Deployment of an unreliable robotic sensor network for spatial estimation

This paper studies an optimal deployment problem for a network of robotic sensors moving in the real line. Given a spatial process of interest, each individual sensor sends a packet that contains a measurement of the process to a data fusion center. We assume that, due to communication limitations or hardware unreliability, only a fraction of the packets arrive at the center. Using convex analysis, nonsmooth analysis, and combinatorics, we show that, for various fractional rates of packet arrival, the optimal deployment configuration has the following features: agents group into clusters, clusters deploy optimally as if at least one packet from each cluster was guaranteed to reach the center, and there is an optimal cluster size for each fractional arrival rate.