Robot Position Convergency in Simultaneous Localization and Mapping

The robot position estimation is very important to the consistency of the simultaneous localization and mapping (SLAM) problem. This paper presents an analysis of the convergence properties of the robot position estimation in the linear-Guassian SLAM (LG-SLAM) problem based on some properties of positive semi-definite matrixes. It is found that as a whole, the error of the robot position estimation is increasing with time, although it has an upper limit when the robot can see all landmarks all the time. So it is hard to predict the error of the robot position estimation, when there is no any prior knowledge about the environment. This paper also finds that the robot position estimation is determined by the number of landmarks seen by the robot at a time, the times for which a landmark is seen, and the distribution of landmarks in the environment which explains why sometimes the hybrid, metric-topological, SLAM approaches will be better than metric-only SLAM approaches. Experiments have verified our analysis.