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Reversing the Kiwi-Drive formula

Posted on 2011-02-25
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Last Modified: 2016-05-20
We've recently build a kiwidrive robot, and now we want to use it as a musical instrument.
It has three wheels, each with a motor that produces a distinct tone.
The formulas used to calculate motor speeds are as follows:

M1 = 0.5 * X - 0.866 * Y + R
M2 = 0.5 * X + 0.866 * Y + R
M3 = X + R

Since we are no good at math, we need help reversing these formulas so that for a given M1, M2 and M3, we want to calculate X, Y and R.

Thanks!
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Question by:JasonMewes
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Arthur_Wood earned 500 total points
ID: 34978990
solveing the three equations, for the three unkowns (X,Y and R)

R =  0.5 * M1 + 1.5 * M2 - M3
X = -0.5 * M1 - 1.5 * M2 + 2* M3
Y = (1/1.732)*(M2 - M3)

do you need to see the details?

AW


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Author Comment

by:JasonMewes
ID: 34979544
Didn't look quite right, so I double checked:

x = 50, y = 12, r = 97

M1 = 0.5 * x - 0.866 * y + r
M2 = 0.5 * x + 0.866 * y + r
M3 = x + r

r = 0.5 * M1 + 1.5 * M2 - M3
x = -0.5 * M1 - 1.5 * M2 + 2 * M3
y = (1 / 1.732) * (M2 - M3)

yields: x = 39.608, y = -8,43418013856813, z = 107,392

In any case my initial formula was wrong but I would have given you your points anyways if the answer had been correct, but as demonstrated above it doesn't seem to be. Correct me if I made a mistake.

The correct formula should have been:

M1 = -0.5 * X - ( sqrt( 3 ) / 2 ) * Y + R
M2 = -0.5 * X + ( sqrt( 3 ) / 2 ) * Y + R
M3 = X + R

For which the solution seems to be:

X = ( -2 * M3 + M2 + M1 ) / -3
Y = ( M1 - M2 ) * ( sqrt( 3 ) / -3 )
R = ( M3 + M2 + M1 ) / 3

Points to anyone who can verify the validity of the solution.
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Expert Comment

by:Arthur_Wood
ID: 34981319
the original question stated:

M1 = 0.5 * X - 0.866 * Y + R
M2 = 0.5 * X + 0.866 * Y + R
M3 = X + R



now you indicate that the 'correct' formula should have been

M1 = -0.5 * X - ( sqrt( 3 ) / 2 ) * Y + R
M2 = -0.5 * X + ( sqrt( 3 ) / 2 ) * Y + R
M3 = X + R

notice the sign difference on the first factor of M2.

with the new formulae,

M1 +M2 = -X + 2 * R
M3 = X + R

hence R = (M1 + M2 + M3)/3

X = - (M1 + M2) + 2 *(M1 + M2 + M3)/3 = (2 * M3 - M1 - M2)/3 (which is the same as  ( -2 * M3 + M2 + M1 ) / -3)

Y = (M2 - M1) /sqrt(3) = (M2 - M1) * Sqrt(3)/3  which is the same as  ( M1 - M2 ) * ( sqrt( 3 ) / -3 )


AW
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