An Algorithm Applying the Self-Organizing Capabilities of a Reaction–Diffusion Model to Control Active Swarm Robots Using Only Adjacent Module Information

Abstract

This paper introduces an algorithm designed to control self-organizing swarm robots, drawing inspiration from animal herd behaviors. In contrast to traditional methods that necessitate global information or designated leader modules, our algorithm leverages the self-organizing Turing pattern to facilitate the integration and movement of modules without relying on a coordinate system. The proposed method utilizes a "potential value," derived from the Turing pattern, to direct the modules towards the swarm's center, thereby maintaining shape integrity during movement. Our algorithm is validated through a two-dimensional simulation model, wherein each module operates under limited capabilities, including restricted self-drive, absence of module identifiers, local communication, and basic computational abilities. Despite these limitations, the algorithm enables the swarm to exhibit dynamic behaviors such as module accumulation and growth, light-source-directed movement, shape preservation after gap traversal, and self-replication. This decentralized and computationally efficient approach enables dynamic shape control and scalability to extensive swarms. It also addresses the constraints of existing Turing pattern-based methodologies, such as their focus on static shapes and the computational burden of directly solving the reaction–diffusion equation. Our findings underscore the potential of Turing patterns for achieving dynamic and scalable control of resource-constrained swarm robots. This research contributes to the advancement of more robust, adaptable, and versatile swarm robots for diverse applications, including environmental monitoring, construction, and targeted drug delivery. Future work will concentrate on validating the algorithm in a continuous space, developing a physical prototype, and investigating the emergence of hierarchical structures and diverse patterns within the swarm.