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180 Autonomous Mobile Robots

same point in the subsequent sensor update. Problems also arise with symmetric
distributions of landmarks.
If the relative positional information of indistinguishable landmarks is avail-
able then three are sufficient to unambiguously determine pose. Initially two
would appear sufficient, however the ambiguity of identity means that land-
◦
marks may be rotated 180 . Even though only three asymmetrically distributed
indistinguishable landmarks are needed for unambiguous pose determination,
the fewer landmarks required, the better. Is it possible to have reliable pose
updates using only the relative positions of two landmarks? There are a number
of ways that this may be achieved. The simplest is to use distinguishable land-
marks, for instance circles of sufficiently different radii. If indistinguishable
landmarks have to be used then they may be placed in such a configuration
as localization is only required in one half plane. An example would be when
they are against a wall then the robot cannot be localized in the half plane
behind the wall and still be able to detect the landmarks. Use of odometry and
fast updates means that the large pose changes that would cause ambiguity
would never happen between updates or would be detected by the odometry
sensors.

4.5.4 Implementation and Results
The experimental platform is a Magellan Pro-robot equipped with a SICK LMS
200 laser range finder. The range finder has a scanning angle width of 180 ◦
◦
and a resolution of 0.5 . The laser range finder is almost an ideal sensor with
unrivalled accuracy, acquisition time, and range. The main problems are cost,
mass (4.5 kg), and power consumption (17.5 W). The characteristics of this
LMS are detailed in References 28 and 29.
Experiments were performed to test the localization accuracy delivered and
involved driving the robot along a straight line and in a square. The deviation
of the colocation positions from this straight line give an indication of the
localization error in the direction perpendicular to the line. This error depends
approximately linearly on the angular resolution of the laser scanner, the range
and separation of the geometric targets. The localization error was of the order
of 0.02 m at ranges of 0 to 8 m with the laser scanner operating at a resolution
of 0.25 .
◦
Error in the range to the targets introduces error into the position estimation
of the robot. Figure 4.18 illustrates the dependence of the pose uncertainty on
the range error. The origin O is the true position of the robot and O is its worst

case perceived position if the range to the target A is over estimated and that to
target B is underestimated. The error estimate is greatly simplified if a far field
approximation is used which implies

AB << OM (4.41)

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c004” — 2006/3/31 — 16:42 — page 180 — #32