{"id":"https://openalex.org/W4390480904","doi":"https://doi.org/10.1109/tcyb.2023.3340659","title":"Game-Based Approximate Optimal Motion Planning for Safe Human-Swarm Interaction","display_name":"Game-Based Approximate Optimal Motion Planning for Safe Human-Swarm Interaction","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4390480904","doi":"https://doi.org/10.1109/tcyb.2023.3340659","pmid":"https://pubmed.ncbi.nlm.nih.gov/38163300"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2023.3340659","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2023.3340659","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5100404496","display_name":"Man Li","orcid":"https://orcid.org/0000-0002-9776-1628"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Man Li","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053071794","display_name":"Jiahu Qin","orcid":"https://orcid.org/0000-0001-7580-0836"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiahu Qin","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China","Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0001-7580-0836","affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043576277","display_name":"Jiacheng Li","orcid":"https://orcid.org/0000-0003-4410-4824"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiacheng Li","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0003-4410-4824","affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054350814","display_name":"Qingchen Liu","orcid":"https://orcid.org/0000-0002-5892-3591"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingchen Liu","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-5892-3591","affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028730873","display_name":"Yang Shi","orcid":"https://orcid.org/0000-0003-1337-5322"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yang Shi","raw_affiliation_strings":["Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada"],"raw_orcid":"https://orcid.org/0000-0003-1337-5322","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025987638","display_name":"Yu Kang","orcid":"https://orcid.org/0000-0002-8706-3252"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Kang","raw_affiliation_strings":["Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, China","Department of Automation, Institute of Advanced Technology, University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-8706-3252","affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, China","institution_ids":[]},{"raw_affiliation_string":"Department of Automation, Institute of Advanced Technology, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2557,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92205645,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"54","issue":"10","first_page":"5649","last_page":"5660"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9472000002861023,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9472000002861023,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9348999857902527,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9031999707221985,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/swarm-behaviour","display_name":"Swarm behaviour","score":0.6156704425811768},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.6059952974319458},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5950217247009277},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5607551336288452},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.549160897731781},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5327494144439697},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5298882126808167},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.45633476972579956},{"id":"https://openalex.org/keywords/obstacle-avoidance","display_name":"Obstacle avoidance","score":0.43874573707580566},{"id":"https://openalex.org/keywords/motion-planning","display_name":"Motion planning","score":0.43652260303497314},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.43512946367263794},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.422853946685791},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4206130802631378},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3726748824119568},{"id":"https://openalex.org/keywords/mobile-robot","display_name":"Mobile robot","score":0.32856059074401855},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.31685128808021545},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2916593551635742},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.26188546419143677},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23733174800872803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13655385375022888}],"concepts":[{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.6156704425811768},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.6059952974319458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5950217247009277},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5607551336288452},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.549160897731781},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5327494144439697},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5298882126808167},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.45633476972579956},{"id":"https://openalex.org/C6683253","wikidata":"https://www.wikidata.org/wiki/Q7075535","display_name":"Obstacle avoidance","level":4,"score":0.43874573707580566},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.43652260303497314},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.43512946367263794},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.422853946685791},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4206130802631378},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3726748824119568},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.32856059074401855},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31685128808021545},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2916593551635742},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.26188546419143677},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23733174800872803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13655385375022888},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2023.3340659","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2023.3340659","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},{"id":"pmid:38163300","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38163300","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"id":"https://metadata.un.org/sdg/13","display_name":"Climate action"}],"awards":[{"id":"https://openalex.org/G2710557896","display_name":null,"funder_award_id":"62303435","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G832011062","display_name":null,"funder_award_id":"BX20220285","funder_id":"https://openalex.org/F4320335768","funder_display_name":"National Postdoctoral Program for Innovative Talents"},{"id":"https://openalex.org/G8597135142","display_name":null,"funder_award_id":"2308085QF203","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G883240379","display_name":null,"funder_award_id":"2022ZD0120002","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null},{"id":"https://openalex.org/F4320335768","display_name":"National Postdoctoral Program for Innovative Talents","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1595516097","https://openalex.org/W2142430251","https://openalex.org/W2267863633","https://openalex.org/W2409460556","https://openalex.org/W2430619152","https://openalex.org/W2514422855","https://openalex.org/W2789789879","https://openalex.org/W2803623613","https://openalex.org/W2807169404","https://openalex.org/W2891411903","https://openalex.org/W2892245034","https://openalex.org/W2912024007","https://openalex.org/W2995089744","https://openalex.org/W3009350896","https://openalex.org/W3019638220","https://openalex.org/W3119933750","https://openalex.org/W3154507809","https://openalex.org/W3158757609","https://openalex.org/W3173201989","https://openalex.org/W3186359101","https://openalex.org/W3195382357","https://openalex.org/W3202358609","https://openalex.org/W3202626246","https://openalex.org/W4280606239","https://openalex.org/W4285209757","https://openalex.org/W4291910338","https://openalex.org/W4382935962","https://openalex.org/W4386232505","https://openalex.org/W6771607980"],"related_works":["https://openalex.org/W2930076404","https://openalex.org/W2071957557","https://openalex.org/W2596413128","https://openalex.org/W2356867392","https://openalex.org/W2782776446","https://openalex.org/W2155948905","https://openalex.org/W3043170174","https://openalex.org/W1971413691","https://openalex.org/W2050548713","https://openalex.org/W4380590094"],"abstract_inverted_index":{"Safety":[0],"as":[1,48],"a":[2,10,21,31,49,71,131,139,168,215],"fundamental":[3],"requirement":[4],"for":[5,86,127,144],"human-swarm":[6,45],"interaction":[7,46],"has":[8,30],"attracted":[9],"lot":[11],"of":[12,107,190],"attention":[13],"in":[14,52,70,167],"recent":[15],"years.":[16],"Most":[17],"existing":[18],"approaches":[19],"solve":[20],"constrained":[22],"optimization":[23,55],"problem":[24,47],"at":[25],"each":[26],"time":[27,61],"step,":[28],"which":[29,53],"high":[32],"real-time":[33],"requirement.":[34],"To":[35],"deal":[36],"with":[37,76,104],"this":[38,40],"challenge,":[39],"article":[41],"formulates":[42],"the":[43,54,59,77,88,105,109,113,119,128,145,158,163,173,183,191],"safe":[44,151],"Stackerberg-Nash":[50],"game,":[51],"is":[56,66,186,194],"performed":[57],"over":[58],"entire":[60],"domain.":[62],"The":[63,93,188,200],"leader":[64,146],"robot":[65],"supposed":[67],"to":[68,80,90,101,149],"be":[69,209],"dominant":[72],"position,":[73],"interacting":[74],"directly":[75],"human":[78,174,184],"operator":[79],"realize":[81,150],"trajectory":[82],"tracking":[83,142],"and":[84,138,152,176,198],"responsible":[85],"guiding":[87],"swarm":[89],"avoid":[91],"obstacles.":[92],"follower":[94],"robots":[95],"always":[96],"take":[97],"their":[98,178],"best":[99],"responses":[100],"leader's":[102],"behavior":[103],"purpose":[106],"achieving":[108],"desired":[110,169],"formation.":[111],"Following":[112],"bottom-up":[114],"principle,":[115],"we":[116],"first":[117],"design":[118],"best-response":[120],"controllers,":[121],"that":[122,157,205],"is,":[123],"Nash":[124],"equilibrium":[125],"strategies,":[126],"followers.":[129],"Then,":[130],"Lyapunov-like":[132],"control":[133],"barrier":[134],"function-based":[135],"safety":[136,206],"controller":[137,143],"learning-based":[140],"formation":[141,171],"are":[147],"designed":[148,159],"robust":[153],"cooperation.":[154],"We":[155],"show":[156,204],"controllers":[160],"can":[161,207],"make":[162],"robotic":[164],"swarms":[165],"move":[166],"geometric":[170],"following":[172],"command":[175,185],"modify":[177],"motion":[179],"trajectories":[180],"autonomously":[181],"when":[182,212],"unsafe.":[187],"effectiveness":[189],"proposed":[192],"approach":[193],"verified":[195],"through":[196],"simulation":[197],"experiments.":[199],"experiment":[201],"results":[202],"further":[203],"still":[208],"guaranteed":[210],"even":[211],"there":[213],"exists":[214],"dynamic":[216],"obstacle.":[217]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}