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Formation control for multi-UAVs systems based on Kullback-Leibler divergence

This paper presents a formation control method for multi unmanned aerial vehicles (UAVs) systems. The first step is to design two probability density functions describing to the desired formation and current formation, respectively. Then, through minimizing the Kullback-Leibler divergence, this method is able to bring the UAVs to a desired formation and stabilizes the desired formation in all initial conditions except the case where a pair of UAVs are in the same initial position. The gradient of Kullback-Leibler divergence is calculated using Monte Carlo method, by means of which it is not necessary to preplan route for every UAV and to take extra measure to avoid collisions between any two UAVs during the motion. At the end of this paper, the proposed method is adopted to carry out to some numerical simulations in a two-dimensional space and a three-dimensional space, respectively, to illustrate the effectiveness of the method. Conclusions show that the formation of the UAVs can converge to the desired formation under the control law proposed in this paper.