{"id":"https://openalex.org/W3162655786","doi":"https://doi.org/10.1109/lra.2022.3141194","title":"Efficient Analytical Derivatives of Rigid-Body Dynamics Using Spatial Vector Algebra","display_name":"Efficient Analytical Derivatives of Rigid-Body Dynamics Using Spatial Vector Algebra","publication_year":2022,"publication_date":"2022-01-07","ids":{"openalex":"https://openalex.org/W3162655786","doi":"https://doi.org/10.1109/lra.2022.3141194","mag":"3162655786"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2022.3141194","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2022.3141194","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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 Robotics and Automation Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2105.05102","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101570823","display_name":"Shubham Singh","orcid":"https://orcid.org/0000-0002-5825-7330"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shubham Singh","raw_affiliation_strings":["Department of Aerospace Engineering, The University of Texas at Austin, Austin, TX, USA","University of Texas at Austin"],"raw_orcid":"https://orcid.org/0000-0002-5825-7330","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, The University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"University of Texas at Austin","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049959252","display_name":"Ryan P. Russell","orcid":"https://orcid.org/0000-0001-7672-0408"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ryan P. Russell","raw_affiliation_strings":["Department of Aerospace Engineering, The University of Texas at Austin, Austin, TX, USA","University of Texas at Austin"],"raw_orcid":"https://orcid.org/0000-0001-7672-0408","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, The University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"University of Texas at Austin","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029126529","display_name":"Patrick M. Wensing","orcid":"https://orcid.org/0000-0002-9041-5175"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick M. Wensing","raw_affiliation_strings":["Department of Aerospace & Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA","University of Notre Dame"],"raw_orcid":"https://orcid.org/0000-0002-9041-5175","affiliations":[{"raw_affiliation_string":"Department of Aerospace & Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7442,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.82904336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"7","issue":"2","first_page":"1776","last_page":"1783"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10879","display_name":"Robotic Locomotion and Control","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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":0.9941999912261963,"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/T12810","display_name":"Real-time simulation and control systems","score":0.9753999710083008,"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/computer-science","display_name":"Computer science","score":0.6476173400878906},{"id":"https://openalex.org/keywords/inverse-kinematics","display_name":"Inverse kinematics","score":0.5742273330688477},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5505424737930298},{"id":"https://openalex.org/keywords/inverse-dynamics","display_name":"Inverse dynamics","score":0.49930429458618164},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.492288738489151},{"id":"https://openalex.org/keywords/humanoid-robot","display_name":"Humanoid robot","score":0.4864763915538788},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.48535099625587463},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.44233936071395874},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4156843423843384},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.38625645637512207},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37594473361968994},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3613284230232239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1988200843334198},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19357308745384216}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6476173400878906},{"id":"https://openalex.org/C17816587","wikidata":"https://www.wikidata.org/wiki/Q1501872","display_name":"Inverse kinematics","level":3,"score":0.5742273330688477},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5505424737930298},{"id":"https://openalex.org/C187523126","wikidata":"https://www.wikidata.org/wiki/Q17098330","display_name":"Inverse dynamics","level":3,"score":0.49930429458618164},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.492288738489151},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.4864763915538788},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.48535099625587463},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.44233936071395874},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4156843423843384},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.38625645637512207},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37594473361968994},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3613284230232239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1988200843334198},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19357308745384216},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lra.2022.3141194","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2022.3141194","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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 Robotics and Automation Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2105.05102","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.05102","pdf_url":"https://arxiv.org/pdf/2105.05102","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2105.05102","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.05102","pdf_url":"https://arxiv.org/pdf/2105.05102","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1526408511","display_name":null,"funder_award_id":"CMMI-1835186","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G8632909241","display_name":null,"funder_award_id":"CMMI-1835013","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W618254468","https://openalex.org/W1607986725","https://openalex.org/W1971908862","https://openalex.org/W1984068279","https://openalex.org/W1987941491","https://openalex.org/W2061271987","https://openalex.org/W2087617385","https://openalex.org/W2099082465","https://openalex.org/W2101340954","https://openalex.org/W2120633566","https://openalex.org/W2151845580","https://openalex.org/W2158782408","https://openalex.org/W2198582666","https://openalex.org/W2754732998","https://openalex.org/W2771691050","https://openalex.org/W2804452275","https://openalex.org/W2804623852","https://openalex.org/W2811427562","https://openalex.org/W2902093375","https://openalex.org/W2906487027","https://openalex.org/W2942655345","https://openalex.org/W3000557965","https://openalex.org/W3081791272","https://openalex.org/W3091666534","https://openalex.org/W3104730803","https://openalex.org/W3162655786","https://openalex.org/W3194488868","https://openalex.org/W4289145348","https://openalex.org/W6753054155"],"related_works":["https://openalex.org/W2745063183","https://openalex.org/W2129850190","https://openalex.org/W4256317079","https://openalex.org/W2295425790","https://openalex.org/W1991876829","https://openalex.org/W4389009354","https://openalex.org/W2962851396","https://openalex.org/W2786331404","https://openalex.org/W4389401105","https://openalex.org/W2572731987"],"abstract_inverted_index":{"An":[0],"essential":[1],"need":[2],"for":[3,70,92,137,173,181],"many":[4],"model-based":[5],"robot":[6],"control":[7],"algorithms":[8],"is":[9,90,108],"the":[10,20,26,35,60,71,121,129,149,175,182],"ability":[11],"to":[12,39,143,148,169],"quickly":[13],"and":[14,78,103,115,134,145],"accurately":[15],"compute":[16],"partial":[17,73,130,176],"derivatives":[18,74,131,177],"of":[19,22,25,54,75,132,167,178],"equations":[21],"motion.":[23],"State":[24],"art":[27],"approaches":[28,112],"often":[29],"use":[30],"analytical":[31,155],"methods":[32,45],"based":[33,85],"on":[34,86],"chain":[36],"rule":[37],"applied":[38],"existing":[40,118],"dynamics":[41,136,180],"algorithms.":[42],"Although":[43],"these":[44,87],"are":[46,57,171],"an":[47,117],"improvement":[48],"over":[49],"finite":[50],"differences":[51],"in":[52,113,124],"terms":[53],"accuracy,":[55],"they":[56],"not":[58],"always":[59],"most":[61],"efficient.":[62],"This":[63],"letter":[64],"provides":[65],"a)":[66],"closed-form":[67],"spatial-vector":[68],"expressions":[69],"first-order":[72],"inverse":[76,133,179],"dynamics,":[77],"b)":[79],"a":[80,158],"highly":[81],"efficient":[82],"recursive":[83],"algorithm":[84,107,119],"expressions,":[88],"which":[89],"applicable":[91],"robots":[93,138],"with":[94],"general":[95],"multi-DoF":[96],"Lie":[97],"group":[98],"joints":[99],"(e.g.,":[100],"revolute,":[101],"spherical,":[102],"floating":[104],"base).":[105],"The":[106],"benchmarked":[109],"against":[110,116],"chain-rule":[111],"Fortran":[114],"from":[120,140],"Pinocchio":[122,152],"library":[123],"C++.":[125],"Tests":[126],"consider":[127],"computing":[128],"forward":[135],"ranging":[139],"kinematic":[141],"chains":[142],"humanoids":[144],"quadrupeds.":[146],"Compared":[147],"previous":[150],"open-source":[151],"implementation,":[153],"our":[154],"results":[156],"uncover":[157],"key":[159],"computational":[160],"restructuring":[161],"that":[162],"enables":[163],"efficiency":[164],"gains.":[165],"Speedups":[166],"up":[168],"1.4x":[170],"reported":[172],"calculating":[174],"50-DoF":[183],"Talos":[184],"humanoid.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4}],"updated_date":"2026-07-04T07:58:01.006859","created_date":"2025-10-10T00:00:00"}