Sculpting Chaos: Task-Specific Robotic Control with a Novel Hopfield System and False Attractors

Abstract

This study introduces a novel robotic control paradigm, “chaos redirection,” which utilizes a single chaotic Hopfield Neural Network (HNN). We introduce “false attractors” synthetic trajectories created by applying controlled temporal shifts to the HNN’s state variables. This method allows a single chaotic source to be sculpted into distinct, task-specific behaviors for autonomous robots. We apply this framework to three applications: area cleaning, systematic search, and security patrol. Quantitative, statistically validated analysis demonstrates the successful generation of functionally distinct behaviors, including high-frequency, confined re-visitation for security patrols; maximized exploratory efficiency for search tasks; and high-entropy, non-repetitive paths for thorough cleaning. Our findings establish this as a robust and computationally efficient framework for applications requiring unpredictable, yet structured, behavior.