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.
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?
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.
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?
So... is this a Segway?
Needs an animation!
Neat!
Useful revision of the engineering kinematics I covered a while ago.