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[DPRG] Borenstein's UMBMark
Subject: [DPRG] Borenstein's UMBMark
From: David
dpa at io.isem.smu.edu
Date: Thu May 22 04:44:36 CDT 2008
Howdy,
Erik writes:
> I'm not sure I would classify Teeter-Totter as a "normal" three wheeled
> robot. The third (non-drive) wheel is just a regular wheel, not a castor,
> so it resists sideways motion. My intent was that it statically balance on
> just the two drive wheels and that the non-drive wheel only comes into
> play when it needs the extra leverage to go uphill or through the deeper
> grass (otherwise the drive wheels stand still and the body summersaults
> around the axle). By the day of the contest, I hadn't gotten the balance
> quite right, so it leaned on the third wheel when stopped or driving
> straight forward.
Ah. I stand corrected.
> However, when executing the turns the balance was close
> enough that the third wheel would leave the ground enough not to drag.
I think that is why your odometry is accurate and not pulled off
by sideways friction of the tail/nose wheels like Randy is
experiencing.
However, the crux of the matter is the location of the robot's
center of gravity (CG),
For a "normal" three wheeled robot with differential drive and a
castering tail wheel, the robot's weight is distributed between
the drive wheels and the tail wheel. Too much weight on the drive
wheels and the robot is not stable, and tends to tip over on it's
nose when braking or going down hill. Too much weight on the
tail wheel and the drive wheels tend to slip in a turn, which
messes up the odometry.
Here's a little diagram which illustrates this in the context
of a two wheel balancing robot:
<http://www.geology.smu.edu/~dpa-www/robo/nbot/advantages.html>
Borenstein puts it this way in his paper "Where Am I?" in Chapter 5.3,
"Reduction of Odometry Errors:"
"Vehicles with caster wheels that bear a significant portion of the
overall weight are likely to induce slippage when reversing
direction. Conversely if the caster wheels bear only a small
portion of the overall weight, then slippage will not occur
when reversing direction."
This is probably what Randy and Dave are describing, and is a
result of the robot geometry and GC placement.
I have found in my own three-wheel robots (SR04, LegoBot, Rainwaters
Cat) that the most effective placement of the CG is very slightly
behind and _below_ the main axis of the drive wheels:
<http://www.geology.smu.edu/~dpa-www/gif/CG.gif>
This prevents the robot from tipping over on its nose and still allows
for accurate odometry.
> (And there's the other matter of the second "third" wheel, so it's really
> an unconventional 4 wheeled robot in which only 2 or 3 wheels are active
> at once)
Perhaps it's a balancing robot with training wheels? :)
regards,
dpa
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