Hyperchaotic Trajectory Planning for Quadrotor Surveillance of Infrastructure with Integrated Collision Avoidance

This paper explores the application of a three-dimensional quadratic map, which intrinsically evolves within a cubic structure, thus the space-filling property of the resulting hyperchaotic system naturally extends across this cubic volume. The intrinsic space-filling property of the resulting cubic attractor allows for improved area coverage and adaptability. Due to the affine-invariant nature of chaotic systems, the attractor can be scaled and fitted according to application-specific requirements. The cubic attractor is utilized to achieve higher unpredictability and improved coverage efficiency in quadrotor-based surveillance, as it occupies more volume and moves unpredictably within its allocated space in the path planning framework. The path planning algorithm inherently avoids collisions between the quadrotor and the infrastructure being monitored. The proposed algorithm and generated unpredictable trajectories are validated by simulations and the real-world quadrotor experiments with two trajectories at different initial conditions. Then, at a specific parameter value, the cubic attractor degenerates into 12 disjointed sheets, reducing significantly its divergence and space-filling properties. Building on this, a hypothesis is presented to strategically exploit this structured formulation to guarantee collision-free simultaneous operation of four quadrotors without relying on temporal scheduling. Simulations are shown to support the hypothesis.