Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map

Lazaros Moysis, Karthikeyan Rajagopal, Aleksandra V. Tutueva, Christos Volos, Beteley Teka and Denis N. Butusov
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Lazaros Moysis: Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Karthikeyan Rajagopal: Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
Aleksandra V. Tutueva: Youth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, 197376 St Petersburg, Russia
Christos Volos: Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Beteley Teka: Department of Electronics Engineering, Defence University College of Engineering, Bishoftu 1041, Ethiopia
Denis N. Butusov: Youth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, 197376 St Petersburg, Russia

Mathematics, 2021, vol. 9, issue 15, 1-16

Abstract: 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.

Keywords: chaos; pseudo-random bit generator; path planning; chaotic mobile robot; UAV (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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