Mobile robots as remote sensors for spatial point process models

Abstract

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 lambda 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. KeywordsSpatial point processes, remote sensing, mobile robots, coverage, stopping rule Disciplines Electrical and Computer Engineering | Engineering | Systems Engineering Comments missing image.gifThis conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/716Mobile robots as remote sensors for spatial point process models Paul Reverdy and Daniel E. KoditschekAbstract-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.Mobile robots have been extensively used as platforms for remote sensors in recent years. Much of the statisticallyrigorous research on such platforms has focused on sensing and mapping continuous fields using various models. This has led to a series of results that focus on coordinating a set of robotic vehicles The mobile sensor network literature has placed significantly less emphasis on spatial point process models, which are statistical models that capture the distribution of discrete objects in space. Point process models are the subject of extensive study in the statistical literature [7] and have proven useful in numerous applied fields. In ecology, point process models have been used to study the distribution of plants in a domain [8], [9], [10], while in search and rescue they have been used to study the distribution of distress calls in a service area [11], and in disaster management they have been used for modeling the distribution of forest fires [12].Consideration of spatial point process models has recently begun to appear in the robotics literature, albeit l...