Kartierung von mobilen Robotern in Innenräumen Submitted to the

This thesis addresses the Simultaneous Localization and Mapping (SLAM) problem, a key prob-lem for any truly autonomous mobile robot. The task for the robot is to build a map of its environment and simultaneously determine its own position in the map while moving. The problem is examined from an estimation-theoretic perspective. The focus is on the core estimation algorithm which provides an estimate for the map and robot pose from two sensor inputs: The first sensor is odometry, i.e. the observation of the robot’s movement from the revo-lution of its wheels. The second is the observation of environment features, so called landmarks. The optimal solution based on maximum likelihood or least square estimation needs excessive computation time, i.e. O((n + p) 3) for n landmarks and p robot poses. Popular approaches like Extended Kalman Filter (EKF) are more efficient but still need O(n 2) computation time and suffer from linearization errors. The first contribution of this thesis is an analysis of SLAM, in particular under the aspect of the inherent uncertainty structure of a map estimate. The key result can be phrased as “Certainty of relations despite uncertainty of positions”. The discussion further analyzes the linearizatio