On the Structure and Solution of the Simultaneous Localisation and Map Building Problem

Paul Michael Newman Doctor of Philosophy The University of Sydney March 1999 On the Structure and Solution of the Simultaneous Localisation and Map Building Problem This thesis is concerned with the simultaneous localisation and map building (SLAM) problem. The SLAM problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. The map and robot location estimates obtained from a successful SLAM system provide essential information upon which high level tasks such as path planning are predicated. A practicable solution to the SLAM problem is of inestimable value in the quest to create a truly autonomous mobile robot. The thesis has three principal theoretical contributions. The first is the elucidation of the structure of the SLAM problem. This is achieved by the analysis of a conventional and well known SLAM algorithm using global coordinates called, in this thesis, the Absolute Map Filter or AMF. Using this algorithm, three convergence theorems central to the SLAM problem are proved for the first time. They prove that the uncertainty in the estimated map decreases monotonically and achieves a defined lower bound. Futhermore, in the limit as the number of landmark observations increases, the relationship between landmarks becomes perfectly known. These proofs constitute the second theoretical contribution of the thesis. The third principal theoretical contribution of this thesis is the development of a novel SLAM solution capable of solving the SLAM problem in real time. This algorithm is called the Geometric Projection Filter or GPF. Rather than estimate the location of landmarks in global coordinates it estimates the relationships between individual landmarks. The convergence properties of this algorithm are derived and compared with those of the conventional AMF algorithm. An implementation of the GPF and the AMF is provided on a custom built subsea vehicle. The performance of the two filters are compared and shown to have the properties predicted by the preceding theoretical analysis. This implementation constitutes the fourth principal contribution of the thesis. It shows that the GPF can be used as the basis of a substantive real time deployment of a mobile robot in an initially unknown environment.