{"id":"https://openalex.org/W2566428922","doi":"https://doi.org/10.1145/3018610.3018629","title":"Formal foundations of 3D geometry to model robot manipulators","display_name":"Formal foundations of 3D geometry to model robot manipulators","publication_year":2016,"publication_date":"2016-12-22","ids":{"openalex":"https://openalex.org/W2566428922","doi":"https://doi.org/10.1145/3018610.3018629","mag":"2566428922"},"language":"en","primary_location":{"id":"doi:10.1145/3018610.3018629","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3018610.3018629","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"type":"preprint","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/A5004449937","display_name":"Reynald Affeldt","orcid":"https://orcid.org/0000-0002-2327-953X"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Reynald Affeldt","raw_affiliation_strings":["AIST, Japan"],"affiliations":[{"raw_affiliation_string":"AIST, Japan","institution_ids":["https://openalex.org/I73613424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107271231","display_name":"Cyril Cohen","orcid":"https://orcid.org/0000-0003-3540-1050"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cyril Cohen","raw_affiliation_strings":["Inria, France"],"affiliations":[{"raw_affiliation_string":"Inria, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004449937"],"corresponding_institution_ids":["https://openalex.org/I73613424"],"apc_list":null,"apc_paid":null,"fwci":0.48309909,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.72476006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"30","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9921000003814697,"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":0.9921000003814697,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10653","display_name":"Robot Manipulation and Learning","score":0.982699990272522,"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/quaternion","display_name":"Quaternion","score":0.7653933763504028},{"id":"https://openalex.org/keywords/screw-theory","display_name":"Screw theory","score":0.7177442908287048},{"id":"https://openalex.org/keywords/scara","display_name":"SCARA","score":0.6548205614089966},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5913808345794678},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.5773194432258606},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.5380728840827942},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5044165849685669},{"id":"https://openalex.org/keywords/rigid-body","display_name":"Rigid body","score":0.4943277835845947},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45814085006713867},{"id":"https://openalex.org/keywords/robot-kinematics","display_name":"Robot kinematics","score":0.4264466166496277},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.42248275876045227},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.42081621289253235},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4004063308238983},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3347119688987732},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2458178699016571},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2271289825439453},{"id":"https://openalex.org/keywords/mobile-robot","display_name":"Mobile robot","score":0.1040116548538208}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.7653933763504028},{"id":"https://openalex.org/C18788176","wikidata":"https://www.wikidata.org/wiki/Q7891441","display_name":"Screw theory","level":3,"score":0.7177442908287048},{"id":"https://openalex.org/C158732272","wikidata":"https://www.wikidata.org/wiki/Q1484792","display_name":"SCARA","level":3,"score":0.6548205614089966},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5913808345794678},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.5773194432258606},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.5380728840827942},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5044165849685669},{"id":"https://openalex.org/C145980571","wikidata":"https://www.wikidata.org/wiki/Q192788","display_name":"Rigid body","level":2,"score":0.4943277835845947},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45814085006713867},{"id":"https://openalex.org/C74222875","wikidata":"https://www.wikidata.org/wiki/Q16000312","display_name":"Robot kinematics","level":4,"score":0.4264466166496277},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.42248275876045227},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.42081621289253235},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4004063308238983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3347119688987732},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2458178699016571},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2271289825439453},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.1040116548538208},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3018610.3018629","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3018610.3018629","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W318050187","https://openalex.org/W1486558830","https://openalex.org/W1498091397","https://openalex.org/W1509235676","https://openalex.org/W1526117436","https://openalex.org/W1560094997","https://openalex.org/W1564897360","https://openalex.org/W1569094508","https://openalex.org/W1646312512","https://openalex.org/W1649228311","https://openalex.org/W1750856813","https://openalex.org/W1768814311","https://openalex.org/W2082183470","https://openalex.org/W2091456056","https://openalex.org/W2113181166","https://openalex.org/W2134124371","https://openalex.org/W2147877794","https://openalex.org/W2164688709","https://openalex.org/W2277766137","https://openalex.org/W2305158040","https://openalex.org/W2566428922","https://openalex.org/W2951164375","https://openalex.org/W2963504389","https://openalex.org/W6630702416"],"related_works":["https://openalex.org/W2914794850","https://openalex.org/W2165354764","https://openalex.org/W2377423241","https://openalex.org/W2372996908","https://openalex.org/W2084751898","https://openalex.org/W2917119513","https://openalex.org/W3037787320","https://openalex.org/W2792156965","https://openalex.org/W2030376804","https://openalex.org/W1921647739"],"abstract_inverted_index":{"We":[0,91],"are":[1],"interested":[2],"in":[3,34,63],"the":[4,15,28,35,44,49,52,57,66,76,97,123,133,156],"formal":[5],"specification":[6],"of":[7,10,27,30,51,56,59,65,99,107,112,122,126],"safety":[8],"properties":[9],"robot":[11,61,146,158],"manipulators":[12],"down":[13],"to":[14,42,95,144,155],"mathematical":[16],"physics.":[17],"To":[18],"this":[19,150],"end,":[20],"we":[21,102,118,148],"have":[22],"been":[23],"developing":[24,88],"a":[25,60,81,104,120],"formalization":[26,72,121],"mathematics":[29],"rigid":[31,127],"body":[32,128],"transformations":[33],"Coq":[36],"proof-assistant.":[37],"It":[38],"can":[39],"be":[40],"used":[41],"address":[43],"forward":[45],"kinematics":[46],"problem,":[47],"i.e.,":[48],"computation":[50],"position":[53],"and":[54,68,86,115,136],"orientation":[55],"end-effector":[58],"manipulator":[62],"terms":[64],"link":[67],"joint":[69],"parameters.":[70],"Our":[71],"starts":[73],"by":[74,87,152],"extending":[75],"Mathematical":[77],"Components":[78],"library":[79],"with":[80],"new":[82],"theory":[83,106],"for":[84],"angles":[85],"three-dimensional":[89,108],"geometry.":[90],"use":[92],"these":[93],"theories":[94],"formalize":[96,103,145],"foundations":[98],"robotics.":[100],"First,":[101],"comprehensive":[105],"rotations,":[109],"including":[110],"exponentials":[111],"skew-symmetric":[113],"matrices":[114],"quaternions.":[116],"Then,":[117],"provide":[119],"various":[124],"representations":[125],"transformations:":[129],"isometries,":[130],"homogeneous":[131],"representation,":[132],"Denavit-Hartenberg":[134],"convention,":[135],"screw":[137],"motions.":[138],"These":[139],"ingredients":[140],"make":[141],"it":[142],"possible":[143],"manipulators:":[147],"illustrate":[149],"aspect":[151],"an":[153],"application":[154],"SCARA":[157],"manipulator.":[159]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
