An entropy-based framework for dynamic clustering and coverage problems

In this paper, we consider the general class of coverage and clustering problems in a dynamic environment, and propose a computationally efficient framework to address them. We define the problem of achieving instantaneous coverage as a combinatorial optimization problem in a Maximum Entropy Principle framework. We then extend the framework to a dynamic environment, thereby allowing us to address the inherent trade-off between the resolution of the clusters and the computation cost, and provides flexibility to a variety of dynamic specifications. The proposed framework addresses both the coverage as well as tracking aspects of the problem. The determination of cluster centers and their associated velocity field is cast as a control design problem ensuring that the algorithm achieves progressively better coverage with time. Simulation results presented in the paper demonstrate that the proposed algorithm achieves target coverage costs five to seven times faster than related frame-by-frame methods, with the additional ability to identify natural clusters in the dataset.