Regulated Morphogen Gradients for Target Surrounding and Adaptive Shape Formation

In swarm robotics, developing algorithms for self-organizing minimalistic robots has become a popular research topic. Unlike others, minimalistic robots may not be able to self-localize themselves, making it very challenging to accomplish missions such as surrounding a target, whose position is typically unknown. In target surroundings, reaching a target and joining the swarm do not always lead to a satisfactory enclosure of the target. Furthermore, it is impossible for individual minimalistic robots to figure out what a global shape of the swarm should be without a collective decision making. In this article, we make use of diffusion and reaction of two morphogens for target surrounding and formation of a circular shape swarm. We show that the proposed method is able to adaptively form shapes surrounding multiple targets. Computer simulations and physical experiments using Kilobots are performed to assess the performance of the proposed algorithm.