Decentralized Scalable Exploration via Emergent Adaptive Lévy Walks on Minimal-Sensing Platforms

Efficient autonomous exploration with palm-sized nano-UAVs remains challenging due to severe limitations in sensing, computation, and flight endurance. We present a lightweight sensor-driven L\'evy walk (SDLW) controller for aerial robots weighing under 50 grams and equipped with sparse local sensing. The method combines discrete L\'evy step-length sampling with a sensor-reactive heading policy using directional range measurements. Each robot independently samples its L\'evy exponent from a uniform prior to diversify exploration without inter-robot communication for exploration control. Each robot then selects headings using a von Mises distribution that biases motion toward open directions while preserving superdiffusive exploration properties. The controller operates at constant computational cost, enabling scalable multi-UAV exploration. Simulation results show coverage improvements of 79.6% in open arenas, 43.1% in rooms-and-corridors layouts, and 13.6% in cluttered environments, with collision reductions of 13.0%, 7.1%, and 1.4%, respectively, relative to a uniform-heading L\'evy walk baseline. This work provides a practical framework for scalable multi-robot exploration on minimal-sensing, resource-constrained nano-UAVs.