A distributed service-matching coverage via heterogeneous mobile agents

We propose a distributed deployment solution for a group of mobile agents that should provide a service for a dense set of targets. The agents are heterogeneous in a sense that their quality of service (QoS), modeled as a spatial Gaussian distribution, is different. To provide the best service, the objective is to deploy the agents such that their collective QoS distribution is as close as possible to the density distribution of the targets. We propose a distributed consensus-based expectation-maximization (EM) algorithm to estimate the target density distribution, modeled as a Gaussian mixture model (GMM). The GMM not only gives an estimate of the targets' distribution, but also partitions the area to subregions, each of which is represented by one of the GMM's Gaussian bases. We use the Kullback-Leibler divergence (KLD) to evaluate the similarity between the QoS distribution of each agent and each Gaussian basis/subregion. Then, a distributed assignment problem is formulated and solved as a discrete optimal mass transport problem that allocates each agent to a subregion by taking the KLD as the assignment cost. We demonstrate our results by a sensor deployment for event detection where the sensor's QoS is modeled as an anisotropic Gaussian distribution.