Page 369 - Autonomous Mobile Robots

Map Building and SLAM Algorithms 359

9.4.1 Building Independent Local Maps
Each local map can be built as follows: at a given instant t j , a new map is initial-
ized using the current vehicle location as base reference B j . Then, the vehicle
performs a limited motion (say k j steps) acquiring sensor information about
the neighboring environment features F j . The standard EKF-based techniques
B j B j B j
presented in previous sections are used to obtain a local map M = (ˆ x , P ).
F j F j F j
This local map is independent of any prior estimation of the vehicle location
because it is built relative to the initial vehicle location B j . The local map
depends only on the odometry and sensor data obtained during the k j steps.
This implies that, under the common assumption that process and measure-
ment noise are white random sequences, two local maps built with the same
robot from disjoint sequences of steps are functions of independent stochastic
variables. Therefore, the two maps will be statistically independent and uncor-
related. As there is no need to compute the correlations between features in
different local maps and the size of local maps is bounded, the cost of local
map building is constant per step, independent from the size of the global map.
The decision to close map M j and start a new local map is made once
the number of features in the current local map reaches a maximum, or the
uncertainty of the vehicle location with respect to the base reference of the cur-
rent map reaches a limit, or no matchings were found by the data association
process for the last sensor measurements (a separate region of the environment
is observed). Note that the new local map M j+1 will have the current vehicle
position as base reference, which corresponds to the last vehicle position in
map M j . Thus, the relative transformation between the two consecutive maps
B j
x j+1 = x is part of the state vector of map M j .
B j+1
9.4.2 Local Map Joining
Given two uncorrelated local maps:

B B B
M = (ˆ x , P ); F ={B, F 0 , F 1 , ... , F n }
F F F
B B B
M = (ˆ x , P ); E ={B , E 0 , E 1 , ... , E m }
E E E
where a common reference has been identified F i = E j , the goal of map joining
is to obtain one full stochastic map:

B B B
M = (ˆ x , P )
F+E F+E F+E
containing the estimates of the features from both maps, relative to a common
base reference B, and to compute the correlations appearing in the process.
Given that the features from the first map are expressed relative to reference B,

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c009” — 2006/3/31 — 16:43 — page 359 — #29