An efficient distributed topo-geometric spatial density estimation method for multi-robot systems

A fundamental challenge in multi-robot systems is that global information is needed to succeed in some tasks, while the system's computation and sensing are fundamentally distributed. This paper considers the problem of estimating the relative density of robots in particular regions of the environment, but without wishing to incur the cost of obtaining a consistent metric representation. We compute a probability density function that describes positions of the robots within the system by leveraging properties of the underlying communication network. We introduce three different strategies for using and combining local measurements via a modified Parzen window kernel density method. The result is a representation that is most accurate near to the querying robot but which maintains qualitative properties of the global density. We argue that this a useful relaxation of the problem because it is meaningful from the perspective of the robots within the system itself. Validation takes the form of simulations with hundreds of simple robots.