Optimal path planning using Cross-Entropy method

This paper addresses the problem of optimizing the navigation of an intelligent mobile in a real world environment, described by a map. The map is composed of features representing natural landmarks in the environment. The vehicle is equipped with a sensor which allows it to obtain range and bearing measurements from observed landmarks during the execution. These measurements are correlated with the map to estimate its position. The optimal trajectory must be designed in order to control a measure of the performance for the filtering algorithm used for the localization task. As the mobile state and the measurements are random, a well-suited measure can be a functional of the approximate posterior Cramer-Rao bound. A natural way for optimal path planning is to use this measure of performance within a (constrained) Markovian decision process framework. However, due to the functional characteristics, dynamic programming method is generally irrelevant. To face that, we investigate a learning approach based on the cross-entropy method