Page 156 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Navigation as a Filtering Process

odometer was only registering 1.2 miles from the curve, then I might never have re-
ceived my rock. No self-respecting robot would have had an uncertainty window of
.75 miles after having driven only .5 miles, but such an uncertainty might have been
reasonable, after, say, 20 miles. Thus, uncertainty and the window of acceptance
cannot be a simple constant.

For optimal navigation, our filter window needs to be as small as possible and no smaller.
In navigation, we (hopefully) know the true distances and directions very accurately,
but we may be uncertain of how far we have traveled, and in exactly which direction.
The margin of error is therefore a variable that depends upon how far we have trav-
eled since our last correction. The German bombers, described in Chapter 7, received
their only longitudinal correction just before the target and this was for a good reason.
By minimizing the distance to be estimated, the margin for error from that point to
the target was minimized. The same principle applies for other parameters such as
heading.
Uncertainty is thus the gauge of how open we must make our filter to keep from
missing our landmarks. The longer the robot runs without a correction, the larger its
uncertainty and the higher the risk that it will accept false data.
When we are fortunate enough to acquire valid navigation data, it may only pertain
to one relative axis or the heading. After such a fix, we might become more certain
of, say our lateral position, but not of our longitudinal position. Although most
buildings are relatively orthogonal, this correction may translate to a mix of x and y
in the global coordinate system, but that doesn’t matter.
Global navigation corrections (such as GPS) apply to all global axes, but do not
directly tell us our heading (though we can of course infer this from successive
fixes). Many other types of corrections will be with respect to the vehicle’s frame of
reference. For example, if our robot is going down a hall and using the walls for navi-
gation, our corrections should tell us its lateral position and its heading, but they tell
us nothing about its distance traveled. In this case, our uncertainty in the corrected
axes will diminish, but the uncertainty in the uncorrected axes will continue to
accumulate. The solution is to treat all corrections as being relative to our frame of
reference. Thus, a GPS fix is treated as both a lateral and a longitudinal correction.

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