[...]... simultaneous localization and map building (EKF-SLAM in short), based primarily on the works by Smith and Cheeseman [79] and Dissanayake et al [31] In Section 1.2, explicit formulas for two mobile platforms are presented First, we show the case of a simple linear one-dimensional mobile robot, the monobot Then, we extend the analysis to the more realistic case of a planar mobile robot Spatial landmark compatibility... deployment of uniquely identifiable man-made beacons to aid in localization Unfortunately, there exist multiple situations where this is not possible, and a map must still be constructed without environment contamination An alternative approach explored in this work is the use of temporal and spatial landmark quality measures to validate observations J Andrade- Cetto and A Sanfeliu: Envir Learn f Ind Mob Rob.,... error for each landmark Their use is crucial for the solution of data association in SLAM [21, 70] We have realized however, that in situations with moderate scene dynamics, spatial landmark compatibility may not suffice in the search for data association matches Consider for example the case when a landmark is occluded for a short period of time A spatial compatibility test would not have any information... validate observations J Andrade- Cetto and A Sanfeliu: Envir Learn f Ind Mob Rob., STAR 23, pp 1–47, 2006 © Springer-Verlag Berlin Heidelberg 2 1 Simultaneous Localization and Map Building During the course of our research we have tested and implemented SLAM solutions for indoor mobile robots with a laser range scanner, based mainly on the algorithm described in this chapter, and with the extensions... ) In other words, we want an estimator that keeps the uncertainty ellipse for Pr,k+1|k+1 as small as possible Fortunately, we can resort to the Kalman filter, a recursive stochastic state estimator for partially observed non-stationary processes that gives an optimal state estimate in the least squares sense In the typical full-covariance EKF 6 1 Simultaneous Localization and Map Building based approach... map building The material covered summarizes the work of many researchers during the past 15 years, and will constitute a starting point for our view of the mobile robot localization and map building problem Full covariance EKF SLAM Before delving into the mathematical formulation that builds up the full covariance Extended Kalman Filter approach to Simultaneous Localization and 1.1 Extended Kalman Filter... addressed in Section 1.3 Finally, in Section 1.4, our planar mobile robot configuration is used to evaluate the original full-covariance Extended Kalman Filter algorithm to Simultaneous Localization and Map Building as reported by Dissanayake et al [31], including the spatial landmark compatibility tests [70], versus our improved algorithm, the EKF-SLAM-LV, with both temporal and spatial landmark quality tests,... and to guarantee positive semi-definiteness of Pk+1|k+1 , with Pk+1|k+1 = (I − Kk+1 H) Pk+1|k (I − Kk+1 H) + Kk+1 Rk+1 Kk+1 (1.23) The above expression is commonly referred as the Joseph form of the a posteriori state error covariance matrix Its derivation is discussed in detail in Appendix A The properties of positive semi-definite (psd) matrices are enumerated in Section B for completeness of the discussion... Convergence properties One important property of the estimation-theoretic approach to SLAM is that the map is asymptotically convergent That is, in the original full covariance KF-based SLAM formulation the map state error covariance submatrix associated with the landmark estimates decreases monotonically as successive observations take place Formally speaking, det Pf,k+1|k+1 ≤ det Pf,k|k (1.24) Another... book, such as full observability, temporal landmark quality, unscented vehicle transformations, etc Figure 1.1 plots a series of snapshots of a test run of our SLAM algorithm with our mobile robot Marco from Figure 1.2 A 3d partial representation of the final map built is shown in Figure 1.3 In the plots the reader can see for example, localization variances as level curves around wall endpoints These are . Barcelona Spain cetto@ iri.upc.edu sanfeliu@ iri.upc.edu ISSN print edition: 161 0-7 438 ISSN electronic edition: 161 0-7 42X ISBN-10 3-5 4 0-3 279 5-9 Springer Berlin HeidelbergNew Yo rk ISBN-13 97 8-3 -5 4 0-3 279 5-0 . Mechatronic Systems {Recent Advances 191 p. 2002 [ 3-5 4 0-4 4159-X] Juan Andrade- Cetto  Alberto Sanfeliu Environment Learning for Indoor Mobile Robots AS tochastic State Estimation Appr oach to Simultaneous. [ 3-5 4 0-0 025 1-0 ] Vol. 3: Natale, C. Interaction Control of Robot Manipulators { Six-degrees-of-freedom Tasks 120 p. 2003 [ 3-5 4 0-0 0159-X] Vo l. 2: Antonelli, G. Underwater Robots {Motion and Force