{"id":"https://openalex.org/W2594131758","doi":"https://doi.org/10.1137/s0097539797326289","title":"Motion Planning of Legged Robots","display_name":"Motion Planning of Legged Robots","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2594131758","doi":"https://doi.org/10.1137/s0097539797326289","mag":"2594131758"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539797326289","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539797326289","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cs/9909006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105370783","display_name":"Jean\u2010Daniel Boissonnat","orcid":null},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Jean-Daniel Boissonnat","raw_affiliation_strings":["Geometry, Algorithms and Robotics"],"affiliations":[{"raw_affiliation_string":"Geometry, Algorithms and Robotics","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043040182","display_name":"Olivier Devillers","orcid":"https://orcid.org/0000-0003-4275-5068"},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Olivier Devillers","raw_affiliation_strings":["Geometry, Algorithms and Robotics"],"affiliations":[{"raw_affiliation_string":"Geometry, Algorithms and Robotics","institution_ids":["https://openalex.org/I4210099593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041225170","display_name":"Sylvain Lazard","orcid":"https://orcid.org/0000-0002-6032-0802"},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sylvain Lazard","raw_affiliation_strings":["Geometry, Algorithms and Robotics"],"affiliations":[{"raw_affiliation_string":"Geometry, Algorithms and Robotics","institution_ids":["https://openalex.org/I4210099593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5105370783"],"corresponding_institution_ids":["https://openalex.org/I4210099593"],"apc_list":null,"apc_paid":null,"fwci":0.4145,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.74849398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"1","first_page":"218","last_page":"246"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.9467999935150146,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6555459499359131},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.599989652633667},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5875144600868225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5085691213607788},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.49737265706062317},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4502130448818207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3341846466064453},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33258914947509766},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.29660630226135254},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12453112006187439},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10308173298835754}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6555459499359131},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.599989652633667},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5875144600868225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5085691213607788},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.49737265706062317},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4502130448818207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3341846466064453},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33258914947509766},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.29660630226135254},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12453112006187439},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10308173298835754},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":13,"locations":[{"id":"doi:10.1137/s0097539797326289","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539797326289","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cs/9909006","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/9909006","pdf_url":"https://arxiv.org/pdf/cs/9909006","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":"pmh:hdl:10068/40525","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/40525","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.10.9693","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.9693","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3214.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.7303","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.7303","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sop.inria.fr/prisme/publis/bdl-mplr.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.29.4921","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.4921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3214.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.341.9273","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.341.9273","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/9909006v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.699.6219","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.699.6219","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/inria-00099289/document/","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01179461v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01179461","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.wafr.org/","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:inria-00073475v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00073475","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RR-3214, INRIA. 1997","raw_type":"Reports"},{"id":"pmh:oai:HAL:inria-00099289v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00099289","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing, 2000, 30 (1), pp.218-246. &#x27E8;10.1137/S0097539797326289&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.cs/9909006","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cs/9909006","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-journal"},{"id":"mag:2594131758","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cs/9909006","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/9909006","pdf_url":"https://arxiv.org/pdf/cs/9909006","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":0.6899999976158142,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W49234980","https://openalex.org/W1582550272","https://openalex.org/W1997271799","https://openalex.org/W2020590137","https://openalex.org/W2022072413","https://openalex.org/W2028348452","https://openalex.org/W2041019458","https://openalex.org/W2061311037","https://openalex.org/W2091315626","https://openalex.org/W2092394151","https://openalex.org/W2121318827","https://openalex.org/W2147106864","https://openalex.org/W4242657188"],"related_works":["https://openalex.org/W2144969807","https://openalex.org/W2122668213","https://openalex.org/W2110072346","https://openalex.org/W119243154","https://openalex.org/W2165739402","https://openalex.org/W1530589852","https://openalex.org/W2072897554","https://openalex.org/W1980745281","https://openalex.org/W2112023787","https://openalex.org/W1506391767","https://openalex.org/W2149735608","https://openalex.org/W1592281747","https://openalex.org/W163770788","https://openalex.org/W2773147430","https://openalex.org/W2125302094","https://openalex.org/W1480113909","https://openalex.org/W2810386942","https://openalex.org/W2182310728","https://openalex.org/W2116446610","https://openalex.org/W2906881562"],"abstract_inverted_index":{"We":[0,115,152],"study":[1],"the":[2,6,17,30,35,54,57,62,71,82,90,95,98,111,162,207],"problem":[3],"of":[4,11,22,56,65,92,94,97,106,150,209],"computing":[5,158],"free":[7,86],"space":[8,87,130],"${\\cal":[9,122,159,177,210],"F}$":[10,123,160,178],"a":[12,26,47,104,203],"simple":[13],"legged":[14],"robot":[15,24,38,58,72,99,112],"called":[16,81],"spider":[18],"robot.":[19],"The":[20,37,85],"body":[21,55,96],"this":[23],"is":[25,39,89,113,138,187,202],"single":[27],"point":[28,134],"and":[29,53],"legs":[31],"are":[32,165,196],"attached":[33],"to":[34,41,198],"body.":[36],"subject":[40],"two":[42],"constraints:":[43],"each":[44],"leg":[45],"has":[46],"maximal":[48],"extension":[49],"R":[50],"(accessibility":[51],"constraint)":[52],"must":[59],"lie":[60],"above":[61],"convex":[63],"hull":[64],"its":[66,76],"feet":[67,77],"(stability":[68],"constraint).":[69],"Moreover,":[70],"can":[73],"only":[74],"put":[75],"on":[78],"some":[79],"regions,":[80],"foothold":[83,163],"regions.":[84],"${\\mathcal{F}}$":[88],"set":[91,105],"positions":[93],"such":[100],"that":[101,120],"there":[102],"exists":[103],"accessible":[107],"footholds":[108,135],"for":[109,131,146,157,206],"which":[110],"stable.":[114],"present":[116,154],"an":[117,139,155,189],"efficient":[118],"algorithm":[119,156,175],"computes":[121,176],"in":[124,172,179],"$O(n^2\\log":[125],"n)$":[126,181],"time":[127,182],"using":[128,183],"$O(n^2\\alpha(n))$":[129],"n":[132,170],"discrete":[133],"where":[136],"$\\alpha(n)$":[137],"extremely":[140,190],"slowly":[141,191],"growing":[142,192],"function":[143],"($\\alpha(n)\\leq":[144],"3$":[145],"any":[147],"practical":[148],"value":[149],"n).":[151],"also":[153,188],"when":[161],"regions":[164],"pairwise":[166],"disjoint":[167],"polygons":[168],"with":[169],"edges":[171],"total.":[173],"This":[174],"$O(n^2\\alpha_8(n)\\log":[180],"$O(n^2\\alpha_8(n))$":[184],"space.":[185],"($\\alpha_8(n)$":[186],"function.)":[193],"These":[194],"results":[195],"close":[197],"optimal":[199],"since":[200],"$\\Omega(n^2)$":[201],"lower":[204],"bound":[205],"size":[208],"F}$.":[211]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
