{"id":"https://openalex.org/W7104917543","doi":"https://doi.org/10.48550/arxiv.2511.07330","title":"Roundabout Constrained Convex Generators: A Unified Framework for Multiply-Connected Reachable Sets","display_name":"Roundabout Constrained Convex Generators: A Unified Framework for Multiply-Connected Reachable Sets","publication_year":2025,"publication_date":"2025-11-10","ids":{"openalex":"https://openalex.org/W7104917543","doi":"https://doi.org/10.48550/arxiv.2511.07330"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.07330","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.07330","pdf_url":"https://arxiv.org/pdf/2511.07330","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.07330","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xie, Peng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Peng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089595627","display_name":"Sabin Diaconescu","orcid":"https://orcid.org/0009-0006-0310-2127","observed_orcids":["https://orcid.org/0009-0006-0310-2127"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diaconescu, Sabin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Stoican, Florin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stoican, Florin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102709386","display_name":"Amr Alanwar","orcid":"https://orcid.org/0000-0003-2941-519X","observed_orcids":["https://orcid.org/0000-0003-2941-519X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alanwar, Amr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10142","display_name":"Formal Methods in Verification","score":0.7925000190734863,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10142","display_name":"Formal Methods in Verification","score":0.7925000190734863,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.1282999962568283,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.02199999988079071,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/multiply-connected-regions","display_name":"multiply connected regions","score":0.7070000171661377},{"id":"https://openalex.org/keywords/topological-holes","display_name":"topological holes","score":0.7720000147819519},{"id":"https://openalex.org/keywords/set-representation","display_name":"set representation","score":0.6309999823570251},{"id":"https://openalex.org/keywords/minkowski-sum","display_name":"Minkowski sum","score":0.7519999742507935},{"id":"https://openalex.org/keywords/linear-operators","display_name":"linear operators","score":0.6100000143051147},{"id":"https://openalex.org/keywords/collision-avoidance","display_name":"collision avoidance","score":0.6790000200271606},{"id":"https://openalex.org/keywords/safety-critical-control","display_name":"safety-critical control","score":0.9240000247955322},{"id":"https://openalex.org/keywords/reachable-sets","display_name":"reachable sets","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C109157449","wikidata":"https://www.wikidata.org/wiki/Q7371221","display_name":"Roundabout","level":2,"score":0.6625000238418579},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5267999768257141},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5263000130653381},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5260000228881836},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4555000066757202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4447999894618988},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.4311999976634979},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40700000524520874},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4032999873161316},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3853999972343445},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.37470000982284546},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.34220001101493835},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.3386000096797943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3303000032901764},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.28349998593330383},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2777000069618225},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C94618114","wikidata":"https://www.wikidata.org/wiki/Q7301169","display_name":"Real representation","level":3,"score":0.2694999873638153},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C79487989","wikidata":"https://www.wikidata.org/wiki/Q934680","display_name":"Vehicle dynamics","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.25870001316070557},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.25589999556541443}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.07330","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.07330","pdf_url":"https://arxiv.org/pdf/2511.07330","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2511.07330","doi":"https://doi.org/10.48550/arxiv.2511.07330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.07330","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.07330","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.07330","pdf_url":"https://arxiv.org/pdf/2511.07330","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7510426044464111}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7104917543.pdf","grobid_xml":"https://content.openalex.org/works/W7104917543.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1,75],"introduces":[2],"Roundabout":[3],"Constrained":[4],"Convex":[5],"Generators":[6],"(RCGs),":[7],"a":[8,57,66],"set":[9,58],"representation":[10,24,60,69,122],"framework":[11,30,112],"for":[12,107],"modeling":[13],"multiply":[14],"connected":[15],"regions":[16,126],"in":[17,45],"control":[18,50],"and":[19,48,65,87,100],"verification":[20],"applications.":[21],"The":[22,74,111],"RCG":[23],"extends":[25],"the":[26,121],"constrained":[27],"convex":[28,90],"generators":[29],"by":[31],"incorporating":[32],"an":[33],"inner":[34],"exclusion":[35],"zone,":[36],"creating":[37],"sets":[38],"with":[39,89,115],"topological":[40],"holes":[41],"that":[42,61,70,127],"naturally":[43],"arise":[44],"collision":[46],"avoidance":[47],"safety-critical":[49],"problems.":[51],"We":[52,93],"present":[53],"two":[54],"equivalent":[55],"formulations:":[56],"difference":[59],"provides":[62],"geometric":[63],"intuition":[64],"unified":[67],"parametric":[68],"facilitates":[71],"computational":[72,105],"implementation.":[73],"establishes":[76],"closure":[77],"properties":[78],"under":[79],"fundamental":[80],"operations,":[81],"including":[82,97],"linear":[83],"transformations,":[84],"Minkowski":[85],"sums,":[86],"intersections":[88],"generator":[91],"sets.":[92],"derive":[94],"special":[95],"cases,":[96],"roundabout":[98,101],"zonotopes":[99],"ellipsotopes,":[102],"which":[103],"offer":[104],"advantages":[106],"specific":[108],"norm":[109],"selections.":[110],"maintains":[113],"compatibility":[114],"existing":[116],"optimization":[117],"solvers":[118],"while":[119],"enabling":[120],"of":[123],"non-convex":[124],"feasible":[125],"were":[128],"previously":[129],"challenging":[130],"to":[131],"model":[132],"efficiently.":[133]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-11-12T00:00:00"}