{"id":"https://openalex.org/W2115927594","doi":"https://doi.org/10.1177/0278364909354391","title":"Roll and Pitch Motion Analysis of a Biologically Inspired Quadruped Water Runner Robot","display_name":"Roll and Pitch Motion Analysis of a Biologically Inspired Quadruped Water Runner Robot","publication_year":2009,"publication_date":"2009-12-04","ids":{"openalex":"https://openalex.org/W2115927594","doi":"https://doi.org/10.1177/0278364909354391","mag":"2115927594"},"language":"en","primary_location":{"id":"doi:10.1177/0278364909354391","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0278364909354391","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/A5101538702","display_name":"Hyun Soo Park","orcid":"https://orcid.org/0000-0001-6613-0738"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hyun Soo Park","raw_affiliation_strings":["NanoRobotics Laboratory, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NanoRobotics Laboratory, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA,","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081327846","display_name":"Steven Floyd","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven Floyd","raw_affiliation_strings":["NanoRobotics Laboratory, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NanoRobotics Laboratory, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA,","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079968392","display_name":"Metin Sitti","orcid":"https://orcid.org/0000-0001-8249-3854"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Metin Sitti","raw_affiliation_strings":["NanoRobotics Laboratory, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NanoRobotics Laboratory, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.6745,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.72988592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"10","first_page":"1281","last_page":"1297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9997000098228455,"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":0.9997000098228455,"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/T11170","display_name":"Biomimetic flight and propulsion mechanisms","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11192","display_name":"Underwater Vehicles and Communication Systems","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/drag","display_name":"Drag","score":0.6874675154685974},{"id":"https://openalex.org/keywords/added-mass","display_name":"Added mass","score":0.6303110122680664},{"id":"https://openalex.org/keywords/thrust","display_name":"Thrust","score":0.6106337308883667},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5631189346313477},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5479958653450012},{"id":"https://openalex.org/keywords/moment-of-inertia","display_name":"Moment of inertia","score":0.5443820357322693},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.5401976704597473},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.47082024812698364},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.463580846786499},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.463421493768692},{"id":"https://openalex.org/keywords/torque","display_name":"Torque","score":0.43845129013061523},{"id":"https://openalex.org/keywords/center-of-mass","display_name":"Center of mass (relativistic)","score":0.43079033493995667},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.35648781061172485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33088448643684387},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.32972633838653564},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.3157879114151001},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.31573206186294556},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28890812397003174},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.1714422106742859},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13116520643234253},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.12759602069854736}],"concepts":[{"id":"https://openalex.org/C72921944","wikidata":"https://www.wikidata.org/wiki/Q206621","display_name":"Drag","level":2,"score":0.6874675154685974},{"id":"https://openalex.org/C122312997","wikidata":"https://www.wikidata.org/wiki/Q4681030","display_name":"Added mass","level":3,"score":0.6303110122680664},{"id":"https://openalex.org/C79420006","wikidata":"https://www.wikidata.org/wiki/Q533668","display_name":"Thrust","level":2,"score":0.6106337308883667},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5631189346313477},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5479958653450012},{"id":"https://openalex.org/C10238366","wikidata":"https://www.wikidata.org/wiki/Q165618","display_name":"Moment of inertia","level":2,"score":0.5443820357322693},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.5401976704597473},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.47082024812698364},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.463580846786499},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.463421493768692},{"id":"https://openalex.org/C144171764","wikidata":"https://www.wikidata.org/wiki/Q48103","display_name":"Torque","level":2,"score":0.43845129013061523},{"id":"https://openalex.org/C36185635","wikidata":"https://www.wikidata.org/wiki/Q17006925","display_name":"Center of mass (relativistic)","level":3,"score":0.43079033493995667},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.35648781061172485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33088448643684387},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.32972633838653564},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.3157879114151001},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.31573206186294556},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28890812397003174},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.1714422106742859},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13116520643234253},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.12759602069854736},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.0},{"id":"https://openalex.org/C47513753","wikidata":"https://www.wikidata.org/wiki/Q3502299","display_name":"Energy\u2013momentum relation","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/0278364909354391","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0278364909354391","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Clean water and sanitation","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/6"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W774034202","https://openalex.org/W1956264703","https://openalex.org/W2020178413","https://openalex.org/W2041703890","https://openalex.org/W2071406810","https://openalex.org/W2083751598","https://openalex.org/W2089562210","https://openalex.org/W2102069286","https://openalex.org/W2102446685","https://openalex.org/W2107869318","https://openalex.org/W2108623852","https://openalex.org/W2124835078","https://openalex.org/W2129736998","https://openalex.org/W2133859362","https://openalex.org/W2136903173","https://openalex.org/W2139372276","https://openalex.org/W2142117965","https://openalex.org/W2151431293","https://openalex.org/W2158321967","https://openalex.org/W2162034128","https://openalex.org/W2188319348","https://openalex.org/W3139610437","https://openalex.org/W4232993041","https://openalex.org/W4236573885","https://openalex.org/W4252925458","https://openalex.org/W4365800133"],"related_works":["https://openalex.org/W2087745542","https://openalex.org/W2285922472","https://openalex.org/W2366076529","https://openalex.org/W4232465408","https://openalex.org/W4379743905","https://openalex.org/W2334285609","https://openalex.org/W4242956596","https://openalex.org/W2080300541","https://openalex.org/W4309321466","https://openalex.org/W4306195278"],"abstract_inverted_index":{"In":[0],"this":[1,73],"paper,":[2],"the":[3,56,66,77,94,100,103,108,119,123,159,166,196],"roll":[4,45,52,78,161,186],"and":[5,18,25,49,131,152,162,177],"pitch":[6,95,120,163,197],"dynamics":[7,61],"of":[8,47,80,125,165],"a":[9,19,43,69,113,146],"biologically":[10],"inspired":[11],"quadruped":[12],"water":[13,67,88,148],"runner":[14,149],"robot":[15,21],"are":[16,62,90,140,169],"analyzed,":[17],"stable":[20,147,160],"design":[22],"is":[23,32,40,97,127,150,183,188],"proposed":[24],"tested.":[26],"The":[27],"robot\u2019s":[28],"foot\u2014water":[29,57],"interaction":[30,58],"force":[31,102],"derived":[33],"using":[34],"drag":[35],"equations.":[36],"Roll":[37,60],"direction":[38,96],"instability":[39],"attributed":[41],"to":[42,171,191],"small":[44],"moment":[46,79,121],"inertia":[48,81],"large":[50],"instantaneous":[51],"moments":[53,85],"generated":[54,86],"by":[55,64,87,99],"forces.":[59],"modeled":[63],"approximating":[65],"as":[68],"linear":[70],"spring.":[71],"Using":[72],"model,":[74],"estimates":[75],"on":[76,107,143],"that":[82,185],"can":[83,117,136],"endure":[84],"interactions":[89],"derived.":[91],"Instability":[92],"in":[93],"caused":[98],"thrust":[101],"four":[104],"feet":[105],"exert":[106],"water.":[109],"To":[110],"correct":[111],"this,":[112],"circular":[114],"tail":[115,133],"which":[116,135],"negate":[118],"around":[122],"center":[124],"mass":[126],"proposed.":[128],"Both":[129],"passive":[130],"active":[132],"designs":[134],"cope":[137],"with":[138,195],"disturbances":[139,192],"introduced.":[141],"Based":[142],"these":[144],"analyses,":[145],"designed,":[151],"built.":[153],"Experimental":[154],"high-speed":[155],"video":[156],"footage":[157],"demonstrates":[158],"motion":[164,187],"robot.":[167],"Simulations":[168],"used":[170],"estimate":[172],"robustness":[173],"against":[174],"disturbances,":[175],"waves,":[176],"leg":[178],"running":[179],"frequency":[180],"variations.":[181],"It":[182],"found":[184],"more":[189],"sensitive":[190],"when":[193],"compared":[194],"direction.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}