Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map
This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect...
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MDPI AG
2021-08-01
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| author | Lazaros Moysis Karthikeyan Rajagopal Aleksandra V. Tutueva Christos Volos Beteley Teka Denis N. Butusov |
| author_facet | Lazaros Moysis Karthikeyan Rajagopal Aleksandra V. Tutueva Christos Volos Beteley Teka Denis N. Butusov |
| author_sort | Lazaros Moysis |
| collection | DOAJ |
| description | This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves. |
| first_indexed | 2024-03-10T09:12:17Z |
| format | Article |
| id | doaj.art-a5369ce59ac94823b16f3d41cf0b57e7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:12:17Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-a5369ce59ac94823b16f3d41cf0b57e72023-11-22T05:57:12ZengMDPI AGMathematics2227-73902021-08-01915182110.3390/math9151821Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic MapLazaros Moysis0Karthikeyan Rajagopal1Aleksandra V. Tutueva2Christos Volos3Beteley Teka4Denis N. Butusov5Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceCenter for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, IndiaYouth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, 197376 St Petersburg, RussiaLaboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceDepartment of Electronics Engineering, Defence University College of Engineering, Bishoftu 1041, EthiopiaYouth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, 197376 St Petersburg, RussiaThis work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.https://www.mdpi.com/2227-7390/9/15/1821chaospseudo-random bit generatorpath planningchaotic mobile robotUAV |
| spellingShingle | Lazaros Moysis Karthikeyan Rajagopal Aleksandra V. Tutueva Christos Volos Beteley Teka Denis N. Butusov Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map Mathematics chaos pseudo-random bit generator path planning chaotic mobile robot UAV |
| title | Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map |
| title_full | Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map |
| title_fullStr | Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map |
| title_full_unstemmed | Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map |
| title_short | Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map |
| title_sort | chaotic path planning for 3d area coverage using a pseudo random bit generator from a 1d chaotic map |
| topic | chaos pseudo-random bit generator path planning chaotic mobile robot UAV |
| url | https://www.mdpi.com/2227-7390/9/15/1821 |
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