
Unbelievable balancing robot - stabilizes an articulated inverted pendulum  - JonnieCache
http://hackaday.com/2010/11/27/balancing-inverted-pendulums
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wwalker3
The guy whose thesis this was comments on it here:
[http://www.reddit.com/r/math/comments/ebql6/double_inverted_...](http://www.reddit.com/r/math/comments/ebql6/double_inverted_pendulum_crosspost_from_rphysics/)

I had guessed they were using visual sensing because of how the two halves of
the pendulum were painted in contrasting, bright colors, but I was wrong.
There are angular sensors at the joints of the pendulum, and a position sensor
in the wagon at the bottom. The control system also needs the velocities of
the parts of the pendulum, which it gets through a state observer
(<http://en.wikipedia.org/wiki/State_observer>).

The interesting part for me was how the control system stands the pendulum up:
it figures out the potential energy the pendulum will have when upright, then
jerks the wagon around to add that amount of energy into the system as kinetic
energy, then guides the system around a constant-energy landscape until it's
upright. Pretty clever!

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palish
So how much would it cost to build one of those robots?

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wwalker3
It looks like a big linear motor like in the video is probably $1000 to $2000
dollars. Angle sensors are pretty cheap (just a few bucks). Then you'd need an
A/D-D/A board to control it with ($500 to $1000).

~~~
hartror
And a smart PHD student, which are pretty cheap I hear ;)

~~~
sdfghjkjhg
Although the 'smart' ones are something of an endangered species

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mkramlich
don't worry, one day some smart PhD student will create a robot that's smart
enough to replace smart PhD students

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JonnieCache
Allow me to draw your attention to this astounding diagram my friend showed
me: <http://en.wikipedia.org/wiki/File:All.png>

_"The colour of each pixel indicates whether either pendulum of a double
pendulum flips within 10 (green), within 100 (red), 1000 (purple) or 10000
(blue). Those that don't flip within 10000 are plotted white. The angle that
the upper pendulum makes with the vertical initially ranges from -3 at the
left-hand side of the plot to +3 at the right-hand side. The angle that the
lower pendulum initial makes with the vertical ranges from -3 at the top to +3
at the bottom."_

Mathematics people: Does this image represent the landscape this robot walks
in any way?

~~~
brown9-2
_within 10 (green), within 100 (red), 1000 (purple) or 10000 (blue)_

What are the units being discussed here - "within 10" of what?

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JonnieCache
on the wiki page it says "oscillations"

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bld
My controls lab in college (University of Washington, Aeronautics &
Astronautics) had an inverted pendulum. I designed a controller to balance it
and maintain position along the track for a controls class. We took a picture
of Gumby standing on top of it for our report. It used rotary optical encoders
to measure the angle, and a motor driven belt to move the base along the
track. Somebody in our department developed a controller to flip the inverted
pendulum up and balance it. Another stabilized a jointed pendulum in various
configurations (both arms up, one up & one down, one down & one up). All are
non-trivial problems. Combining them is commendable.

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sanj
Original video: <http://vimeo.com/2952236>

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cookietime
My hunch is that balancing a real inverted double pendulum in that way is not
possible (and that the clip is a hoax -- perhaps using servos at the middle
joint to hold it relatively straight at the right time). Would love to be
proven wrong though.

~~~
hartror
The forces involved in double pendulums are very well studied. As other
posters have pointed out the robot has sensors on the two pivot points which
makes it straight forward to counter the movement (once you have a precise
robot, the right force equations and a PHD in physics) once the pendulum
enters the required state.

ps I voted you up from you negative state, I don't see a reason for a downvote
in your comment.

~~~
cookietime
I know a little physics, and understand that the physics of double-pendulums
is well studied (the case where it hangs with a stationary base is a standard
grad school dynamics problem), but what little intuition I have tells me it
can't work and would just collapse. Would _love_ to see an
illustrative/graphical/animated example of how it works.

~~~
hartror
<http://www.cs.washington.edu/homes/marc/learn_ctrl.html>

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pontifier
I love the way the 150 second trial behaves... It makes the task seem
effortless. Swinging the arm slowly and deliberately until the double pendulum
is above the plane of motion, then quick small motions keep the system
straight while longer slower motions swing the now straight system up to
equilibrium...

I think it might be possible to do by hand now that I have seen it done like
that.

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sukuriant
This reminds me considerably of the "Pole Balancing Problem"[1] which was
tackled by neural networks for a long time. It's since been solved by them.
Seeing a real-world version of that problem is pretty cool, though.

[1] The pole-balancing problem isn't exactly like this problem. A single pole
is balanced, rather than two; and even in the double-pole balancing problem,
the two poles both rise from the base, not one pole atop the other. That
should be a minor variation to it.

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iwr
Apparently, it's an application of this:
<http://en.wikipedia.org/wiki/Kalman_filter>

~~~
jsolson
I would immagine that almost every non-trivial robot you find in a research
lab today includes a Kalman filter somewhere.

I know the balancer I worked on
(<https://collab.cc.gatech.edu/humanoids/node/1241>) certainly does, although
from that project I can also tell you that most Kalman filter implementations
are probably incorrect. It's fairly easy to implement a filter which behaves
quite well but does not actually behave like a Kalman filter.

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jimwise
Note that this experiment (balancing an inverted pendulum, then moving on to
balancing an articulated inverted pendulum) is one of the examples from the
original Papert LOGO papers of neat robotics problems which grade schoolers
can understand and start working on (using the LOGO turtle or similar), but
which can be refined as far as the student wishes to take it.

~~~
JabavuAdams
A crucial difference is that a 2-link pendulum is a chaotic system. It's much
harder from a control-theory point of view.

~~~
mgw
I agree. While the inverted pendulum is fairly straight forward to implement
with a PI controller, the 2-link pendulum is quite an accomplishment.

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roadnottaken
Does anyone know if a human has ever done that?

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hugh3
I'm pretty sure it's impossible for a human. On the other hand we can do
amazing feats of balance that no robot can do, like walking quickly on two
legs across an uneven surface. It's all a matter of specialisation.

~~~
Retric
I think you vastly underestimate people, concider the two tricks at 3:30
<http://www.youtube.com/watch?v=uHDnGp1_W8c> flip something from foot and then
balance it on your head without using your hands. Note unlike the example
pendilum it needs to balance in two directions.

Even more flips,
[http://www.youtube.com/watch?v=w6NgAPmSCKM&feature=relat...](http://www.youtube.com/watch?v=w6NgAPmSCKM&feature=related)

------
est
bnu.edu.cn's lab on triple inverted pendulum, 2 axis

<http://v.youku.com/v_show/id_XMjMzMTkyMzY=.html>

and quadro

<http://v.youku.com/v_show/id_XMjMzMTk2NDA=.html>

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vtrac
Neat. Reminds me of something I built in college:
<http://www.youtube.com/watch?v=Lfh9upwZWA0>

I must admit that mine was quite a bit simpler.

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Twisol
That's pretty awesome. Actually, I'd like to see it balance _itself_ on a
(double) pendulum.

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cma
Could make a camera tri-pod (in this case, "mono-pod") that fits in your
pocket.

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rbanffy
The title is a little bit exaggerated... But the robot is very interesting.

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JonnieCache
To those of us without a background in hard mathematics or engineering but
with enough knowledge to know what it means that a double pendulum is a
chaotic system, this video is initially quite staggering. Perhaps it doesnt
fit the literal semantic meaning of "unbelievable," but then if we all spoke
completely literally language wouldn't be much fun.

~~~
rbanffy
OK. The robot is impressive. It's just that the title felt... Digg-ish...

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JonnieCache
Now that you mention it you're right, it does have that SUPERLATIVE NOUN -
VERBS AN ADJECTIVE NOUN! structure doesn't it. I shall have to take a long
look in the mirror.

~~~
rbanffy
:-)

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albertcardona
Pencil balancer in 2D, using very fast silicon retina cameras:

<http://www.ini.uzh.ch/~conradt/Projects/PencilBalancer/>

(The cameras: <http://siliconretina.ini.uzh.ch> )

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theblackbox
Saw a lecture by Tobi Delbruck at my uni last month and was really impressed
by this application among others. Seems like some really interesting
technology. Can post a link to the lecture recording (audio) if anyone wants
it?

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chl
That'd be great!

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theblackbox
<http://www.deityproject.com/Delbruck.WMA>

also of interest,

<http://www.deityproject.com/Kuipers.WMA>

Ben Kuipers takes us through his investigations to date on the subject of
robotic cognition - using some very adorable footage of a "research student"
(actually the students 2yo son) to show just how far we have yet to go.
Focusses on the "grasp" function of human object interaction. Bit slow in
places as it's just audio and the slides were important, but could help
someone find further information.

Sorry for WMA, it's the native format my dictaphone uses =S

There is another up there for linguists - Geoff Ketland discusses his notion
of language as platonic solids... I found it VERY interesting stuff.

Note: I'll keep them up for a week or two in case anyone is interested, but
I'll be using the domain for something soon, so can't provide permanent links.

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kevinburke
It's pretty cool, but I've been running it for two hours and it still has not
found a solution.

