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Optimal reorganization of agent formations

In this article we address the problem of determining how a structured formation of autonomous undistinguishable agents can be reorganized into another, eventually non-rigid, formation based on changes in the environment, perhaps unforeseeable. The methodology can also be used to correctly position the agents into a particular formation from an initial set of random locations. Given the information on the agents current location and the final locations, there are n! possible permutations for the n agents. Among these, we seek one that minimizes a total relative measure, e.g. distance traveled by the agents during the switching. We propose a dynamic programming methodology to solve this problem to optimality. Possible applications can be found in surveillance, damage assessment, chemical or biological monitoring, among others, where the switching to another formation, not necessarily predefined, may be required due to changes in the environment.