{"id":"https://openalex.org/W2161497638","doi":"https://doi.org/10.1017/s0263574712000690","title":"Conditional Density Growth (CDG) model: a simplified model of RRT coverage for kinematic systems","display_name":"Conditional Density Growth (CDG) model: a simplified model of RRT coverage for kinematic systems","publication_year":2013,"publication_date":"2013-01-25","ids":{"openalex":"https://openalex.org/W2161497638","doi":"https://doi.org/10.1017/s0263574712000690","mag":"2161497638"},"language":"en","primary_location":{"id":"doi:10.1017/s0263574712000690","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0263574712000690","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B647C1A59760FC0E9DA549BDE3F93C94/S0263574712000690a.pdf/div-class-title-conditional-density-growth-cdg-model-a-simplified-model-of-rrt-coverage-for-kinematic-systems-div.pdf","source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B647C1A59760FC0E9DA549BDE3F93C94/S0263574712000690a.pdf/div-class-title-conditional-density-growth-cdg-model-a-simplified-model-of-rrt-coverage-for-kinematic-systems-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108516951","display_name":"Joel M. Esposito","orcid":"https://orcid.org/0000-0002-6468-9543"},"institutions":[{"id":"https://openalex.org/I189158971","display_name":"United States Naval Academy","ror":"https://ror.org/00znex860","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I189158971","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joel M. Esposito","raw_affiliation_strings":["Department of Systems Engineering, United States Naval Academy, Annapolis, MD 21402, USA"],"affiliations":[{"raw_affiliation_string":"Department of Systems Engineering, United States Naval Academy, Annapolis, MD 21402, USA","institution_ids":["https://openalex.org/I189158971"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108516951"],"corresponding_institution_ids":["https://openalex.org/I189158971"],"apc_list":null,"apc_paid":null,"fwci":0.5443,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7262811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"5","first_page":"733","last_page":"746"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9941999912261963,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/configuration-space","display_name":"Configuration space","score":0.6737524271011353},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6193325519561768},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5667122602462769},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.5651777982711792},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.4789983928203583},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4612817168235779},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.45161110162734985},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.44495075941085815},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.44370636343955994},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.44025540351867676},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4346715211868286},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4120585322380066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38120517134666443},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.354022741317749},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.33791089057922363},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18257850408554077},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11243990063667297}],"concepts":[{"id":"https://openalex.org/C90738871","wikidata":"https://www.wikidata.org/wiki/Q41642869","display_name":"Configuration space","level":2,"score":0.6737524271011353},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6193325519561768},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5667122602462769},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.5651777982711792},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.4789983928203583},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4612817168235779},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.45161110162734985},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.44495075941085815},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.44370636343955994},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44025540351867676},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4346715211868286},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4120585322380066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38120517134666443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.354022741317749},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33791089057922363},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18257850408554077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11243990063667297},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0263574712000690","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0263574712000690","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B647C1A59760FC0E9DA549BDE3F93C94/S0263574712000690a.pdf/div-class-title-conditional-density-growth-cdg-model-a-simplified-model-of-rrt-coverage-for-kinematic-systems-div.pdf","source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0263574712000690","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0263574712000690","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B647C1A59760FC0E9DA549BDE3F93C94/S0263574712000690a.pdf/div-class-title-conditional-density-growth-cdg-model-a-simplified-model-of-rrt-coverage-for-kinematic-systems-div.pdf","source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2161497638.pdf","grobid_xml":"https://content.openalex.org/works/W2161497638.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W63574109","https://openalex.org/W1424654272","https://openalex.org/W1516027685","https://openalex.org/W1971086298","https://openalex.org/W1971315778","https://openalex.org/W2000359213","https://openalex.org/W2003835006","https://openalex.org/W2017001763","https://openalex.org/W2055207897","https://openalex.org/W2058240764","https://openalex.org/W2082784420","https://openalex.org/W2096636360","https://openalex.org/W2104171123","https://openalex.org/W2115904688","https://openalex.org/W2119520718","https://openalex.org/W2124741347","https://openalex.org/W2128990851","https://openalex.org/W2132909874","https://openalex.org/W2147213215","https://openalex.org/W2151402824","https://openalex.org/W2157543942","https://openalex.org/W2158207287","https://openalex.org/W2159722616","https://openalex.org/W2399501438","https://openalex.org/W2611243847","https://openalex.org/W2623660146","https://openalex.org/W2741744871","https://openalex.org/W2798062075","https://openalex.org/W2912484913","https://openalex.org/W2985413008","https://openalex.org/W4235740860","https://openalex.org/W4236470048","https://openalex.org/W4246226690"],"related_works":["https://openalex.org/W2170012729","https://openalex.org/W3086618278","https://openalex.org/W2163515958","https://openalex.org/W2000663367","https://openalex.org/W2893341095","https://openalex.org/W2355760814","https://openalex.org/W4367155206","https://openalex.org/W4322617142","https://openalex.org/W1964917647","https://openalex.org/W2097390272"],"abstract_inverted_index":{"SUMMARY":[0],"It":[1],"has":[2],"been":[3,201],"shown":[4],"before":[5],"that":[6,20,146,168],"the":[7,21,33,42,46,49,64,67,74,79,99,153,158,161,164,169,186,204,209,234,240,251,271],"Rapidly":[8],"Exploring":[9],"Random":[10],"Tree":[11],"(RRT)":[12],"algorithm":[13],"is":[14,176,229,237,242],"probabilistically":[15],"and":[16,19,102,135,160,218,239,263],"resolution":[17],"complete;":[18],"probability":[22],"of":[23,35,73,76,104,131,163,171,198,261,270],"finding":[24],"a":[25,57,71,117,129,191,195,220],"particular":[26],"solution":[27],"path":[28],"can":[29],"be":[30],"related":[31],"to":[32,184,203,211,219,247],"number":[34,75,197],"nodes.":[36],"However,":[37],"little":[38],"analysis":[39],"exists":[40],"on":[41,111],"rate":[43,235],"at":[44],"which":[45,61,108],"tree":[47,65],"covers":[48,66],"configuration":[50,68,92,105,147],"space.":[51],"In":[52],"this":[53,126],"paper,":[54],"we":[55,94,121,143],"present":[56,122],"stochastic":[58],"difference":[59],"equation":[60],"models":[62],"how":[63],"space":[69,106,148],"as":[70,257],"function":[72],"nodes":[77,199],"in":[78,90,245],"tree.":[80,205],"Using":[81,116],"two":[82,112],"simplifying":[83],"assumptions,":[84],"appropriate":[85],"for":[86,98,267],"holonomic,":[87],"kinematic":[88],"systems":[89],"expansive":[91],"spaces,":[93],"derive":[95],"closed-form":[96],"solutions":[97],"expected":[100,154,187,226],"value":[101,227],"variance":[103,241],"coverage,":[107,188],"only":[109],"depend":[110],"easily":[113],"computable":[114],"parameters.":[115],"grid-based":[118],"coverage":[119,149,155,172],"measurement,":[120],"experimental":[123],"evidence":[124,145],"supporting":[125],"model":[127,210,252],"across":[128,173],"range":[130],"dimensions,":[132],"obstacle":[133],"densities,":[134],"parameter":[136],"choices.":[137],"Collecting":[138],"data":[139],"from":[140],"1000":[141],"RRTs,":[142],"provide":[144],"concentrates":[150],"tightly":[151],"around":[152],"predicted":[156],"by":[157],"model;":[159],"results":[162,181],"Chi-squared":[165],"test":[166],"suggest":[167],"distribution":[170],"these":[174,180],"runs":[175],"highly":[177],"Gaussian.":[178],"Together":[179],"enable":[182],"one":[183],"predict":[185],"along":[189],"with":[190,214,222],"confidence":[192],"interval,":[193],"after":[194],"certain":[196],"have":[200],"added":[202],"We":[206],"also":[207],"applied":[208],"an":[212,258],"example":[213],"extremely":[215],"narrow":[216],"passages":[217],"system":[221],"non-holonomic":[223],"kinematics.":[224],"The":[225],"prediction":[228],"still":[230],"qualitatively":[231],"accurate;":[232],"but":[233],"constant":[236],"reduced":[238],"higher.":[243],"Overall,":[244],"addition":[246],"its":[248],"theoretical":[249],"value,":[250],"may":[253],"find":[254],"future":[255],"application":[256],"online":[259],"measure":[260],"search-progress":[262],"problem":[264],"difficulty,":[265],"useful":[266],"adaptive":[268],"variants":[269],"basic":[272],"RRT":[273],"algorithm.":[274]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}