The typical solution to the inverted pendulum problem is something like the segway. A long, tall stick standing on two wheels. When it starts to fall one way a motor drives the base of the stick that way so as to get the base under the center of gravity and stopping it falling over. And vice versa.
But, that is not what humans do when standing on roller skates. The wheels are not powered.
Rather they have knee and hip joints that they can use to swing the skates this way and that and keep their base under their C of G.
A self-balancing bot need not drive the wheels at all.
So, what about a long tall bot standing on two free wheeling wheels? The long tall part being two parts with a hinge in the middle somewhere. As the thing falls over a servo at the hinge drives the lower part in that direction. And vice versa. Thus putting the wheels back under the C of G.
If you want the thing to actually drive forwards or backwards, just deliberately fall in that direction.
Normally when you see an analysis of the inverted pendulum problem it includes a lot of fluff about the mass of the lump at the bottom, that drives the wheels. And the mass at the top. Bla, bla.
We can short circuit all that by making the "head" the massive part, and the rest of it really light.
What then is the mathematical/physical model of this?
I start to understand why dinosaurs, emus, chickens, horses, camels, humans etc have a big heavy mass at the top and long lightweight legs underneath.
Under those circumstances the answer for me has always turned out to be "harder than I thought". OTOH I am usually stubborn enough to complete it and learn something of value.
Oh yeah, everything is always harder than you think when you start.
Sometimes it's better not to know how hard a thing can be. That might put you off even starting. Just get in there and do it. On rare occasions that has led to people stumbling into solutions that all those that know better never thought of.
I don't think you could move by deliberately falling in one direction. Otherwise, skaters could just lean instead of kicking out (or whatever the skating motion is called).
I don't think you could move by deliberately falling in one direction
It sounds counter intuitive but that is exactly what happens.
Try it for yourself. Stand up straight. Then take a bow. As you bend forward at the waist more and more eventually you will worry about falling on your face. You will take a step forward to stop that happening.
If you think about it you see that is what we do all the time when we are walking.
Where does the energy come from? Well, you constantly have to put power in to keep yourself at the normal height off the ground.
Admittedly I have no idea how skaters do what they do. I got a seriously sore bottom when my friends tried to put me on ice a couple of years back.
If you watch any video of a balancing bot moving you will see that it leans into the direction it wants to go.
I don't think you could move by deliberately falling in one direction. Otherwise, skaters could just lean instead of kicking out (or whatever the skating motion is called).
I think you can move in one direction by falling but that direction is down.
I robot with free wheeling wheels would need multiple degrees of freedom with their feet in order to "skate".
When I saw that extra 'arm' with the head-like hand I immediately thought of Larry Niven's Pierson's Puppeteers. Boston Dynamics should make one - it looks like they have all the parts.
3 legs (two front legs), two heads/mouths on two long necks.
For the wheeled legs idea, the Math is the Thing, as Bill Shakespeare so famously said. The usefulness of the concept is beyond doubt, though. As for it being a "nightmare" robot, maybe the presenter is (quite properly) referring to being inspired by Wheelers, which were first described over a hundred years ago, and frightfully depicted in this movie:
Heater.
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The typical solution to the inverted pendulum problem is something like the segway. A long, tall stick standing on two wheels. When it starts to fall one way a motor drives the base of the stick that way so as to get the base under the center of gravity and stopping it falling over. And vice versa.
But, that is not what humans do when standing on roller skates. The wheels are not powered.
Rather they have knee and hip joints that they can use to swing the skates this way and that and keep their base under their C of G.
A self-balancing bot need not drive the wheels at all.
So, what about a long tall bot standing on two free wheeling wheels? The long tall part being two parts with a hinge in the middle somewhere. As the thing falls over a servo at the hinge drives the lower part in that direction. And vice versa. Thus putting the wheels back under the C of G.
If you want the thing to actually drive forwards or backwards, just deliberately fall in that direction.
How hard can it be?
Normally when you see an analysis of the inverted pendulum problem it includes a lot of fluff about the mass of the lump at the bottom, that drives the wheels. And the mass at the top. Bla, bla.
We can short circuit all that by making the "head" the massive part, and the rest of it really light.
What then is the mathematical/physical model of this?
I start to understand why dinosaurs, emus, chickens, horses, camels, humans etc have a big heavy mass at the top and long lightweight legs underneath.
Under those circumstances the answer for me has always turned out to be "harder than I thought". OTOH I am usually stubborn enough to complete it and learn something of value.
Sometimes it's better not to know how hard a thing can be. That might put you off even starting. Just get in there and do it. On rare occasions that has led to people stumbling into solutions that all those that know better never thought of.
Isn't that what humans do?
http://blogs.discovermagazine.com/inkfish/2014/09/26/walking-really-is-just-falling-and-catching-yourself/#.WJJvJFMrLcs
Try it for yourself. Stand up straight. Then take a bow. As you bend forward at the waist more and more eventually you will worry about falling on your face. You will take a step forward to stop that happening.
If you think about it you see that is what we do all the time when we are walking.
Where does the energy come from? Well, you constantly have to put power in to keep yourself at the normal height off the ground.
Admittedly I have no idea how skaters do what they do. I got a seriously sore bottom when my friends tried to put me on ice a couple of years back.
If you watch any video of a balancing bot moving you will see that it leans into the direction it wants to go.
All in all I think it is doable.
I think you can move in one direction by falling but that direction is down.
I robot with free wheeling wheels would need multiple degrees of freedom with their feet in order to "skate".
Never mind the wheels. They are just a way of achieving the effect of standing on a frictionless plane.
As such there is no way to move forwards or backwards without something to push against. I think Newton had something to say about that.
Certainly there is no way to fall except down.
Except, you don't have to fall. By wiggling your base under your center of gravity you can prevent that happening.
You could use a standard servo to control balance in another direction.
One step at a time. As it were.
Just now I'm worrying that the balancing system I'm talking about, even in 1d, is impossible to stabilize.
On the other hand, we know it is possible because we have seen humans balancing themselves on cylinders and balls like this.
3 legs (two front legs), two heads/mouths on two long necks.
An a accelerometer like the module Parallax sells.
Fast enough.
Stick in an algorithm or two,
Im sure you can code it.
https://learn.adafruit.com/adafruit-bno055-absolute-orientation-sensor/overview Oh yeah. But which ones?
@erco,
That could be me.
Ah, so that's why we don't hear from Moderator Monkey any more. Switched careers.
Sorry Heater, but my first thought on this was, the family cat should be crated during the testing phase.
On refection I think I should start with a more traditional balancing bot. I can't see how to even start modeling the dynamics of this thing.
http://www.pbs.org/wnet/nature/spy-in-the-wild-about/14810/
"We're sorry, but this video is not available in your region due to right restrictions."
I think they mean "wrong" restrictions!