Novel 3D Chaotic Quadrotor Trajectories for Infrastructure Monitoring

Novel 3D Chaotic Quadrotor Trajectories for Infrastructure Monitoring | 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 Novel 3D Chaotic Quadrotor Trajectories for Infrastructure Monitoring Harisankar Ravikumar, Mohammed Samshad, Sishu Shankar Muni, Abhishek kaushik This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6904874/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper demonstrates the use of twoand three-dimensional chaotic maps for 3D boundary surveillance around infrastructures by providing unpredictable trajectories. The topology of the chaotic attractor is crucial for achieving unpredictable paths while monitoring critical infrastructures. Utilized Johnny Svensson system is a complicated chaotic attractor, which appears to be some sort of two-dimensional projection of the torus if viewed from one of its angled sides. This paper extends this twodimensional chaotic map to a three-dimensional one by adding a z-dimension to create spatial depth on the attractor and also scale down x-dimension by a factor of 0.35. The resulting three-dimensional chaotic attractor has an intricate point cloud structure resembling more like an annular cylinder, hence yielding a strong structural framework for path planning of quadrotors in infrastructure surveillance. A Hyperchaotic map presented here uses the divergence of consecutive iterates of the discrete map and results in unpredictable flight paths. Core void space within the 3D attractor can be allocated to essential infrastructure because the attractor’s chaotic nature inherently stops the generation of points within the central void after neglecting the transients. Introducing and implementing a collision avoidance algorithm, quadrotor flight paths are designed not to cross the crucial central area. This prevents infrastructure from interference by surveillance trajectories. Through the utilization of these inherent properties of chaotic systems, the quadrotor can move around complex infrastructures while having unpredictable trajectories and enhancing the reliability of surveillance operations. Implementing a discrete chaotic map on a low-cost microcontroller validates its practical feasibility and real-time suitability, especially for power- and resource-constrained nano quadricopters. This work explores the space-filling and unpredictability properties of chaotic quadrotor trajectories. The space-filling nature is quantitatively validated using the Voxel Coverage Ratio (VCR) metric by evaluating the trajectory’s occupancy within a discretized bounded volume. To assess the unpredictability of the trajectories, an Extended Kalman Filter (EKF) under a constant velocity model is applied. The variation in Euclidean distance error between the predicted and actual trajectory points, in the absence of measurement noise, demonstrates the inherent unpredictability of the motion. Also, the waypoints from the proposed theoretical framework are validated through real-world implementation on a Fury micro quadcopter, confirming the practical feasibility and robustness of the approach. Robotics Applied Mathematics Quadrotor Boundary surveillance Unpredictable trajectories Hyperchaotic map Non autonomous discrete memristor map Infrastructure Monitoring Boundry surveillance Full Text Additional Declarations The authors declare no competing interests. Supplementary Material is not available with this version. Cite Share Download PDF Status: Posted Version 1 posted 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-6904874","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471926143,"identity":"a3392735-7b98-48f6-b8a2-5a66e5f7480e","order_by":0,"name":"Harisankar Ravikumar","email":"","orcid":"","institution":"Digital University Kerala","correspondingAuthor":false,"prefix":"","firstName":"Harisankar","middleName":"","lastName":"Ravikumar","suffix":""},{"id":471926727,"identity":"7e1612ba-c6d7-4574-ab85-1c70bde544cc","order_by":1,"name":"Mohammed Samshad","email":"","orcid":"","institution":"Indian Institute of Technology Kanpur","correspondingAuthor":false,"prefix":"","firstName":"Mohammed","middleName":"","lastName":"Samshad","suffix":""},{"id":471926728,"identity":"64574a37-17eb-4915-b533-2c8128a5cfde","order_by":2,"name":"Sishu Shankar Muni","email":"","orcid":"","institution":"Digital University Kerala","correspondingAuthor":false,"prefix":"","firstName":"Sishu","middleName":"Shankar","lastName":"Muni","suffix":""},{"id":471926729,"identity":"0a793f9a-f863-4765-b202-7275d974de09","order_by":3,"name":"Abhishek kaushik","email":"data:image/png;base64,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","orcid":"","institution":"Digital University Kerala","correspondingAuthor":true,"prefix":"","firstName":"Abhishek","middleName":"","lastName":"kaushik","suffix":""}],"badges":[],"createdAt":"2025-06-16 11:08:18","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6904874/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6904874/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84829496,"identity":"1df3f544-8ffc-4693-8a8a-52d7d238ef4f","added_by":"auto","created_at":"2025-06-17 18:30:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3418065,"visible":true,"origin":"","legend":"","description":"","filename":"RSSpringerformatisr2NDPAPERCopy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6904874/v1_covered_c60fe803-6910-49fa-9b20-9559ef2b58ce.pdf"}],"financialInterests":"\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003eSupplementary Material is not available with this version.\u003c/p\u003e","formattedTitle":"\u003cp\u003eNovel 3D Chaotic Quadrotor Trajectories for Infrastructure Monitoring\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Digital University Kerala","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Quadrotor, Boundary surveillance, Unpredictable trajectories, Hyperchaotic map, Non autonomous discrete memristor map, Infrastructure Monitoring, Boundry surveillance","lastPublishedDoi":"10.21203/rs.3.rs-6904874/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6904874/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper demonstrates the use of twoand three-dimensional chaotic maps for 3D boundary surveillance around infrastructures by providing unpredictable trajectories. The topology of the chaotic attractor is crucial for achieving unpredictable paths while monitoring critical infrastructures.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eUtilized Johnny Svensson system is a complicated chaotic attractor, which appears to be some sort of two-dimensional projection of the torus if viewed from one of its angled sides. This paper extends this twodimensional chaotic map to a three-dimensional one by adding a z-dimension to create spatial depth on the attractor and also scale down x-dimension by a factor of 0.35. The resulting three-dimensional chaotic attractor has an intricate point cloud structure resembling more like an annular cylinder, hence yielding a strong structural framework for path planning of quadrotors in infrastructure surveillance. A Hyperchaotic map presented here uses the divergence of consecutive iterates of the discrete map and results in unpredictable flight paths. Core void space within the 3D attractor can be allocated to essential infrastructure because the attractor’s chaotic nature inherently stops the generation of points within the central void after neglecting the transients. Introducing and implementing a collision avoidance algorithm, quadrotor flight paths are designed not to cross the crucial central area. This prevents infrastructure from interference by surveillance trajectories. Through the utilization of these inherent properties of chaotic systems, the quadrotor can move around complex infrastructures while having unpredictable trajectories and enhancing the reliability of surveillance operations. Implementing a discrete chaotic map on a low-cost microcontroller validates its practical feasibility and real-time suitability, especially for power- and resource-constrained nano quadricopters. This work explores the space-filling and unpredictability properties of chaotic quadrotor trajectories. The space-filling nature is quantitatively validated using the Voxel Coverage Ratio (VCR) metric by evaluating the trajectory’s occupancy within a discretized bounded volume. To assess the unpredictability of the trajectories, an Extended Kalman Filter (EKF) under a constant velocity model is applied. The variation in Euclidean distance error between the predicted and actual trajectory points, in the absence of measurement noise, demonstrates the inherent unpredictability of the motion. Also, the waypoints from the proposed theoretical framework are validated through real-world implementation on a Fury micro quadcopter, confirming the practical feasibility and robustness of the approach.\u003c/p\u003e","manuscriptTitle":"Novel 3D Chaotic Quadrotor Trajectories for Infrastructure Monitoring","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-17 18:21:51","doi":"10.21203/rs.3.rs-6904874/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4cc5c162-eb74-4455-9304-08b16760ca18","owner":[],"postedDate":"June 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":50114344,"name":"Robotics"},{"id":50114345,"name":"Applied Mathematics"}],"tags":[],"updatedAt":"2025-06-17T18:21:51+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-17 18:21:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6904874","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6904874","identity":"rs-6904874","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}