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