Abstract
Self-organized pattern formation enables swarm robots to interact with local environments to self-organize into intricate structures generated by gene regulatory network (GRN) control methods without global knowledge. Previous studies have reported that it is challenging to maintain pattern formation stability during maneuvering in the environment due to local morphogenetic reaction rules. Motivated by the mechanism of the GRN in multi-cellular organisms, we propose a novel cellular reaction gene regulatory network (CR-GRN) for pattern formation maneuvering control. In CR-GRN, a cellular reaction network is creatively proposed to depict the robots, environment, virtual target pattern, and their interaction to generate emergent swarm behavior in multi-robot systems. A novel diffusion equation is proposed to simulate the process of morphogen diffusion among cells to ensure stable adaptive pattern generation. In addition, genes, proteins, and morphogens are used to define the internal and external states of cells and form a feedback regulation network. Simulation experiments are conducted to validate the proposed method. The results show that the CR-GRN can satisfy the requirements of turning curvature and maintain the robot's uniformity based on the proposed algorithm. This proves that robots using the CR-GRN can cooperate more effectively to cope in a complicated environment, and maintain a stable formation during maneuvering.