Article Title]{Multi-Robot Collaborative 3D Path Planning Based On Game Theory and Particle Swarm Optimization Hybrid  Method

Article Title]{Multi-Robot Collaborative 3D Path Planning Based On Game Theory and Particle Swarm Optimization Hybrid Method | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Article Title]{Multi-Robot Collaborative 3D Path Planning Based On Game Theory and Particle Swarm Optimization Hybrid Method Hong Qiu, Wentao Yu, Gan Zhang, Xuan Xia, Kun Yao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5185711/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract Multi-robot path planning in 3D environment is complex and challenging task that needs to consider not only the high quality and safety of the paths, but also the coordination between robots. Aiming at this problem, a collaborative 3D path planning scheme using game theory and Particle Swarm Optimization hybrid method (GTPHM) is presented in paper. Firstly, a cost function is formulated to transform path planning into an optimization problem, for which the multi-robot space motion equation is designed to satisfy the dynamic constraints. Then, a game theory-based multi-robot path planning framework is established, using collision costs and multi-objective heuristic functions as game gains to maintain the game-theoretic interaction between robots. In the improved particle swarm optimization algorithm(PSO), the particle space position transformation method designed according to the three-dimensional space vector, used as a strategy update mechanism based on game theory. For collisions avoidance between robots, each robot adjusts its Cooperative strategy based on the behavior of the other robots. Each robot chooses the optimal cooperative strategy, and then gradually approach the Nash equilibrium. Comparative experimental results show that GTPHM can effectively guide multi-robot to plan a safe and collision-free path from the starting point to the target point in mountain and city complex 3D environment. Multi-robot Path planning Game theory Particle swarm optimization Multi-robot systems Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 31 Oct, 2024 Reviews received at journal 22 Oct, 2024 Reviewers agreed at journal 12 Oct, 2024 Reviewers agreed at journal 12 Oct, 2024 Reviewers agreed at journal 08 Oct, 2024 Reviewers agreed at journal 08 Oct, 2024 Reviewers agreed at journal 08 Oct, 2024 Reviewers agreed at journal 07 Oct, 2024 Reviewers agreed at journal 06 Oct, 2024 Reviewers invited by journal 06 Oct, 2024 Editor assigned by journal 04 Oct, 2024 Submission checks completed at journal 04 Oct, 2024 First submitted to journal 01 Oct, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5185711","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":372755273,"identity":"c12cc8c8-faf4-4501-a466-b9dd87a0876a","order_by":0,"name":"Hong Qiu","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hong","middleName":"","lastName":"Qiu","suffix":""},{"id":372755274,"identity":"4d5b1729-56a3-4c2e-bd63-660740cfbe70","order_by":1,"name":"Wentao Yu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYDADfhBRASIOEFbM2AAiJUHkmQRStBgcIFaLwfHe4w9+VBxO3Hz8+DOJgz8Y5PhuJDB+LsCn5cy5xMaeM4cTt53JMZM4kMBgLHkjgVl6Bh4tZjdyDBt424BabvCwSX9IYEjccCOBjZkHn5b7bwwb/wK1bJ7B/gxkSz1hLTd4DJtBtmyQYAA7LMGAkBb7MzmGs2XOpBvPOJNjbHEgTcJw5pmHzdL4tEi2nzH4+KbCWra//fjDGwdsbOT5jicf/IxPCxQ0wxgSDLCIIgTqiFE0CkbBKBgFIxUAAC3jVDhIeo5WAAAAAElFTkSuQmCC","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":true,"prefix":"","firstName":"Wentao","middleName":"","lastName":"Yu","suffix":""},{"id":372755275,"identity":"5a218bb6-2dae-4873-b2e4-399a975dbd4b","order_by":2,"name":"Gan Zhang","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Gan","middleName":"","lastName":"Zhang","suffix":""},{"id":372755276,"identity":"252a2f7b-4d4a-4657-a7a9-bb3ed4716802","order_by":3,"name":"Xuan Xia","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xuan","middleName":"","lastName":"Xia","suffix":""},{"id":372755277,"identity":"9b7bd9c1-2f17-4c21-b30b-bd4dfb80d5e6","order_by":4,"name":"Kun Yao","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Kun","middleName":"","lastName":"Yao","suffix":""}],"badges":[],"createdAt":"2024-10-01 08:38:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5185711/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5185711/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":70627303,"identity":"6e36cbaf-a489-4057-9553-7ea3c752c0d5","added_by":"auto","created_at":"2024-12-05 04:54:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":21368862,"visible":true,"origin":"","legend":"","description":"","filename":"MultiRobotCollaborative3DPathPlanningBasedOnGameTheoryandParticleSwarmOptimizationHybridMethod.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5185711/v1_covered_56b87e47-24c2-4e61-91c1-fb2685212899.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Article Title]{Multi-Robot Collaborative 3D Path Planning Based On Game Theory and Particle Swarm Optimization Hybrid Method","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Multi-robot Path planning, Game theory, Particle swarm optimization, Multi-robot systems","lastPublishedDoi":"10.21203/rs.3.rs-5185711/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5185711/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMulti-robot path planning in 3D environment is complex and challenging task that needs to consider not only the high quality and safety of the paths, but also the coordination between robots. Aiming at this problem, a collaborative 3D path planning scheme using game theory and Particle Swarm Optimization hybrid method (GTPHM) is presented in paper. Firstly, a cost function is formulated to transform path planning into an optimization problem, for which the multi-robot space motion equation is designed to satisfy the dynamic constraints. Then, a game theory-based multi-robot path planning framework is established, using collision costs and multi-objective heuristic functions as game gains to maintain the game-theoretic interaction between robots. In the improved particle swarm optimization algorithm(PSO), the particle space position transformation method designed according to the three-dimensional space vector, used as a strategy update mechanism based on game theory. For collisions avoidance between robots, each robot adjusts its Cooperative strategy based on the behavior of the other robots. Each robot chooses the optimal cooperative strategy, and then gradually approach the Nash equilibrium. Comparative experimental results show that GTPHM can effectively guide multi-robot to plan a safe and collision-free path from the starting point to the target point in mountain and city complex 3D environment.\u003c/p\u003e","manuscriptTitle":"Article Title]{Multi-Robot Collaborative 3D Path Planning Based On Game Theory and Particle Swarm Optimization Hybrid Method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-05 04:54:21","doi":"10.21203/rs.3.rs-5185711/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-31T21:03:06+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-22T09:23:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"281676617576582078441520997195209301020","date":"2024-10-12T12:51:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"8001530420372225213554185029196254392","date":"2024-10-12T06:12:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"81892691865207516708153180997551278243","date":"2024-10-09T01:11:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"212419195630428486216148533903985045780","date":"2024-10-08T10:56:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"275492495242824918399569540633431739032","date":"2024-10-08T05:04:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"252855805338816738150194185092057951622","date":"2024-10-07T04:48:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"54130856299398156740347491704082319500","date":"2024-10-06T21:46:10+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-10-06T17:33:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-10-04T14:26:40+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-10-04T14:26:22+00:00","index":"","fulltext":""},{"type":"submitted","content":"The Journal of Supercomputing","date":"2024-10-01T08:29:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"e8f08d56-77ed-48b1-ac79-04bf4a51140c","owner":[],"postedDate":"December 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-01-16T19:23:21+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-05 04:54:21","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5185711","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5185711","identity":"rs-5185711","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}