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From: WELLS <WELLS@CTSD2.JSC.NASA.GOV>
Subject: Re: RPM -> Speed
Message-ID: <1993Feb18.013838.2386@aio.jsc.nasa.gov>
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Date: Thu, 18 Feb 1993 01:38:38 GMT
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In article <1lrnqiINNbvs@charnel.ecst.csuchico.edu> Michael Favor, 
favor@ecst.csuchico.edu writes:
>I understood "3" to be the simplified form of (Pi * TractionFactor), so
>unless your wheels have better than 98% traction efficiency, you might
>actually be _increasing_ the error, as well as the formula complexity.

This is good discussion. It may seem trivial but educating, informing 
and stimulation of periferal ideas seem to be noble side benefits of the 
excellent humor in these here annals.
A complete explanation of the presented equation was what Alan tried to 
do in the original response with attention to dimensions and I share his 
frustration. Pi times the outer diameter of the wheel is its outer 
circumference. Its circumference is an approximation of the distance it 
will travel in one revolution. This distance times the wheel angular 
speed in number of revolutions per minute is the hub speed. The primary 
sources of error in distance traveled or speed measurement of a wheel 
driven robot are wheel slip and effective diameter uncertainties. Drive 
transmission slip must also be considered if slip can happen between the 
encoder and the wheel, but this can be grouped with wheel slip. Wheel 
slip error can be positive or negative depending on how the robot is 
operated (quick start or stop,) and on what surface (sand, concrete, 
carpet, plastic, bumps, hills, etc.). Diameter uncertainty is a function 
of things such as tire type (solid, pneumatic, rubber, plastic, metal, 
radial, round, oval, or flat cross section, etc.), tire wear and  tire 
load. Each application will be a trade of many of these as well as time 
and cost. In any case effort will be made to minimize the error. In the 
case of a mail delivery robot (which has been in daily supervised 
autonomous use in our office halls for over a year) solid, low profile, 
hard rubber wheels, slow starts, slow stops and hard plastic floors are 
the choices. In our case as with other hard wheels, "Pi" gets you a 
better answer than "3". Indeed, linear motion error is very small, 
originally 2.5 inches in 40 feet (traction efficiency about 99.5%). Our 
biggest errors in position estimation are produced with wheel slip in 
turns and during urgent stops. Since there is no directional information 
other than wheel angle, it is necessary that position and heading be 
automatically and frequently corrected using sonar information.

Apologies for any anxiety that Pi*d caused.

Sincerely, Dennis.
