Wheeled Inverted Pendulum Model

scaron.info

32 points·pillars··9 comments

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Very cool.

As an aside: thanks to the author for pre-rendering the latex as the page looks pretty much the same with JS on or off.

Pre-render your latex!

https://katex.org/

That whole page is so crisp and clean.

World's first video of 56 transition controls for a triple inverted pendulum

https://www.youtube.com/watch?v=I5GvwWKkBmg

Very cool. tl;dw: an inverted triple pendulum has 2^3 = 8 equilibria, since each arm of the pendulum can either be up or down (naturally, all but one equilibria are unstable), and this controller is able to make all 8*7 = 56 transitions between them.

Control theory is one of those things that shouldn't possibly work, yet here we are.

Being absolutely no expert in control theory, I implemented a PID-controlled segway in Algodoo physics sandbox a long time ago without any linearization, simply adjusting the coefficients by eye: http://www.algodoo.com/algobox/details.php?id=156819

I wonder how much of an improvement would the linearization yield in this case, given that it only works for small angles (which I imply from "see how to linearize and discretize it for small angles" in the article), and I guess that for large angles there won't be enough wheel grip anyway if torque would suffice, even with linearized control.

Well, it's a nice occasion to revisit an old project and try, then.

So... is this a Segway?

Needs an animation!

Sounds like a job for Reanimate!

https://github.com/reanimate/reanimate

https://reanimate.github.io/

Is this the same control system that is used on the first style Segway by Dean Kamen, or is it different since there is a mass at the top of the pendulum?

Neat!

Useful revision of the engineering kinematics I covered a while ago.

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