{"id":"https://openalex.org/W2005559889","doi":"https://doi.org/10.1137/040609860","title":"Nonpositive Curvature and Pareto Optimal Coordination of Robots","display_name":"Nonpositive Curvature and Pareto Optimal Coordination of Robots","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2005559889","doi":"https://doi.org/10.1137/040609860","mag":"2005559889"},"language":"en","primary_location":{"id":"doi:10.1137/040609860","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040609860","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5111742669","display_name":"Robert Ghrist","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert Ghrist","raw_affiliation_strings":["University of Illinois at Urbana Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065104734","display_name":"Steven M. LaValle","orcid":"https://orcid.org/0000-0003-4841-2584"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven M. Lavalle","raw_affiliation_strings":["Information Trust Institute"],"affiliations":[{"raw_affiliation_string":"Information Trust Institute","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111742669"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":2.8456,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.91035166,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"5","first_page":"1697","last_page":"1713"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9991000294685364,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9926000237464905,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6549104452133179},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6106509566307068},{"id":"https://openalex.org/keywords/pareto-optimal","display_name":"Pareto optimal","score":0.515252411365509},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49996137619018555},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48979759216308594},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.48931118845939636},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.48506656289100647},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4612179696559906},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45535826683044434},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.4464607834815979},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4187321960926056},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.2504785358905792},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24565079808235168},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23621845245361328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1512250304222107},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14100071787834167},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13624680042266846}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6549104452133179},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6106509566307068},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.515252411365509},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49996137619018555},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48979759216308594},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.48931118845939636},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.48506656289100647},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4612179696559906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45535826683044434},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.4464607834815979},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4187321960926056},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.2504785358905792},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24565079808235168},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23621845245361328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1512250304222107},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14100071787834167},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13624680042266846},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040609860","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040609860","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.127.5451","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.5451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uiuc.edu/~lavalle/papers/GhrLav06.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W20444823","https://openalex.org/W206461320","https://openalex.org/W1903576784","https://openalex.org/W1978301848","https://openalex.org/W2004815408","https://openalex.org/W2015425624","https://openalex.org/W2022020194","https://openalex.org/W2045403423","https://openalex.org/W2053265348","https://openalex.org/W2064943409","https://openalex.org/W2103929204","https://openalex.org/W2113952543","https://openalex.org/W2117496121","https://openalex.org/W2126558792","https://openalex.org/W2126876121","https://openalex.org/W2129668160","https://openalex.org/W2132457975","https://openalex.org/W2135647874","https://openalex.org/W2138361531","https://openalex.org/W2141967156","https://openalex.org/W2143031621","https://openalex.org/W2149906774","https://openalex.org/W2152358681","https://openalex.org/W2158844420","https://openalex.org/W2166462345","https://openalex.org/W2169742265","https://openalex.org/W2404844938","https://openalex.org/W2802620382","https://openalex.org/W3040586665","https://openalex.org/W3140662957","https://openalex.org/W4300449797"],"related_works":["https://openalex.org/W1917675986","https://openalex.org/W2763149318","https://openalex.org/W2374829073","https://openalex.org/W2109083094","https://openalex.org/W2015189571","https://openalex.org/W2767216510","https://openalex.org/W1989514163","https://openalex.org/W150790229","https://openalex.org/W2914819562","https://openalex.org/W2600802857"],"abstract_inverted_index":{"Given":[0],"a":[1,6,13,21,36,78],"collection":[2],"of":[3,54,70,84,131],"robots":[4],"sharing":[5],"common":[7],"environment,":[8],"assume":[9],"that":[10,29,124,137],"each":[11,30],"possesses":[12],"graph":[14],"(a":[15],"one\u2010dimensional":[16],"complex":[17],"also":[18,135],"known":[19,148],"as":[20],"roadmap)":[22],"approximating":[23],"its":[24],"configuration":[25],"space":[26,128],"and,":[27],"furthermore,":[28],"robot":[31],"wishes":[32],"to":[33,35],"travel":[34],"goal":[37],"while":[38],"optimizing":[39],"elapsed":[40],"time.":[41],"We":[42,76,134],"consider":[43],"vector\u2010valued":[44],"(or":[45],"Pareto)":[46],"optima":[47,61],"for":[48,142],"collision\u2010free":[49],"coordination":[50,127],"on":[51,81,106,121],"the":[52,82,88,117,122,125,138],"product":[53],"these":[55],"roadmaps":[56],"with":[57,144],"collision\u2010type":[58],"obstacles.":[59],"Such":[60],"are":[62,74,95],"by":[63,99],"no":[64],"means":[65],"unique:":[66],"in":[67,87],"fact,":[68],"continua":[69],"Pareto":[71],"optimal":[72,85],"coordinations":[73,86],"possible.":[75],"prove":[77],"finite":[79],"bound":[80,119,140],"number":[83],"physically":[89],"relevant":[90],"case":[91],"where":[92],"all":[93],"obstacles":[94,146],"cylindrical":[96],"(i.e.,":[97],"defined":[98],"pairwise":[100],"collisions).":[101],"The":[102],"proofs":[103],"rely":[104],"crucially":[105],"perspectives":[107],"from":[108],"geometric":[109],"group":[110],"theory":[111],"and":[112],"CAT(0)":[113],"geometry.":[114],"In":[115],"particular,":[116],"finiteness":[118,139],"depends":[120],"fact":[123],"associated":[126],"is":[129],"devoid":[130],"positive":[132],"curvature.":[133],"demonstrate":[136],"holds":[141],"systems":[143],"moving":[145],"following":[147],"trajectories.":[149]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
