Interactive Planning and Sensing in Spatiotemporally Varying Uncertain Environments

Abstract

We address planar path-planning for a mobile vehicle to traverse a workspace with minimum exposure to an unknown spatially and temporally varying scalar field, which we call the threat field. The threat field is estimated by a finite number of mobile sensors that can take pointwise measurements with finite sampling frequency. We address this problem using an iterative bidirectional interaction between planning and sensor placement phases. Owing to this interaction, sensors are placed at locations where the threat field measurements are of most relevance to the path-planning problem. We provide theoretical conditions under which this iterative sensing-planning algorithm is convergent. This algorithm includes considerations for finite durations of time required for the various computations involved therein. Numerical simulation results and prior theoretical results with time-invariant threat fields indicate that not only is the proposed algorithm convergent, but it also produces near optimal paths.