Reliable Robot Localization

1Static Set-membership State Estimation

1.1. Introduction

A state estimation problem can be dealt with by set-membership approaches, where both the uncertainties on the model and the measurements errors are known. By known, we mean that an unknown actual value is guaranteed to lie within bounds that delineate the uncertainties, thus defining a solution set (Walter and Piet-Lahanier 1988, Cerone 1996, Veres and Norton 1996, Maksarov and Norton 1996).

The estimation then consists of reducing this set of feasible values by means of operators, where other approaches would have minimized an error criterion. The computations are not performed in a probabilistic way but based on deterministic operations on the bounds of the set. This approach is significantly different from usual methods: here, we do not assume a probability distribution in the calculations. Furthermore, the bounding property of such an approach is guaranteed even though the system is nonlinear. This quality is of particular importance in mobile robotics where several problems present nonlinearities, the case of a range-only localization being one of them (Caiti et al. 2005).

Range-only state estimation

A telling example of set-membership state estimation is the localization of a mobile robot among beacons. This kind of application has already been appropriately presented in Drevelle (2011) to introduce set-membership methods. We will use it as a guiding thread of this book, first in this chapter in a static context ...