{"id":"https://openalex.org/W2112642534","doi":"https://doi.org/10.1109/acc.2007.4283045","title":"Tight formation flying and sphere packing","display_name":"Tight formation flying and sphere packing","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2112642534","doi":"https://doi.org/10.1109/acc.2007.4283045","mag":"2112642534"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4283045","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4283045","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-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/A5003608838","display_name":"Yoonsoo Kim","orcid":"https://orcid.org/0000-0002-0357-9826"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yoonsoo Kim","raw_affiliation_strings":["Department of Engineering, University of Leicester, Leicester, UK","University of Leicester , Leicester"],"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Leicester, Leicester, UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"University of Leicester , Leicester","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007592479","display_name":"Da\u2010Wei Gu","orcid":"https://orcid.org/0000-0001-7475-5041"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Da-Wei Gu","raw_affiliation_strings":["Department of Engineering, University of Leicester, Leicester, UK","University of Leicester , Leicester"],"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Leicester, Leicester, UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"University of Leicester , Leicester","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007050558","display_name":"Ian Postlethwaite","orcid":"https://orcid.org/0000-0002-0267-1831"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ian Postlethwaite","raw_affiliation_strings":["Department of Engineering, University of Leicester, Leicester, UK","University of Leicester , Leicester"],"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Leicester, Leicester, UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"University of Leicester , Leicester","institution_ids":["https://openalex.org/I153648349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003608838"],"corresponding_institution_ids":["https://openalex.org/I153648349"],"apc_list":null,"apc_paid":null,"fwci":0.6736,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75251229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"98","issue":null,"first_page":"1085","last_page":"1090"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11133","display_name":"UAV Applications and Optimization","score":0.9765999913215637,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4331062436103821},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4186254143714905},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37814798951148987},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3306248188018799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2214314043521881}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4331062436103821},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4186254143714905},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37814798951148987},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3306248188018799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2214314043521881}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/acc.2007.4283045","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4283045","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:lra.le.ac.uk:2381/20268","is_oa":false,"landing_page_url":"http://hdl.handle.net/2381/20268","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Journal Article"},{"id":"pmh:oai:nrl.northumbria.ac.uk:10462","is_oa":false,"landing_page_url":"http://nrl.northumbria.ac.uk/id/eprint/10462/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401884","display_name":"Northumbria Research Link (Northumbria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32394136","host_organization_name":"Northumbria University","host_organization_lineage":["https://openalex.org/I32394136"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W247697463","https://openalex.org/W1483484469","https://openalex.org/W1563233701","https://openalex.org/W1587744656","https://openalex.org/W1602384651","https://openalex.org/W1864806140","https://openalex.org/W1977316377","https://openalex.org/W1984732727","https://openalex.org/W2055789678","https://openalex.org/W2074032690","https://openalex.org/W2107940287","https://openalex.org/W2112847394","https://openalex.org/W2124497430","https://openalex.org/W2128928412","https://openalex.org/W2129078098","https://openalex.org/W2129973592","https://openalex.org/W2130519480","https://openalex.org/W2144267444","https://openalex.org/W2146890818","https://openalex.org/W2165744313","https://openalex.org/W2167362932","https://openalex.org/W4238591275","https://openalex.org/W6628979811","https://openalex.org/W6636087901","https://openalex.org/W6679163857"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"In":[0,135],"this":[1,139],"paper,":[2],"we":[3],"introduce":[4],"a":[5,9,120,143],"method":[6],"for":[7,148],"finding":[8,29],"tight":[10,27,140],"formation":[11,28,57,71,141],"of":[12,34,43,138,153],"unmanned":[13],"air":[14],"vehicles":[15],"(UAVs)":[16],"via":[17],"the":[18,26,32,36,44,56,63,69,95,104,107,136,149],"classical":[19],"sphere":[20,64],"packing":[21,65],"scheme.":[22],"We":[23,51,81],"first":[24],"translate":[25],"problem":[30,33],"to":[31,68,126,130],"maximizing":[35],"second":[37],"smallest":[38],"eigenvalue":[39],"<i":[40,47,58,72,77,84,88,114,131],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[41,48,59,73,78,85,89,115,132],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03bb<sub>2</sub>(G)</i>":[42,79],"graph":[45,125],"Laplacian":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L<sub>G</sub></i>":[49],".":[50,80,134],"then":[52],"show":[53,82],"how":[54],"close":[55],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">G<sub>s</sub></i>":[60,116],"obtained":[61],"from":[62],"scheme":[66],"is":[67,91,146],"optimal":[70,150],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">G*</i>":[74,133],"that":[75,83,113,122],"maximizes":[76],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03bb<sub>2</sub>(G*)</i>":[86],"/":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03bb<sub>2</sub>(G<sub>s</sub>)</i>":[90],"relatively":[92],"small":[93],"when":[94],"communication":[96],"strength":[97],"between":[98,106],"two":[99,108],"UAVs":[100],"decays":[101],"slowly":[102],"with":[103],"distance":[105],"UAVs.":[109,155],"This":[110],"result":[111],"implies":[112],"can":[117],"serve":[118],"as":[119],"certificate":[121],"allows":[123],"every":[124],"be":[127],"quantitatively":[128],"compared":[129],"light":[137],"result,":[142],"modelling":[144],"technique":[145],"given":[147],"airborne":[151],"refuelling":[152],"multiple":[154]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
