Formation control of unmanned aerial vehicles (UAVs) has many applications including target tracking, surveillance, terrain mapping, precision agriculture, etc. Although many centralized control methods (single command center/computer controlling the UAVs) exist, there are no standard decentralized control frameworks in the literature. In this paper, we present a novel UAV swarm formation control approach based on a decision theoretic approach. Specifically, we pose the decentralized swarm motion control problem as a Decentralized Markov Decision Process (Dec-MDP). Here, the objective is to drive the swarm from an initial geographical region to another geographical region where the swarm must lie on a certain geometrical surface (e.g., surface of a sphere). As most decision theoretic formulations suffer from the curse of dimensionality, we adapt an approximate dynamic programming method called nominal belief-state optimization (NBO) to solve the formation control problem approximately. We perform simulation studies in MATLAB to validate the performance of the algorithms.
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