A maximum entropy method for multi-AUV grouping

A vector-quantization formulation is used to define a grouping problem for multiple AUVs in a sampled environment. The objective is to minimize a quantization error function. The self-organizing network structure developed by Kohonen is a famous quantization model. Difficulties of applying the Kohonen´s network is that the convergence property is not guaranteed. In addition, learning gains in the Kohonen´s network have to be manually adjusted. This paper proposes a control method for the grouping of multiple AUVs under the structure of the Kohonen´s network. To solve the difficulties encountered in the framework of Kohonen´s network, we incorporate a Lyapunov function of a thermal statistical model to solve the problem of convergence. The position of each AUV is treated as a probability distribution function under thermal equilibrium. The learning gains are determined using the condition of asymptotically stability of the network. The minimization problem is formulated in a Lagrange optimal form with the constraint of maximum entropy. The intervehicle distance is controlled by the optimal distribution of the entropy. We prove that the global-minimum-error of the cost function can be achieved for the grouping