080461025238037},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4148778021335602},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3659725785255432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36268526315689087},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3100811839103699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26318255066871643},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2111838161945343},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19119492173194885},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18335431814193726},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1177/027836499101000305","is_oa":false,"landing_page_url":"https://doi.org/10.1177/027836499101000305","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.950.9073","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.950.9073","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ijr.sagepub.com/content/10/3/240.full.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W176279239","https://openalex.org/W659484996","https://openalex.org/W1496369266","https://openalex.org/W1499641851","https://openalex.org/W1536101558","https://openalex.org/W1537482913","https://openalex.org/W1570709545","https://openalex.org/W1582353822","https://openalex.org/W1660115652","https://openalex.org/W1968056475","https://openalex.org/W1968645154","https://openalex.org/W1990717797","https://openalex.org/W1990777642","https://openalex.org/W1993267444","https://openalex.org/W2034908680","https://openalex.org/W2035368390","https://openalex.org/W2062691475","https://openalex.org/W2069999698","https://openalex.org/W2078064020","https://openalex.org/W2085858255","https://openalex.org/W2102642497","https://openalex.org/W2129440705","https://openalex.org/W2135622428","https://openalex.org/W2146563043","https://openalex.org/W2148074472","https://openalex.org/W2150474239","https://openalex.org/W2734684709","https://openalex.org/W2798909945","https://openalex.org/W2899687701","https://openalex.org/W2911709767","https://openalex.org/W3035196051","https://openalex.org/W3096982975","https://openalex.org/W3166175008","https://openalex.org/W4241187624","https://openalex.org/W4301263231"],"related_works":["https://openalex.org/W4386576538","https://openalex.org/W60923334","https://openalex.org/W4382519919","https://openalex.org/W2125322432","https://openalex.org/W1981326443","https://openalex.org/W2063945179","https://openalex.org/W134667518","https://openalex.org/W2087304636","https://openalex.org/W1988771669","https://openalex.org/W4224254018"],"abstract_inverted_index":{"The":[0,135],"problem":[1],"of":[2,13,27,41,109,118,124,130,154,161],"finding":[3],"the":[4,10,18,28,62,84,115,128,140,152,155,162],"relative":[5],"position":[6,158],"and":[7,17,47,68,139,159],"orientation":[8,160],"between":[9],"reference":[11],"frames":[12],"a":[14,24,94],"link-mounted":[15],"sensor":[16],"link":[19],"has":[20],"been":[21],"formulated":[22],"as":[23],"kinematic":[25,63],"equation":[26,64],"form":[29],"H":[30,32,35,37],"l":[31],"x":[33,36],"=":[34],"c":[38],"in":[39,147],"terms":[40],"homogeneous":[42],"transformation":[43],"matrices":[44],"by":[45],"Shiu":[46],"Ahmad":[48],"(1987).":[49],"In":[50],"this":[51],"article,":[52],"normal":[53],"ized":[54],"quaternions":[55],"(Euler":[56],"parameters)":[57],"are":[58,81,101,133],"used":[59],"to":[60,78,105],"transform":[61],"into":[65],"two":[66,97],"simple":[67],"structured":[69],"linear":[70],"systems":[71,80],"with":[72,88],"rank-deficient":[73],"coefficient":[74],"matrices.":[75],"Closed-form":[76],"solutions":[77],"these":[79,131],"derived":[82],"using":[83],"generalized":[85],"inverse":[86],"method":[87],"singular-value":[89],"decomposition":[90],"analysis.":[91],"To":[92],"obtain":[93],"unique":[95],"solution,":[96],"distinct":[98],"robot":[99],"movements":[100],"required.":[102],"This":[103],"leads":[104],"an":[106],"overdetermined":[107],"system":[108],"equations.":[110],"A":[111,122],"criterion":[112],"for":[113,127],"selecting":[114],"independent":[116],"set":[117,123],"equations":[119,132],"is":[120],"developed.":[121],"closed-form":[125],"formulae":[126,142],"solution":[129,141],"derived.":[134],"selection":[136],"crite":[137],"rion":[138],"can":[143],"be":[144],"easily":[145],"incorporated":[146],"application":[148],"programs":[149],"that":[150],"require":[151],"calculation":[153],"rela":[156],"tive":[157],"sensor.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":8}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}