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Q. For a year now, I have been researching a solution
to the problem of reliably determining a robot’s
position to within one inch in a . 25 square mile
area. Cost is a major design consideration (ideally less than
$1,000). Lasers cannot deal with obstacles (and I’m also
pretty sure my dogs won’t tolerate the goggles). GPS
augmentation is prohibitively expensive. I’ve found a few
RF designs, but none that can be built on a budget that
would be approved by my CFO (wife). Hopefully, you can
provide me a solution or point me in the right direction.
P.S. I really enjoy your column!
— Thanks, Roger
A. First off, thanks for the kudos! I don’t know why you
need such exacting accuracy; it will definitely be a
challenge since I don’t think there is anything that
can provide that level of accuracy that is built into a
roving vehicle. You’re going to need to “instrument” your
environment some how.
Even differential GPS can only get an accuracy of — at
best — one meter. One paper that I read — www.gdgps.
net/system-desc/papers/ion_paper_2000.pdf — suggests
a sophisticated Internet-based correction method for differential
GPS that can get an estimated accuracy of about 20 cm. So
clearly, GPS by itself cannot get you what you want. Regardless,
that will set you back way more than your $1000 limit. RF
systems are very uncertain for determining ranges well and
clearly IR rangers are of limited value outdoors. Okay, that
takes care of what WON’T work for you. Now, let’s step off
of the deep end and speculate on what might do what you
want in your limited area of a quarter mile.
My first thought would be to position two video cameras
at right angles to each other on tall towers aimed down on
the area within which you are tracking your robot. I realized,
however, that I was thinking a quarter acre, not quarter mile.
That wouldn’t work because you couldn’t get the whole space
in the frame at a useful resolution. So, strike that idea.
However, those sensors at right angles to each other
might work in another way. If you’ve ever seen a contractor
14 SERVO 12.2008
dig a hole, some of them will dig down to the correct
depth and place a spinning laser to show the depth all
around the hole. But as you’ve noted, your dog and probably
your neighbors wouldn’t be too happy about that. Too bad,
since that laser would be fairly easy to detect with a camera
on a stepper motor, whose angles could then be compared
with each other to get an absolute location of the source
of light to a pretty good resolution. With more sensors,
even more resolution could be gained. So, what else can
we use? Sonar is out since the sound waves will spread out
too far as they move away from the robot.
How about this idea: put a bright rotating red (blue,
green, whatever) light on the top of your robot. This will be
reasonably directional with minimal dispersion of the light —
and you can perhaps make the point source even more
directional with a tube limiting the direction of the light
from the reflector. Next, put a video camera with a limited
field of view and a filter on the lens that will admit only the
color that you are looking for at the four corners of your
area. Place it high enough so that there is nothing blocking
the view of the area. This assumes, of course, that you don’t
have much in the way of shrubs and trees. Some barriers
are okay as long as at least two adjacent cameras can see
the target. Now, scan the cameras using a motor that can
be precision turned like a stepper motor or a servo. I would
use an encoder to further enhance the accuracy of the positioning. By using a Cartesian coordinate system and some
basic trigonometry, you can calculate the location of the
robot within the property by comparing the readings from
two orthogonal (fancy word for “at right angles”) cameras.
The biggest resolution limiter is the cross section of the
point source (the light). You can’t be more accurate than the
width of that point source as seen by the camera. I think this
will work but you’ll need a computer to coordinate the readings,
calculate the angles, and come up with the actual range.
The light will need to be strong enough to reach the cameras
at a brightness that will stand out against the ambient light.
It will need to adjust according to the light outside so that
it doesn’t swamp the cameras at night. Sadly, I can think of