Interactive Planning and Sensing in Uncertain Environments with Task-Driven Sensor Placement

Abstract

We consider the problem of planning the path of a vehicle, called the actor, to traverse a threat field with minimum threat exposure. The threat field is an unknown, time-invariant, and strictly positive scalar field defined on a compact 2D spatial domain estimated by a network of mobile sensors. The threat field is assumed to be finitely parametrized by coefficients of spatial basis functions. Estimates of these parameters are constructed using measurements from the sensors. A novelty of this problem setup is that the actor can request the sensors to reposition themselves. The actor and the sensors interact iteratively. At each iteration, Dijkstra's algorithm is used to determine the actor's path with minimum expected threat exposure. Next, a set of grid points “near” this path are identified. Finally, the next set of sensor locations is determined to maximize the confidence of threat field estimates on these grid points, the threat field estimate is accordingly updated, and the iteration repeats. We study the convergence of these iterations and the actor's performance under this interactive sensor placement method. We compare the proposed method to a typical information-driven sensor placement approach. We demonstrate that in comparison, not only is the proposed method faster by at least two orders of magnitude, but in certain situations also results in improved actor performance.