Bio-Inspired Energy Distribution for Programmable Matter

In systems of active programmable matter, individual modules require a constant supply of energy to participate in the system's collective behavior. These systems are often powered by an external energy source accessible by at least one module and rely on module-to-module power transfer to distribute energy throughout the system. While much effort has gone into addressing challenging aspects of power management in programmable matter hardware, algorithmic theory for programmable matter has largely ignored the impact of energy usage and distribution on algorithm feasibility and efficiency. In this work, we present an algorithm for energy distribution in the amoebot model that is loosely inspired by the growth behavior of Bacillus subtilis bacterial biofilms. These bacteria use chemical signaling to communicate their metabolic states and regulate nutrient consumption throughout the biofilm, ensuring that all bacteria receive the nutrients they need. Our algorithm similarly uses communication to inhibit energy usage when there are starving modules, enabling all modules to receive sufficient energy to meet their demands. As a supporting but independent result, we extend the amoebot model's well-established spanning forest primitive so that it self-stabilizes in the presence of crash failures. We conclude by showing how this self-stabilizing primitive can be leveraged to compose our energy distribution algorithm with existing amoebot model algorithms, effectively generalizing previous work to also consider energy constraints.