I. Introduction

To efficiently solve many tasks envisioned to be carried out by mobile robots including transportation, search and rescue, or automated vacuum cleaning robots need a map of the environment. The availability of an accurate map allows for the design of systems that can operate in complex environments only based on their on-board sensors and without relying on external reference system like, e.g., GPS. The acquisition of maps of indoor environments, where typically no GPS is available, has been a major research focus in the robotics community over the last decades. Learning maps under pose uncertainty is often referred to as the simultaneous localization and mapping (SLAM) problem. In the literature, a large variety of solutions to this problem is available. These approaches can be classified either as filtering or smoothing. Filtering approaches model the problem as an on-line state estimation where the state of the system consists in the current robot position and the map. The estimate is augmented and refined by incorporating the new measurements as they become available. Popular techniques like Kalman and information filters [28], [3], particle filters [22], [12], [9], or information filters [7], [31] fall into this category. To highlight their incremental nature, the filtering approaches are usually referred to as on-line SLAM methods. Conversely, smoothing approaches estimate the full trajectory of the robot from the full set of measurements [21], [5], [27]. These approaches address the so-called full SLAM problem, and they typically rely on least-square error minimization techniques.