Optimal Path Planning for Information based Localization
Résumé
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 implies range and bearing measurements from observed landmarks. These measurements are correlated with the map to estimate the mobile localization through a filtering algorithm. The optimal trajectory can be designed by adjusting a measure of performance for the filtering algorithm used for the localization task. As the state of the mobile and the measurements provided by the sensors are random data, criterion based on the estimation of the Posterior Cramer-Rao Bound (PCRB) is a well-suited measure. A natural way for optimal path planning is to use this measure of performance within a (constrained) Markovian Decision Process framework and to use the Dynamic Programming method for optimizing the trajectory. However, due to the functional characteristics of the PCRB, Dynamic Programming method is generally irrelevant. We investigate two different approaches in order to provide a solution to this problem. The first one exploits the Dynamic Programming algorithm for generating feasible trajectories, and then uses Extreme Values Theory (EV) in order to extrapolate the optimum. The second one is a rare evnt simulation approach, the Cross-Entropy (CE) method introduced by Rubinstein & al. As a result of our implementation, the CE optimization is assessed by the estimated optimum derived from the EV.