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### Topic: Simpler tipping calculations for balancing robot  (Read 1 time)previous topic - next topic

#### jremington #15
##### Feb 13, 2016, 08:46 pm
Quote
Even if you can get an accuracy of 1 deg with sensor fusion it is not good enough.
Nonsense.

#### charliesixpack #16
##### Feb 13, 2016, 09:22 pm
Nonsense.
Hard to argue with reasoning like that. #### MarkT #17
##### Feb 14, 2016, 12:17 am
But its rate of change of tilt that matters, absolute angle is best corrected from wheel acceleration
as I've mentioned (partly because the distribution of mass may change and thus the perfect balance
angle will be different from run to run if the battery is moved/changed or a payload added).
[ I will NOT respond to personal messages, I WILL delete them, use the forum please ]

#### jremington #18
##### Feb 14, 2016, 05:11 amLast Edit: Feb 14, 2016, 06:19 am by jremington
It is interesting that for a falling inverted pendulum, the rate of change of theta (tilt) is proportional to theta (for theta << 1 radian).

This follows directly from the equation of motion about a point of unstable equilibrium:
theta dot = sqrt(g/l)*theta
where l is the distance from the pivot point to the center of mass.

#### charliesixpack #19
##### Feb 14, 2016, 02:37 pm
It is interesting that for a falling inverted pendulum, the rate of change of theta (tilt) is proportional to theta (for theta << 1 radian).

This follows directly from the equation of motion about a point of unstable equilibrium:
theta dot = sqrt(g/l)*theta
where l is the distance from the pivot point to the center of mass.
(theta dot)dot = sqrt(g/l)*theta

#### jremington #20
##### Feb 14, 2016, 05:09 pmLast Edit: Feb 14, 2016, 05:14 pm by jremington
Actually, from freshman physics,

(theta dot) dot = (g/l)*theta

for small theta. Solving this leads to what I posted in reply #18 (apropos of MarkT's statement) and is left for as an exercise for the reader.

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