Evaluation of a robot learning and planning via extreme value theory

This paper presents a methodology for the evaluation of a path planning algorithm based on a learning approach. Here this evaluation procedure is applied for the problem of optimizing the navigation of a mobile robot in a known environment. A metric map composed of landmarks representing natural elements is given to define the best trajectory which permits to guarantee a localization performance during its execution. The vehicle is equipped with a sensor which enables it to obtain range and bearing measurements from landmarks. These measurements are matched with the map to estimate its position. As the mobile state and the measurements are stochastic, the optimal planning scheme considered in this paper deals with posterior Cramer-Rao Bound as a performance measure. Because of the nature of the cost function, classical optimization algorithms like dynamic programming are irrelevant. Therefore, we propose to achieve the optimization step with the Cross Entropy algorithm for optimization to generate trajectories from a suitable parameterized probability density functions family. Nevertheless, although the convergence of this algorithm can be assessed with the analysis of the stationarity of its intrinsic parameters, we are not able to quantify the level of convergence around the optimal value. As a consequence, an external investigation can be applied from an alternative stochastic procedure followed by an analysis via extreme value theory.