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[DPRG] Laser rangefinder

Subject: [DPRG] Laser rangefinder
From: John Swindle swindle at compuserve.com
Date: Sun Apr 20 11:02:51 CDT 2014

Hey Paul, Jason, and all,

Jason: Thanks for talking about the laser rangefinder at the last 
meeting.

Paul: Now that there's a high-resolution, accurate, affordable 
laser rangefinder, you can do localization from known targets 
(such as bicycle reflectors) in the arena (your back yard).

We thought about something similar a couple years ago, but you 
taught me that triangulation was useless for localization because 
the pointing accuracy would have to be a very small fraction of a 
degree to get something close to a few inches of accuracy. I'd 
thought you could triangulate to more reflectors and improve the 
accuracy, but geometry shows that merely completes the circle of 
uncertainty, without improving anything.

That's why (AFAIK) all localizers use trilateration, not 
triangulation (or it uses something totally different, like 
projecting an image on the ceiling). That's why the audio 
localizer was useful for large arenas that did not have ceilings.

But now, you could do the same with the laser rangefinder, so 
long as it can pan to at least two known targets. (You'll need 
three targets if you allow the robot to venture beyond a line 
formed by the two targets.) The accuracy of the panning is 
irrelevant.

Some things to be aware of:

Repeatability: Jason said his rangefinder gave millimeter 
resolution at 40 feet. The resolution is great. In most cases, 40 
feet would be good, but in a yard, the range needs to be more 
than 50 feet, up to about 200 feet. That can probably be handled 
with lenses. The rangefinder has to simultaneously give these 
three features: resolution (got it), accuracy (has nothing to do 
with resolution and the two are often confused with one another), 
and repeatability (absolutely the most important feature, 
trumping the other two). Although I like to use median filters, 
and although I would average 4,000 readings if the audio 
localizer were fast enough to do so, I would nevertheless be 
suspicious of a measurement algorithm which was overly dependent 
on thousands of readings in order to get one valid result.

Best target: I suspect that having bright targets, such as bike 
reflectors, would help the algorithm to choose the correct range.

Obfuscation (or is it occultation?): Camera and laser localizers 
are thwarted by obstacles. The audio localizer didn't have that 
problem. But, I suspect that several bike reflectors could be 
placed in the yard at places where the robot would always see a 
couple of them. Kinda like using the satellites that are heard by 
a GPS receiver.

To help with that last part: The solution to Apollonius's problem 
can be expanded to 3D so that the beacon reflectors may be 
elevated above most obstacles in the yard, that is, changing the 
formula from LORAN to GPS. Or, for large spaces, the nearest 
reflection can be ignored and the farthest ones can be used. The 
farthest ones are where the elevation angle is the smallest and 
has a smaller effect on the error. This introduces a new problem 
of making sure that the laser is at the best elevation angle to 
see the reflectors.

So, I need to get me one of those laser rangefinders.

Best to y'all,
John Swindle

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