Planning expected-time optimal paths for searching known environments

In this paper we address the problem of finding time optimal search paths in known environments. In particular, the task is to search a known environment for an object whose unknown location is characterized by a known probability density function (pdf). With this formulation, the time required to find the object is a random variable induced by the choice of search path together with the pdf for the object´s location. The optimization problem is to find the path that yields the minimum expected value of the time required to find the object. We propose a two layered approach. Our algorithm first determines an efficient ordering of visiting regions in a decomposition that is defined by critical curves that are related to the aspect graph of the space to be searched. It then generates locally optimal trajectories within each of these regions to construct a complete continuous path. We have implemented this algorithm and present results.