{"id":"https://openalex.org/W7140233352","doi":"https://doi.org/10.48550/arxiv.2603.22146","title":"From Singleton Obstacles to Clutter: Translation Invariant Compositional Avoid Sets","display_name":"From Singleton Obstacles to Clutter: Translation Invariant Compositional Avoid Sets","publication_year":2026,"publication_date":"2026-03-23","ids":{"openalex":"https://openalex.org/W7140233352","doi":"https://doi.org/10.48550/arxiv.2603.22146"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.22146","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22146","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.22146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Solanki, Prashant","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Solanki, Prashant","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Van Beers, Jasper","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Van Beers, Jasper","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"De Visser, Coen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"De Visser, Coen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.4284999966621399,"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":0.4284999966621399,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.11100000143051147,"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/T10524","display_name":"Traffic control and management","score":0.09589999914169312,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/monotonic-function","display_name":"Monotonic function","score":0.6115000247955322},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5698000192642212},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.507099986076355},{"id":"https://openalex.org/keywords/singleton","display_name":"Singleton","score":0.5002999901771545},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.47609999775886536},{"id":"https://openalex.org/keywords/clutter","display_name":"Clutter","score":0.4722999930381775},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.41999998688697815},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.40299999713897705},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.36629998683929443}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6468999981880188},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6115000247955322},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5698000192642212},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.5002999901771545},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.47609999775886536},{"id":"https://openalex.org/C132094186","wikidata":"https://www.wikidata.org/wiki/Q641585","display_name":"Clutter","level":3,"score":0.4722999930381775},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.41999998688697815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4090999960899353},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3984000086784363},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3652999997138977},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.31929999589920044},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31029999256134033},{"id":"https://openalex.org/C40422974","wikidata":"https://www.wikidata.org/wiki/Q741248","display_name":"Assertion","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.274399995803833},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C6683253","wikidata":"https://www.wikidata.org/wiki/Q7075535","display_name":"Obstacle avoidance","level":4,"score":0.2703999876976013}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.22146","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22146","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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.22146","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22146","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.44060018658638,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,127],"paper":[1],"studies":[2],"obstacle":[3,25,67],"avoidance":[4],"under":[5,145],"translation":[6,55],"invariant":[7],"dynamics":[8],"using":[9],"an":[10,24,149],"avoid-side":[11],"travel":[12],"cost":[13],"Hamilton":[14],"Jacobi":[15],"formulation.":[16],"For":[17],"running":[18],"costs":[19],"that":[20,33,79],"are":[21,122],"zero":[22,41],"outside":[23,43],"and":[26,47,97,124,148],"strictly":[27,49],"negative":[28,50],"inside":[29],"it,":[30],"we":[31,111],"prove":[32],"the":[34,44,62,80,89,92,138,154],"value":[35,63,75],"function":[36],"is":[37,48,68,164],"non-positive":[38],"everywhere,":[39],"equals":[40],"exactly":[42,51,87],"avoid":[45,95],"set,":[46],"on":[52,153,166],"it.":[53],"Under":[54],"invariance,":[56],"this":[57],"yields":[58,128],"a":[59,72,99,113,129,157,167,172],"reuse":[60,136],"principle:":[61],"of":[64,83,91,103,120,131,156],"any":[65],"translated":[66,84,93],"obtained":[69],"by":[70],"translating":[71],"single":[73],"template":[74,85],"function.":[76],"We":[77],"show":[78],"pointwise":[81],"minimum":[82],"values":[86],"characterizes":[88],"union":[90],"single-obstacle":[94],"sets":[96],"provides":[98],"conservative":[100,132],"inner":[101],"certificate":[102],"unavoidable":[104],"collision":[105],"in":[106,117,171],"clutter.":[107],"To":[108],"reduce":[109],"conservatism,":[110],"introduce":[112],"blockwise":[114],"composition":[115],"framework":[116,163],"which":[118],"subsets":[119],"obstacles":[121],"merged":[123],"solved":[125],"jointly.":[126],"hierarchy":[130],"certificates":[133],"from":[134],"singleton":[135],"to":[137],"exact":[139],"clutter":[140,159,174],"value,":[141],"together":[142],"with":[143],"monotonicity":[144],"block":[146],"merging":[147],"exactness":[150],"criterion":[151],"based":[152],"existence":[155],"common":[158],"avoiding":[160],"control.":[161],"The":[162],"illustrated":[165],"Dubins":[168],"car":[169],"example":[170],"repeated":[173],"field.":[175]},"counts_by_year":[],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2026-03-25T00:00:00"}