A computationally efficient solution to the simultaneous localisation and map building (SLAM) problem

Abstract

The theoretical basis of the solution to the simultaneous localisation and map building (SLAM) problem where an autonomous vehicle starts in an unknown location in an unknown environment and then incrementally build a map of landmarks present in this environment while simultaneously using this map to compute absolute vehicle location is now well understood 5 , 6 ] . Although a number of SLAM implementations have appeared in the recent literature 4, 3], the need to maintain the knowledge of the relative relationships between all the landmark location estimates contained in the map makes SLAM computationally intractable in implementations containing more t h a n few tens of landmarks. In this paper the theoretical basis and a practical implementation of a computationally e cient solution to SLAM is presented. The paper shows that it is indeed p ossible to remove a large percentage of the landmarks from the map without making the map building process statistically inconsistent. Furthermore i t is shown that the e ciency of the SLAM can be maintained b y judicious selection of landmarks, to be p r eserved in the map, based on their information content.

A Kalman filtering approach to the representation of kinematic quantities by the hippocampal-entorhinal complex

“…This situation represents ''pure path integration'' by the rat, and results in progressive enlargement of the uncertainty ellipsoid (Dissanayake et al 2001). If we measured the summed activity of a population of place cells at a particular time (we assume the distribution is Gaussian), we might expect the distribution's volume to increase in this case.…”

“…It was shown by us that the computational demands on the subject are also considerable during this period, but can be reduced by minimizing control inputs on the part of the subject. We then presented Dissanayake et al (2001) convergence result for a static environment, which proves that a subject can build a perfect (or converged) map of the environment from imperfect control inputs and observations. This result was used to show that the brain can acquire any kinematic tuning.…”

“…2a is sufficient to describe the subsequent Kalman filter dynamics. The asymptotic approach of the mapping uncertainty to zero was nicely demonstrated by Dissanayake et al (2001) with an autonomous motor vehicle.…”

“…The random variables w(k) and v(k) will be assumed continuous and normally distributed, with covariance matrices R(k) and Q(k), respectively. Further discussion of these state equations may be found in Gelb (1984) or Dissanayake et al (2001).…”

“…Convergence and measurement conditions for the mapping uncertainty Dissanayake et al (2001) proved for the quantity U map the following 2 properties, valid for arbitrary observations and control inputs in a static environment:…”