{"id":"https://openalex.org/W2580422331","doi":"https://doi.org/10.1109/lra.2017.2658018","title":"Eigenmodes of Nonlinear Dynamics: Definition, Existence, and Embodiment into Legged Robots with Elastic Elements","display_name":"Eigenmodes of Nonlinear Dynamics: Definition, Existence, and Embodiment into Legged Robots with Elastic Elements","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2580422331","doi":"https://doi.org/10.1109/lra.2017.2658018","mag":"2580422331"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2017.2658018","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2017.2658018","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766","2377-3774"],"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":["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/A5086621714","display_name":"Dominic Lakatos","orcid":"https://orcid.org/0000-0002-1841-9972"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]},{"id":"https://openalex.org/I4210126231","display_name":"Robotic Research (United States)","ror":"https://ror.org/035w78024","country_code":"US","type":"company","lineage":["https://openalex.org/I4210126231"]},{"id":"https://openalex.org/I4391767788","display_name":"Institute of Robotics","ror":"https://ror.org/002cfhw56","country_code":null,"type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4391767788"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Dominic Lakatos","raw_affiliation_strings":["Robotic Mechatronic Center, German Aerospace Center (DLR), We\u00dfling, Germany","Robotic Mechatronic Center (RMC), Institute of Robotics and Mechatronics,","Technical University Munich, Chair of Sensor Based Robots and Intelligent Assistance Systems, Department of Informatics, D-85748 Garching, Germany","German Aerospace Center (DLR), D-82234 Oberpfaffenhofen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1841-9972","affiliations":[{"raw_affiliation_string":"Robotic Mechatronic Center, German Aerospace Center (DLR), We\u00dfling, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Robotic Mechatronic Center (RMC), Institute of Robotics and Mechatronics,","institution_ids":["https://openalex.org/I4210126231","https://openalex.org/I4391767788"]},{"raw_affiliation_string":"Technical University Munich, Chair of Sensor Based Robots and Intelligent Assistance Systems, Department of Informatics, D-85748 Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"German Aerospace Center (DLR), D-82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005657289","display_name":"Werner Friedl","orcid":"https://orcid.org/0000-0003-3002-7274"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]},{"id":"https://openalex.org/I4210126231","display_name":"Robotic Research (United States)","ror":"https://ror.org/035w78024","country_code":"US","type":"company","lineage":["https://openalex.org/I4210126231"]},{"id":"https://openalex.org/I4391767788","display_name":"Institute of Robotics","ror":"https://ror.org/002cfhw56","country_code":null,"type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4391767788"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Werner Friedl","raw_affiliation_strings":["Robotic Mechatronic Center, German Aerospace Center (DLR), We\u00dfling, Germany","Technical University Munich, Chair of Sensor Based Robots and Intelligent Assistance Systems, Department of Informatics, D-85748 Garching, Germany","German Aerospace Center (DLR), D-82234 Oberpfaffenhofen, Germany","Robotic Mechatronic Center (RMC), Institute of Robotics and Mechatronics,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Robotic Mechatronic Center, German Aerospace Center (DLR), We\u00dfling, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Technical University Munich, Chair of Sensor Based Robots and Intelligent Assistance Systems, Department of Informatics, D-85748 Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"German Aerospace Center (DLR), D-82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Robotic Mechatronic Center (RMC), Institute of Robotics and Mechatronics,","institution_ids":["https://openalex.org/I4210126231","https://openalex.org/I4391767788"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080814983","display_name":"Alin Albu\u2010Sch\u00e4ffer","orcid":"https://orcid.org/0000-0001-5343-9074"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]},{"id":"https://openalex.org/I4210126231","display_name":"Robotic Research (United States)","ror":"https://ror.org/035w78024","country_code":"US","type":"company","lineage":["https://openalex.org/I4210126231"]},{"id":"https://openalex.org/I4391767788","display_name":"Institute of Robotics","ror":"https://ror.org/002cfhw56","country_code":null,"type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4391767788"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Alin Albu-Schaffer","raw_affiliation_strings":["Department of Informatics, Chair of Sensor Based Robots and Intelligent Assistance Systems, Technical University Munich, Munich, Germany","Robotic Mechatronic Center, German Aerospace Center (DLR), We\u00dfling, Germany","Robotic Mechatronic Center (RMC), Institute of Robotics and Mechatronics,","Technical University Munich, Chair of Sensor Based Robots and Intelligent Assistance Systems, Department of Informatics, D-85748 Garching, Germany","German Aerospace Center (DLR), D-82234 Oberpfaffenhofen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Chair of Sensor Based Robots and Intelligent Assistance Systems, Technical University Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Robotic Mechatronic Center, German Aerospace Center (DLR), We\u00dfling, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Robotic Mechatronic Center (RMC), Institute of Robotics and Mechatronics,","institution_ids":["https://openalex.org/I4210126231","https://openalex.org/I4391767788"]},{"raw_affiliation_string":"Technical University Munich, Chair of Sensor Based Robots and Intelligent Assistance Systems, Department of Informatics, D-85748 Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"German Aerospace Center (DLR), D-82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0903,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.73555598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9998999834060669,"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":0.9998999834060669,"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9922999739646912,"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/T10784","display_name":"Muscle activation and electromyography studies","score":0.9695000052452087,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.748945415019989},{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.6152212619781494},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6127797961235046},{"id":"https://openalex.org/keywords/multibody-system","display_name":"Multibody system","score":0.5653835535049438},{"id":"https://openalex.org/keywords/pendulum","display_name":"Pendulum","score":0.5397925972938538},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5219516158103943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5092328786849976},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.4977414906024933},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.48411452770233154},{"id":"https://openalex.org/keywords/double-pendulum","display_name":"Double pendulum","score":0.4694233536720276},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.46851444244384766},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.4503426253795624},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4353076219558716},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.32337427139282227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31408628821372986},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2808833122253418},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23005476593971252},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2129269242286682},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2081974744796753}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.748945415019989},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.6152212619781494},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6127797961235046},{"id":"https://openalex.org/C67865112","wikidata":"https://www.wikidata.org/wiki/Q1917564","display_name":"Multibody system","level":2,"score":0.5653835535049438},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.5397925972938538},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5219516158103943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5092328786849976},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.4977414906024933},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.48411452770233154},{"id":"https://openalex.org/C167183279","wikidata":"https://www.wikidata.org/wiki/Q1243208","display_name":"Double pendulum","level":4,"score":0.4694233536720276},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.46851444244384766},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.4503426253795624},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4353076219558716},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32337427139282227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31408628821372986},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2808833122253418},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23005476593971252},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2129269242286682},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2081974744796753},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lra.2017.2658018","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2017.2658018","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766","2377-3774"],"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:elib.dlr.de:111916","is_oa":false,"landing_page_url":"https://doi.org/10.1109/LRA.2017.2658018>.","pdf_url":null,"source":{"id":"https://openalex.org/S4377196266","display_name":"elib (German Aerospace Center)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2898391981","host_organization_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","host_organization_lineage":["https://openalex.org/I2898391981"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Zeitschriftenbeitrag"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W199714776","https://openalex.org/W1487127700","https://openalex.org/W1504362584","https://openalex.org/W1559840026","https://openalex.org/W1966612479","https://openalex.org/W1969366849","https://openalex.org/W1981918565","https://openalex.org/W1983815930","https://openalex.org/W1985875375","https://openalex.org/W2008342119","https://openalex.org/W2009317155","https://openalex.org/W2010026582","https://openalex.org/W2014739471","https://openalex.org/W2016582414","https://openalex.org/W2073195712","https://openalex.org/W2081115468","https://openalex.org/W2092020325","https://openalex.org/W2111253117","https://openalex.org/W2121829700","https://openalex.org/W2129224530","https://openalex.org/W2144834630","https://openalex.org/W2149606028","https://openalex.org/W2161427949","https://openalex.org/W2161643831","https://openalex.org/W2170320699","https://openalex.org/W2178708843","https://openalex.org/W2333075870","https://openalex.org/W2559460007","https://openalex.org/W2958420352","https://openalex.org/W6608250194","https://openalex.org/W6765718806"],"related_works":["https://openalex.org/W2612646280","https://openalex.org/W1963494060","https://openalex.org/W1544534375","https://openalex.org/W2366496871","https://openalex.org/W2727944915","https://openalex.org/W1988157353","https://openalex.org/W2149145472","https://openalex.org/W2669735925","https://openalex.org/W3090237748","https://openalex.org/W3216306759"],"abstract_inverted_index":{"Pogo-stick":[0],"bouncing":[1],"or":[2],"the":[3,30,80,92,118,130,139,151,173,200],"spring":[4],"loaded":[5],"inverted":[6],"pendulum":[7],"represents":[8],"fundamental":[9,155],"dynamics":[10,33,73,81,110],"models":[11,22,45],"for":[12,63,126,137],"hopping":[13],"and":[14],"running":[15],"in":[16,24,74,86,100,180],"legged":[17,159],"locomotion.":[18],"However,":[19,79],"these":[20,43],"conceptual":[21],"are":[23,149,169],"general":[25,87],"of":[26,34,61,82,94,120,142,153,164,175],"lower":[27],"order":[28],"than":[29],"elastic":[31,182],"multibody":[32,143],"versatile":[35],"segmented":[36,83],"legs.":[37],"The":[38,59],"question":[39],"how":[40],"to":[41,69,129],"embody":[42],"simple":[44],"into":[46,158],"real":[47],"robot":[48,183],"leg":[49,167],"designs":[50,168],"still":[51],"has":[52],"not":[53],"been":[54],"completely":[55],"answered":[56],"so":[57],"far.":[58],"concept":[60,119],"eigenmodes":[62,148],"linear":[64,127],"systems":[65,144,160],"provides":[66],"a":[67,135,188],"tool":[68],"separate":[70],"high-dimensional,":[71],"coupled":[72],"one-dimensional":[75],"(1-D)":[76],"invariant":[77],"ones.":[78],"legs":[84],"is":[85,123,161],"nonlinear":[88,131],"such":[89,145],"that":[90,146,193],"even":[91],"existence":[93,174],"periodic":[95],"motions,":[96],"as":[97],"appearing":[98],"typically":[99],"locomotion":[101,156],"tasks,":[102],"cannot":[103],"be":[104,197],"generally":[105],"guaranteed":[106],"without":[107],"changing":[108],"intrinsic":[109],"behavior":[111],"substantially":[112],"by":[113,199],"control.":[114],"This":[115],"letter":[116],"extends":[117],"eigenmodes,":[121],"which":[122,171],"well":[124],"known":[125],"systems,":[128],"case.":[132],"By":[133],"proposing":[134],"method":[136],"selecting":[138],"design":[140],"parameters":[141],"desired":[147],"achieved,":[150],"problem":[152],"embodying":[154],"modes":[157,179],"resolved.":[162],"Examples":[163],"practically":[165],"realizable":[166],"provided,":[170],"proof":[172],"invariant,":[176],"1-D":[177],"oscillation":[178],"nonlinear,":[181],"dynamics.":[184],"An":[185],"experiment":[186],"on":[187],"multilegged":[189],"robotic":[190],"system":[191],"validates":[192],"energetic":[194],"efficiency":[195],"can":[196],"gained":[198],"proposed":[201],"approach.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}