Vertical Lego Robot

DU — Fri, 11 May 2007 06:16:35 -0800

Help my robot remain upright. So I'm trying to make a self-balancing robot from Lego. This is not an unsolved problem by any means, even in my chosen medium. However, I seem to be too dumb to figure out how to do it on my own and need a little assistance. Also, I'm adding a wrinkle that may screw the whole thing up.

First of all, I want the entire solution to be pure Lego, which eliminates things like ultrasonic sensors (this is RIS, not NXT), HiTechnic acceleration sensors, etc. But detecting tilt using a stock rotation sensor (geared at 1:25) isn't hard, so that's fine.

The next thing is reacting the robot when it detects the tilt. This is the basic inverted pendulum on a cart problem. Long story short (see below), I need some understanding of the physics of the situation. First step: free body diagram. But I'm confused because the torque due to gravity and the torque due to cart acceleration would seem to be happening on different axes (the cart has no moment arm around the axis where the inverted pendulum attaches...). So I googled around and the diagrams I found didn't even mention angular anything at all, just linear forces. Wha?

So that's my first question: In the classic inverted pendulum cart problem, how do you formulate the equations that describe the situation?

Now, here's the wrinkle: Instead of reasonably measuring the tilt of the pendulum at the point where it connects to the cart, I've done something crazy. I've hung a second pendulum from the inverted pendulum and am measuring that. The idea is that the second pendulum will remain vertical and the angle will be the same. However, I've now realized that when the cart is accelerating this secondary pendulum won't be hanging straight down. It may in fact be lined up with the inverted pendulum, making the cart think it is balanced.

This is the real reason I need the mathematical model. I need to know if my cockamamie¹ setup is at all feasible or if the dual pendulum concept is self-defeating. Maybe someone can even provide a direct proof that this won't work.

¹The cockamamieness actually has a purpose. I ultimately want to balance the robot in two dimensions on top of a single spherical "wheel". Because I need to measure both pitch and roll, I don't think I can measure at the axis, which is how I came up with the pendulum tilt sensor concept. I realize that this would be a hard problem even without limiting myself to Lego and even if I weren't an idiot.

yoga and periods

jennyb — Tue, 02 Mar 2004 06:55:41 -0800

I've gotten conflicting answers from physicians, teachers, and Google searches so I come to you for anecdotal evidence: Is it really dangerous for menstruating women to practice inverted yoga postures? Has anyone you know ever suffered negative consequences from practicing inversions during her period?

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Vertical Lego Robot

yoga and periods