Distributed formation control with permutation symmetries

In distributed control applications such as coverage or consensus by multiple mobile agents, a great new challenge is the development of motion algorithms that dynamically determine the positions of the agents in the formation using only local information. In this paper, we address this challenge using two novel ideas. First, we represent a formation as a rotational and translational invariant configuration in the free space and employ distributed consensus algorithms to guarantee that all agents agree on the rotation and translation of the final formation configuration. Second, local market-based coordination protocols dynamically determine a permutation of the agents in the formation, while artificial potential fields are used to drive the group of agents to the desired formation. Integration of the overall system results in a distributed, multi- agent, hybrid system which, under a connectivity assumption on the underlying communication network, is shown to always converge to the desired formation. Furthermore, the number of explored permutations is at most polynomial with the number of agents, while scalability of our approach is illustrated by nontrivial computer simulations.