A Chaos-Theoretic Framework for Autonomous Robot Navigation in Complex and Uncertain Environments

Path planning for autonomous robots is a key problem area, particularly when faced with complicated, dynamic, or uncertain environments. Even though traditional techniques (grid-based, graph-based, sampling, and optimization-based) have already been developed to solve this problem, there are notable limitations to scalability, adaptability, and responsiveness with these methods. In this paper, we explore an alternative approach based on chaotic dynamical systems, specifically chaotic attractors like those produced by the Lorenz and Rössler systems. Chaotic systems are defined by several properties that could be leveraged: non-linearity, sensitivity to initial conditions, and dense coverage of the state space are three notable properties that could be used to generate trajectories that are organized, yet ultimately unpredictable. By applying numerical integration (Runge–Kutta) directly to robot motion through MATLAB R2025b simulations, chaotic states support more effective exploration, better obstacle avoidance, and more robust navigation in dynamic or adversarial environments. The paper also examines whether chaotic path planning can be applied in multi-robot systems through state coupled robots that emerge coordinated behavior while maintaining autonomous movement. This paper is a framework for chaos theory supporting adaptable, robust navigating behaviors for purposes such as autonomous vehicles, swarm robotics, and search and rescue and surveillance applications.