Simultaneous Localisation and Map Building

Michael Csorba Doctor of Philosophy Balliol College Michaelmas Term 1997 Simultaneous Localisation and Map Building This thesis examines the problem of localising an Autonomous Guided Vehicle (AGV) travelling in an unknown environment. In this problem, the AGV faces the dual task of modeling the environment and simultaneously localising its position within it. The Simultaneous Localisation and Map Building (SLAM) problem is currently one of the most important goals of AGV research. Solving this problem would allow an AGV to be deployed easily, with very little initial preparation. The AGV would also be exible and able to cope with modi cations in the environment. A solution to the SLAM problem would enable an AGV to would be truly \autonomous. " The thesis examines the SLAM problem from an estimation theoretic point of view. The estimation approach provides a rigorous framework for the analysis and has also proven to be successful in actual applications. The most signi cant contribution of this thesis is to provide, for the rst time, a detailed development of the theory of the SLAM problem. It is shown that correlations arise between errors in the vehicle and the map estimates, and these correlations are identi ed as fundamentally important to the solution of the SLAM problem. It is demonstrated that ignoring these correlations results in the loss of the fundamental structure of the SLAM problem and leads to inconsistency in map and vehicle estimates. The evolution of the map is also examined. It is shown that the map cannot diverge, in particular it is shown that the estimate of individual features in the map, groups of features and relative distances between features cannot diverge. The thesis further examines the theoretical limit to the accuracy of the map and the localisation of the vehicle. The relative nature of the observations are exploited to identify the existence of a limit, and the determination of the limit is also presented. Together, these results show that it is theoretically possible to start at an unknown location in an unknown environment and to build a map by which to navigate. It is identi ed in the thesis that the full solution to the SLAM problem results in a large storage requirement and heavy computational burden. This leads to the need to nd alternative solutions to the SLAM problem that have both a sound theoretical basis and which also permit practical implementations. Two such solutions to the SLAM problem are developed in this thesis. The rst is the Bounded Region (BOR) lter. The BOR lter makes the assumption of bounded errors in the observation and vehicle models, which permits the lter to be formulated without the need to consider correlations. Consequently the storage and the computational requirement of the BOR lter are very low. The second alternative solution developed in this thesis is the Relative (REL) lter. The REL lter estimates the relative distance between features and the relative angle formed by groups of three features. Such estimates can be formed without the need to consider correlations between estimates. The REL lter therefore has a low storage requirement and computational burden. The thesis also investigates the performance of these solutions to the SLAM problem in a real implementation. An AGV equipped with a laser range nder builds a map of features in a corridor and simultaneously localises its own position using the map. Each approach is investigated in detail, in particular the evolution of the map is examined and important aspects of the localisation are identi ed.