Set membership localization and map building for mobile robots

Autonomous navigation of mobile robots requires the continuous estimation of the vehicle position and orientation in a given reference frame (localization problem). When moving in unknown environments, the more challenging problem of building a map, while at the same time localizing within it, must be faced (simultaneous localization and map building, SLAM). By adopting a landmark-based description of the environment, both tasks can be cast as a state estimation problem for an uncertain dynamic system, based on noisy measurements. Under the assumption that both process disturbances and measurement errors are unknown but bounded, the estimation process can be carried out in terms of feasible sets. This chapter reviews efficient set membership localization and mapping techniques for different kinds of available measurements and different classes of approximating regions. An extension of the SLAM algorithm to the case of a team of cooperating robots is also presented. The proposed techniques are validated through extensive numerical simulations and experimental tests performed in a laboratory setup.