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350 Autonomous Mobile Robots

The robustness of JCBB is especially important in loop-closing operations
(Figure 9.4). Due to the big odometry errors accumulated, simple data associ-
ation algorithms would incorrectly match the signaled point with a point feature
previously observed in the pillar. Accepting an incorrect matching will cause
the EKF to diverge, obtaining an inconsistent map. The JC algorithm takes into
account the relative location between the point and the segment and has no
problem in finding the right associations. The result is a consistent and more
precise global map.
Joint compatibility is a highly restrictive criterion, that limits the combin-
atorial explosion of the search. The computational complexity does not suffer
with the increase in vehicle error because the JC of a certain number of measure-
ments fundamentally depends on their relative error (which depends on sensor
and map precision), more than on their absolute error (which depends on robot
error). The JC test is based on the linearization of the relation between the
measurements and the state (Equation [9.6]). JCBB will remain robust to robot
error as long as the linear approximation is reasonable. Thus, the adequacy of
using JCBB is determined by the robot orientation error (in practice, we have
◦
found the limit to be around 30 ). Even if the vehicle motion is unknown (no
odometry is available), as long as it is bounded by within this limit, JCBB can
perform robustly. In these cases, the predicted vehicle motion can be set to
zero (ˆ x R k−1 = 0, Figure 9.5a), with Q k sufficiently large to include the largest
R k
possible displacement. The algorithm will obtain the associations, and during
the estimation stage of the EKF the vehicle motion will be determined and the
environment structure can be recovered (Figure 9.5b).

9.3.3 Relocation
Consider now the data association problem known as vehicle relocation, first
location, global localization, or “kidnapped” robot problem, which can be stated
as follows: given a vehicle in an unknown location, and a map of the envir-
onment, use a set of measurements taken by onboard sensors to determine the
vehicle location within the map. In SLAM, solving this problem is essential to
be able to restart the robot in a previously learned environment, to recover from
localization errors, or to safely close big loops.
When there is no vehicle location estimation, simple location independent
geometric constraints can be used to limit the complexity of searching the cor-
respondence space [30]. Given a pairing p ij = (E i , F j ), the unary geometric
constraints that may be used to validate the pairing include length for seg-
ments, angle for corners, or radius for circular features. Given two pairings
p ij = (E i , F j ) and p kl = (E k , F l ), a binary geometric constraint is a geometric
relation between measurements E i and E k that must also be satisfied between
their corresponding map features F j and F l (e.g., distance between two points,

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c009” — 2006/3/31 — 16:43 — page 350 — #20