Francis Celeste

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

Application of probabilistic PCR5 fusion rule for multisensor target tracking

This paper defines and implements a non-Bayesian fusion rule for combining densities of probabilities estimated by local (non-linear) filters for tracking a moving target by passive sensors. This rule is the restriction to a strict probabilistic paradigm of the recent and efficient proportional conflict redistribution rule no 5 (PCR5) developed in the DSmT framework for fusing basic belief assignments. A sampling method for probabilistic PCR5 (p-PCR5) is defined. It is shown that p- PCR5 is more robust to an erroneous modeling and allows to keep the modes of local densities and preserve as much as possible the whole information inherent to each densities to combine. In particular, p-PCR5 is able of maintaining multiple hypotheses/modes after fusion, when the hypotheses are too distant in regards to their deviations. This new p-PCR5 rule has been tested on a simple example of distributed non-linear filtering application to show the interest of such approach for future developments. The non-linear distributed filter is implemented through a basic particles filtering technique. The results obtained in our simulations show the ability of this p-PCR5-based filter to track the target even when the models are not well consistent in regards to the initialization and real cinematic.

Optimized trajectories for mobile robot with map uncertainty

Abstract In this paper we propose a methodology to generate trajectories for a mobile robot which uses an uncertain geometric map to estimate its position and orientation during its displacement. This methodology is based on the definition of particular paths and on defining a cost function to weigh the trade-off between expected localization gain and the risk due to the map uncertainty.

Optimal Path Planning for Information Based Localization

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. [9]. As a result of our implementation, the CE optimization is assessed by the estimated optimum derived from the EV.

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.

Optimal Strategies for Mobile Robots Based on the Cross-Entropy Algorithm

This paper deals with the problem of optimizing the navigation of an intelligent mobile with respect to the maximization of the performance of the localization algorithm used during execution. It is assumed that a known map composed of features describing natural landmarks in the environment is given. The vehicle is also equipped with a range and bearing sensor to interact with its environment. The measurements are associated with the map to estimate its position. The main goal is to design an optimal path which guarantees the control of a measure of the performance of the map-based localization filter. Thus, a functional of the approximate Posterior Cramer-Rao Bound is used. However, due to the functional properties, classical techniques such as Dynamic Programming is generally not usable. To face that, we investigate a learning approach based on the Cross-Entropy method to stress globally the optimization problem.