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<p>The article aims to explore the use of three-dimensional chaotic maps for 3D boundary surveillance, especially infrastructures, enabling the generation of inherently unpredictable quadrotor trajectories. The topology of the chaotic attractor is crucial for achieving unpredictable paths while monitoring critical infrastructures, making it difficult for adversaries to track the quadrotors. This study employs the Johnny Svensson chaotic system, which resembles a two-dimensional projection of the torus if viewed from one of its angled sides. It extends this two-dimensional chaotic map to a three-dimensional one by adding a <i>z</i>-dimension to create spatial depth on the attractor and also scales down the <i>x</i>-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 chaotic 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 system, the quadrotor can move around complex infrastructures while having unpredictable trajectories and enhancing the reliability of surveillance operations. Implementing this 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 Acceleration 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.</p>

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Novel 3D chaotic quadrotor trajectories for infrastructure monitoring

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Harisankar R.,
  • Mohamed Samshad,
  • Sishu Shankar Muni,
  • Abhishek Kaushik

摘要

The article aims to explore the use of three-dimensional chaotic maps for 3D boundary surveillance, especially infrastructures, enabling the generation of inherently unpredictable quadrotor trajectories. The topology of the chaotic attractor is crucial for achieving unpredictable paths while monitoring critical infrastructures, making it difficult for adversaries to track the quadrotors. This study employs the Johnny Svensson chaotic system, which resembles a two-dimensional projection of the torus if viewed from one of its angled sides. It extends this two-dimensional chaotic map to a three-dimensional one by adding a z-dimension to create spatial depth on the attractor and also scales down the 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 chaotic 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 system, the quadrotor can move around complex infrastructures while having unpredictable trajectories and enhancing the reliability of surveillance operations. Implementing this 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 Acceleration 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.