Mobile robots as remote sensors for spatial point process models

Spatial point process models are a commonly-used statistical tool for studying the distribution of objects of interest in a domain. We study the problem of deploying mobile robots as remote sensors to estimate the parameters of such a model, in particular the intensity parameter λ which measures the mean density of points in a Poisson point process. This problem requires covering an appropriately large section of the domain while avoiding the objects, which we treat as obstacles. We develop a control law that covers an expanding section of the domain and an online criterion for determining when to stop sampling, i.e., when the covered area is large enough to achieve a desired level of estimation accuracy, and illustrate the resulting system with numerical simulations.