This paper addresses the problem of planning paths for a vehicle that are guaranteed to be safe in the presence of bounded uncertainty on the model of the vehicle, its sensors, and on the initial configuration. A new conceptual path planner based on rapidly-exploring random trees is proposed, which uses a set description of the uncertain configurations. A practical implementation of this path planner based on interval analysis is then described. It provides paths that could be safely followed by the vehicle during navigation, whatever the values taken by the uncertain quantities.

This paper is about source localization in a network of sensors from readings of signal strength. Contrary to previously published results, the source signal strength and path loss exponent are not assumed known a priori. The measurement errors are assumed bounded, with known bounds. The problem is then solved both in a centralized and in a distributed context using bounded-error parameter estimation techniques and interval analysis. Simulation results with realistic measurements are provided

Estimating the configuration of a vehicle is crucial for navigation. The most classical approaches are Kalman filtering and Bayesian localization, often implemented via particle filtering. This paper reports on-going experimentation with an attractive alternative approach recently developed and based on interval analysis. Contrary to classical extended Kalman filtering, this approach allows global localization, and contrary to Bayesian localization it provides guaranteed results in the sense that a set is computed that contains all of the configurations that are consistent with the data and hypotheses. The approach is particularly robust to outliers.

In this paper, initial localization problems are solved by using set-membership estimation. The method can be used with any robot and any kind of sensor(s), provided that a computable model of the environment/sensor interaction is available. With a pedagogical aim in mind, it is detailed in the case of the localization of a vehicle from range measurements in a polygonal environment. Salient properties of the method are as follows. First, it does not need any explicit management of matching hypotheses. Second, it is able to deal with ambiguous situations where several radically different vehicle configurations are consistent with the measurements. Third, it can be made robust to outliers. Fourth, it can deal with nonlinear observation models without any approximation. Fifth, the result is guaranteed in the sense that no configuration consistent with the data and the hypotheses can be missed.

When reliable prior bounds on the acceptable errors between the data and corresponding model outputs are available, bounded-error estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, even when the model is nonlinear and the number of data points small. However, when the data may contain outliers, i.e., data points for which these bounds should be violated, this set may turn out to be empty, or at least unrealistically small. The outlier minimal number estimator (OMNE) has been designed to deal with such a situation, by minimizing the number of data points considered as outliers. OMNE has been shown in previous papers to be remarkably robust, even to a majority of outliers. Up to now, it was implemented by random scanning, so its results could not be guaranteed. In this paper, a new algorithm based on set inversion via interval analysis provides a guaranteed OMNE, which is applied to the initial localization of an actual robot in a partially known two-dimensional (2-D) environment. The difficult problems of associating range data to landmarks of the environment and of detecting potential outliers are solved as byproducts of the procedure.

Finding all possible positions of a Stewart platform from the knowledge of the lengths of its limbs amounts to solving a set of nonlinear equations, the number of real solutions of which is, in the general case, unknown a priori. This paper shows how Hansen's algorithm (1992), based upon interval analysis, can be used to get all solutions in an approximate but guaranteed way even when the platform is nonplanar and the equations are nonpolynomial and with real coefficients. Computation is simple enough to be performed on a personal computer.

In a paper recently published (ibid., vol.12, p. 30-8, 1993), Chiang and Sullivan compare a new criterion for image registration called CBC (coincident bit counting) with two criteria that the authors proposed some years ago, namely SSC and DSC (stochastic and deterministic sign change criteria). The authors' nonparametric approach was demonstrated to outperform the conventional image registration criteria for robust registration in the fact that the value of their similarity measure did not take the specific pixel values into account. In light of this observation, Chiang and Sullivan have built the CBC criterion. The CBC method compares the number of coincident bits between the corresponding pixels in two different frames for a fixed amount of displacement. While the authors consider that the CBC is of interest and deserves to be studied, they feel that the comparison made by Chiang and Sullivan was not entirely accurate. Here the authors comment on this comparison and suggest possible further studies.