So I read this article on Segway Theory by Chris Marion and I didn't really understand the math behind it; I only understood the concepts of the algorithms. Could someone please paraphrase the algorithms so I can understand them, especially because I am going into Algebra 2 as a freshman and have never taken calculus. I am definitely confused on converting the voltages of the sensors into acceleration and angular velocity and also the filter algorithms. 
If you really want to understand control theory, you need to have had courses in algebra, trigonometry, matrix theory (linear algebra) and calculus, ending up with a decent understanding that material.
There is no getting around it.
However, the Segway is just a balancing robot and there are plenty of very simple approaches toward making one that works. Look for other websites, examples and explanations to get started.
If the segway center of gravity is below the segway axle center line, balancing should be fairly simple.
If the segway center of gravity is below the segway axle center line,
getting it to fall over would be a challenge. Balancing would be trivial.
PaulS:
getting it to fall over would be a challenge. Balancing would be trivial.
Maybe we should build them with 15 foot diameter wheels and we could hang seats from the axel and that would keep the math easier, and it would be a lot of fun to build given the correct budget.
wwbrown:
Maybe we should build them with 15 foot diameter wheels and we could hang seats from the axel and that would keep the math easier, and it would be a lot of fun to build given the correct budget.
You wouldn't need that large of wheels:
...and yes, such a machine look hella fun (though it wouldn't be cheap to replicate)!
Let's see. How about 4-foot wheels and a seat? Or a monowheel?
I was thinking about the problem all wrong we just need smaller people not bigger wheels.