{"id":"https://openalex.org/W3134351413","doi":"https://doi.org/10.1109/icra48506.2021.9561773","title":"Nth Order Analytical Time Derivatives of Inverse Dynamics in Recursive and Closed Forms","display_name":"Nth Order Analytical Time Derivatives of Inverse Dynamics in Recursive and Closed Forms","publication_year":2021,"publication_date":"2021-05-30","ids":{"openalex":"https://openalex.org/W3134351413","doi":"https://doi.org/10.1109/icra48506.2021.9561773","mag":"3134351413"},"language":"en","primary_location":{"id":"doi:10.1109/icra48506.2021.9561773","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra48506.2021.9561773","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Conference on Robotics and Automation (ICRA)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.05941","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036934435","display_name":"Shivesh Kumar","orcid":"https://orcid.org/0000-0002-6254-3882"},"institutions":[{"id":"https://openalex.org/I33256026","display_name":"German Research Centre for Artificial Intelligence","ror":"https://ror.org/01ayc5b57","country_code":"DE","type":"funder","lineage":["https://openalex.org/I33256026"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Shivesh Kumar","raw_affiliation_strings":["Robotics Innovation Center, DFKI GmbH, Bremen, Germany","German Research Centre for Artificial Intelligence"],"affiliations":[{"raw_affiliation_string":"Robotics Innovation Center, DFKI GmbH, Bremen, Germany","institution_ids":["https://openalex.org/I33256026"]},{"raw_affiliation_string":"German Research Centre for Artificial Intelligence","institution_ids":["https://openalex.org/I33256026"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088500114","display_name":"Andreas Mueller","orcid":"https://orcid.org/0000-0002-2349-9428"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Andreas Muller","raw_affiliation_strings":["Institute of Robotics, Johannes Kepler University, Linz, Austria","JOHANNES KEPLER UNIVERSITY LINZ"],"affiliations":[{"raw_affiliation_string":"Institute of Robotics, Johannes Kepler University, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"JOHANNES KEPLER UNIVERSITY LINZ","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036934435"],"corresponding_institution_ids":["https://openalex.org/I33256026"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02150631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":null,"first_page":"1918","last_page":"1924"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9991000294685364,"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":0.9961000084877014,"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/inverse-dynamics","display_name":"Inverse dynamics","score":0.7774388790130615},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.6738618612289429},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5912245512008667},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.5731642246246338},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.55439293384552},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5447138547897339},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.5080869197845459},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4936572015285492},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4789767265319824},{"id":"https://openalex.org/keywords/rigid-body","display_name":"Rigid body","score":0.4644577205181122},{"id":"https://openalex.org/keywords/multibody-system","display_name":"Multibody system","score":0.4499739110469818},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.4159308671951294},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4112718105316162},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.3991051912307739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38465142250061035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3663811683654785},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2547292709350586},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.22603651881217957},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.18700271844863892},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13376522064208984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08378246426582336}],"concepts":[{"id":"https://openalex.org/C187523126","wikidata":"https://www.wikidata.org/wiki/Q17098330","display_name":"Inverse dynamics","level":3,"score":0.7774388790130615},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.6738618612289429},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5912245512008667},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5731642246246338},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.55439293384552},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5447138547897339},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.5080869197845459},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4936572015285492},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4789767265319824},{"id":"https://openalex.org/C145980571","wikidata":"https://www.wikidata.org/wiki/Q192788","display_name":"Rigid body","level":2,"score":0.4644577205181122},{"id":"https://openalex.org/C67865112","wikidata":"https://www.wikidata.org/wiki/Q1917564","display_name":"Multibody system","level":2,"score":0.4499739110469818},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.4159308671951294},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4112718105316162},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.3991051912307739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38465142250061035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3663811683654785},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2547292709350586},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.22603651881217957},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18700271844863892},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13376522064208984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08378246426582336},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/icra48506.2021.9561773","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra48506.2021.9561773","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Conference on Robotics and Automation (ICRA)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2103.05941","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.05941","pdf_url":"https://arxiv.org/pdf/2103.05941","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"},{"id":"mag:3134351413","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2103.05941.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2103.05941","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.05941","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.05941","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.05941","pdf_url":"https://arxiv.org/pdf/2103.05941","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":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311649","display_name":"Ministry of Education","ror":"https://ror.org/036nq5137"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320321602","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt","ror":"https://ror.org/04bwf3e34"},{"id":"https://openalex.org/F4320326288","display_name":"K2","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3134351413.pdf","grobid_xml":"https://content.openalex.org/works/W3134351413.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1971908862","https://openalex.org/W2010685722","https://openalex.org/W2049437759","https://openalex.org/W2151845580","https://openalex.org/W2155415241","https://openalex.org/W2162036575","https://openalex.org/W2211016660","https://openalex.org/W2297730688","https://openalex.org/W2497564812","https://openalex.org/W2510832559","https://openalex.org/W2734368255","https://openalex.org/W2736021157","https://openalex.org/W2737832245","https://openalex.org/W2754732998","https://openalex.org/W2783824884","https://openalex.org/W2784320602","https://openalex.org/W2804623852","https://openalex.org/W2964222556","https://openalex.org/W2969701144","https://openalex.org/W2973043785","https://openalex.org/W2990512535","https://openalex.org/W2996367923","https://openalex.org/W3134319763","https://openalex.org/W4255617101","https://openalex.org/W4399469378","https://openalex.org/W6767997701","https://openalex.org/W6772590578"],"related_works":["https://openalex.org/W3206521305","https://openalex.org/W2155286978","https://openalex.org/W2083143597","https://openalex.org/W2737832245","https://openalex.org/W819531695","https://openalex.org/W635100070","https://openalex.org/W1503201024","https://openalex.org/W2165433399","https://openalex.org/W809714548","https://openalex.org/W1966155599","https://openalex.org/W2838832949","https://openalex.org/W164371611","https://openalex.org/W2028090589","https://openalex.org/W2149693525","https://openalex.org/W2014343821","https://openalex.org/W2151771131","https://openalex.org/W2126511524","https://openalex.org/W212185190","https://openalex.org/W2163648109","https://openalex.org/W1946534905"],"abstract_inverted_index":{"Derivatives":[0],"of":[1,3,26,49,54,57,71,90,104],"equations":[2,56],"motion":[4,58],"describing":[5],"the":[6,15,46,50,55,72,81,88,93],"rigid":[7],"body":[8],"dynamics":[9],"are":[10],"becoming":[11],"increasingly":[12],"relevant":[13],"for":[14,101],"robotics":[16],"community":[17],"and":[18,24,31,77],"find":[19],"many":[20],"applications":[21],"in":[22,37,74],"design":[23],"control":[25,51],"robotic":[27,106],"systems.":[28],"Controlling":[29],"robots,":[30],"multibody":[32],"systems":[33],"comprising":[34],"elastic":[35],"components":[36],"particular,":[38],"not":[39],"only":[40],"requires":[41],"smooth":[42],"trajectories":[43],"but":[44],"also":[45],"time":[47,69],"derivatives":[48,70],"forces/torques,":[52],"hence":[53],"(EOM).":[59],"This":[60],"paper":[61],"presents":[62],"novel":[63],"n":[64],"<sup":[65],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">th</sup>":[67],"order":[68],"EOM":[73],"both":[75],"closed":[76],"recursive":[78],"forms.":[79],"While":[80],"former":[82],"provides":[83],"a":[84],"direct":[85],"insight":[86],"into":[87],"structure":[89],"these":[91],"derivatives,":[92],"latter":[94],"leads":[95],"to":[96],"their":[97],"highly":[98],"efficient":[99],"implementation":[100],"large":[102],"degree":[103],"freedom":[105],"system.":[107]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
