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woelen
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This is one of the methods to achieve finer control over robotic systems. The mechanism is that a real robotic system has a number of sensors, which
measure some states of the system. By means of a mathematical model, then other states can be derived. One method is to simulate a dynamic model in
real time, which provides access to all relevant system states. The states in such a model of course would drift away over time from the real system
states. Measurements in the real system then are used to keep the states of the dynamic model near the real states. The nice thing is that also
unmeasured states can be kept near the real states and this extra information then can be used to achieve finer/better control.
A whole branch of mathematics has been developed and its main goal is to determine observability and controllability of states which are not directly
measured or controlled. For linear system the math is not that difficult, but for non-linear systems, such as that headless reindeer, the underlying
math can be extremely complicated and quite powerful systems are needed to do the realtime computations.
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franklyn
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The way it was then
The Internet as imagined in 1969
http://www.youtube.com/watch?v=Y0pPfyYtiBc
20 years later an early realization
http://www.youtube.com/watch?v=yFF0oQySsh4
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densest
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@woelen - the modeling you mention sounds very interesting - are there any key books or papers or people to google for to get an idea where that field
is going?
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watson.fawkes
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The
terms observability and controllability are concepts from control theory. Start with the "control theory" page on Wikipedia. One of the references at
the bottom of that page is this paper: Modern Control Theory - A historical perspective. I've skimmed it and it looks like a solid introduction. I find historical survey papers such as
this one are enormously useful, as they help me categorize what I read into the various schools of thought and thus to orient myself within an
unfamiliar field of research more rapidly.
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woelen
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Another interesting read may be about the so-called Kalman filter:
http://en.wikipedia.org/wiki/Kalman_filter
It uses a dynamic model of a system to keep (noisy and inaccurate) measurements and a simulated model close to each other. This has the advantage that
noise is removed (the model has no noise, only the real measurements have noise). It also has the advantage of being able to use additional states
from the model, which are not measured at all. Of course, one must be careful with the latter application and be sure that the underlying dynamic
model is a sufficiently good approximation of the real system for the purpose you are using it.
Be prepared though that this is not easy math! You need university level calculus in order to understand the theory behind the Kalman filter,
non-linear dynamic systems models and the statistics incorporated in the method.
The concepts of controllability and observability are explained here and worked out for linear systems:
http://en.wikibooks.org/wiki/Control_Systems/Controllability...
This theory is not that difficult. Some basic linear algebra, however, is needed for understanding this.
For non-linear systems the situation may be much more complex. Many mechanical systems in robotics are so-called 'non-holonomic' systems, which means
that the number of meaningful controllable freedoms is less than the total number of degrees of freedom. A nice example is a car. In 2D-space (e.g. a
floor), it has three degrees of freedoms (position in x and y-direction and orientation). There are however, only two meaningful controls, being force
in forward/back-direction and steering angle. A car cannot move sideways directly but it can be done indirectly, using the other two controls (e.g.
driving forward for 10 meters and then driving backwards and in the meantime steering somewhat, the classical car parking problem).
http://en.wikipedia.org/wiki/Nonholonomic_system
A very simple model demonstrating non-holonomy is this model of a robotic cart with position (x,y) and orientation phi, which can move
forward/backward with velocity v in the direction of its orientation and which can rotate around its axis with angular velocity w:
Three degrees of freedom:
dx/dt = v*cos(phi)
dy/dt = v*sin(phi)
d(phi)/dt = w
Only two meaningful controls:
dv/dt = k1*F - R1*v
dw/dt = k2*T - R2*w
You apply a force F in forward or backward direction, which leads to an acceleration dv/dt or you apply a torque T, which leads to a rate of change of
angular velocity w (angular acceleration dw/dt). Here, k1 and k2 simply are constants, depending on the mass, rotational inertia and construction of
the cart (e.g. k1=1/M and k2=1/J, M is mass and J is inertia). Here, R1 and R2 are friction-modelling damping constants, which assure that if no force
and torque are applied that the car will come to a standstill.
Just play around with this model in order to get a feeling of the concept of non-holonomy. Use k1 = k2 = R1 = R2 = 1 for simplicity. You'll see that
although you just have two controls, any state (x, y, phi) can be reached, starting from any other initial state. The practical path from one state to
the other may be hard to find though.
In robotics this type of phenomenon is very common. It can be present in the internal workings or in its motional freedom.
[Edited on 16-6-10 by woelen]
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franklyn
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The first and second highest performing supercomputers are now in the far east.
Yes but can you play Pong on them?
1 - Japan
The K Computer, built by Fujitsu, has 68,544 central processing units, each with
eight cores , housed in over 800 racks , it is capable of performing more than 8
quadrillion calculations per second.
2 - China
The Tianhe-1A uses just 14,336 central processing units , because unlike the K
computer, it has 7,168 NVIDIA graphics processors to accelerate computation
and is capable of achieving speeds of 2.57 quadrillion of calculations per second.
who says the PC is dead 
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IrC
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"I'm rounding this to 20 by nominating Clive Sinclair's little 12 once beauty the ZX-80"
I remember the great day I had enough to get my shiny new 8K of ram. Money was tight and damn hard to come by during the Carter years. I built a rack
in 1984 using 10 main boards from the Timex Sinclair ZX-80 for my first parallel processing experiment. You are right the article is very lacking to
omit this amazing for the time machine. Nor do they include the TI 99/4A, the one I wrote my first video game in basic on in 1981. Another one which
should have been on the list making it 21.
This happens when people talk about the past having never lived it.
"Science is the belief in the ignorance of the experts" Richard Feynman
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AndersHoveland
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Perhaps someone should have started a thread about the cost of housing: "25 years later and 3 times less value for the money". The only
improvements there have been in the last 25 years are technological innovations. Other than that, everything else in society has just gotten
worse. The story of humanity I suppose.
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dann2
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Is it true that the estimated computing power of a leech is thrillions of time more that the best supercomputer?
If so, it's a pity it cannot be harnessed.
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AndersHoveland
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Quote: Originally posted by dann2  |
the estimated computing power of a leech is thrillions of time more that the best supercomputer?
If so, it's a pity it cannot be harnessed. |
what exactly are you proposing?
Perhaps in the future all the newest computers will have aquariums built inside! 
Here is what a computer "mouse" might look like:
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Polverone
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| Quote: Originally posted by dann2 |
Is it true that the estimated computing power of a leech is thrillions of time more that the best supercomputer?
If so, it's a pity it cannot be harnessed. |
I think this is a confused interpretation, like someone estimating how much computing power it would take to model a leech and then mistakenly
referring to this estimate as the computing power "of" a leech. Likewise, it would take vast amounts of computing power to model all the chemical
changes taking place in a burning cigarette, but it would be mistaken to refer to the vast computing power of a cigarette. Computing and
things-that-can-be-modeled-by-computing are not generally commensurable.
PGP Key and corresponding e-mail address
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dann2
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I thought it meant the 'computing power' of its brain.
It would take many many supercomputers (if all the sensors and actuators could be built) to do what the leech can do. Sense it's surroundings, move,
mate etc etc.
I am not standing by this. I have not done the calculations necessary to prove it!
It is rather difficult to compare and measure a leech's brain (does it have one?) to a computer.
[Edited on 15-11-2011 by dann2]
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White Yeti
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| Quote: Originally posted by dann2 |
It is rather difficult to compare and measure a leech's brain (does it have one?) to a computer.
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It drives me absolutely insane when people compare a brain to a computer. They are not one and the same. A digital computer is flawless, can perform
mathematical calculations instantly, and can run programs. A brain is flexible, adaptable and imperfect, thus, unable to compute without using a
roundabout method. You cannot compare the two.
There is one danger associated with the way we store data and information nowadays with computers. We live in an age of immense progress in computer
technology, but we keep changing the way we store data. Take a cassette tape, or a phonograph cylinder for example. Those technologies are antiquated
and pretty soon we will no longer have the equipment needed to view data stored on those storage media. As we keep changing the way we store data, we
no longer have records of the past because much of the data is lost.
There is one technology that is reliable no matter what time period you live in, that's the book. The book does not need electricity, it does not need
any external mechanism to retrieve data (other than your eyes and your brain) so it can be passed down from generation to generation. Even though we
have computers and other gadgets, the book remains the most reliable record of the past.
"Ja, Kalzium, das ist alles!" -Otto Loewi
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AndersHoveland
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Unfortunately, books are made of paper. Books only last up to 400 years under normal conditions. No one is going to take the trouble of storing books
in the absence of oxygen and moisture for posterity. Ironically, the clay tablets from ancient civilizations will far outlast modern knowledge which
is stored on paper or disk.
[Edited on 28-12-2011 by AndersHoveland]
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White Yeti
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| Quote: Originally posted by AndersHoveland | | Unfortunately, books are made of paper. Books only last up to 400 years under normal conditions. No one is going to take the trouble of storing books
in the absence of oxygen and moisture for posterity. Ironically, the clay tablets from ancient civilizations will far outlast modern knowledge which
is stored on paper or disk. |
I wouldn't be so sure, books can last much more than 400 years. It depends on the climate in which they are stored. If they are stored in the arid
climates of the mid east, they could easily outlast civilisations, If they were stored in my basement, they wouldn't last more than 20y.
Unfortunately, books are destroyed by fire. Fires in libraries are a significant reason why much information has been lost over centuries.
[Edited on 12-29-2011 by White Yeti]
"Ja, Kalzium, das ist alles!" -Otto Loewi
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Dr.Bob
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I have some old core memory boards that might be readable... That ties together the part of the thread about old computers and the archival storage
issues....
Does anybody have an old PDP-11 that needs a memory upgrade? I think each board holds a whopping 1K! They are somewhere in my basement under a
pile of lab supplies. I also have a power supply for one. That thing was so big that it will hold 12V for several minutes of (a small) load after
being unplugged. Who needs a UPS when you have farads of capacitance?
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Spart
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The reason why those old computers are so expensive in such a small amount of time is due to Moore's Law, which states that approximately every 2
years, computer power doubles. This includes stuff such as processing speed, memory capacity, pixel number and size in digital camera pictures, and
more. It is quite fascinating to think that only after 2 years, humanity's progress with computing hardware doubles.
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White Yeti
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| Quote: Originally posted by Spart | | The reason why those old computers are so expensive in such a small amount of time is due to Moore's Law, which states that approximately every 2
years, computer power doubles. This includes stuff such as processing speed, memory capacity, pixel number and size in digital camera pictures, and
more. It is quite fascinating to think that only after 2 years, humanity's progress with computing hardware doubles. |
That only applies to silicon based processing units, but once we exhaust silicon's potential, the law will no longer apply. Exponential growth must
stop at one point or another.
"Ja, Kalzium, das ist alles!" -Otto Loewi
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woelen
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I think that we already are at the end of silcon's potential. Look at the clock frequencies of processors. They only grow marginally nowadays, due to
heat issues. We still do see progresses, but now that's in the number of cores, less power usage and more efficiency in processing CPU instructions
(less cycles per instruction). But this increase in processing power also will soon find its end.
I do not, however, expect that with the end of the potential of silicon chips there will be an end of the increase of processing power. There may be a
(short) period of stagnation, but soon other technologies will take over. Promising technologies are light-based computing, use of polymers for
computing devices, use of nano-technology and in the somewhat further future even bioelectronic devices may appear.
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White Yeti
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| Quote: Originally posted by woelen | I think that we already are at the end of silcon's potential. Look at the clock frequencies of processors. They only grow marginally nowadays, due to
heat issues. We still do see progresses, but now that's in the number of cores, less power usage and more efficiency in processing CPU instructions
(less cycles per instruction). But this increase in processing power also will soon find its end.
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Silicon's potential is close to being exhausted, but technological developments are still enabling us to make CPU's ever faster and more powerful. The
transistors nowadays are as small as they're going to get, but now IBM is building 3D CPU sammiches:
http://arstechnica.com/hardware/news/2008/06/ibm-demonstrate...
I'm waiting for the development of graphene computers, where transistors can be scaled down to just a few atoms wide. Plus, the added bonus is that
graphene is an amazing conductor of heat, making cooling of 3D chips all that much simpler.
"Ja, Kalzium, das ist alles!" -Otto Loewi
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Diablo
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Quantum Computing
I can't wait to see quantum computer, where a single atom can hold a value of 0,1 or everything in between.
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GreenD
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Quantum computing brings up very interesting philosophical perspectives.
According to the field, there is no possible way to predict any system with absolute precision or accuracy without the predicting device (quantum
computer) being the exact system.
It seems straight forward; the only way to perfectly predict the weather is to "be" the weather, however - this also obviously displays that
predicting the future accurately is impossible (of course, the closer to the present you predict, the more accurate you are). This has a direct
consequence in determinism...
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White Yeti
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I have a prehistoric kitchen scale the flintstones might have used to make cookies, should I post pictures? It goes up by increments of 10g but I
still use it, because quite frankly, I don't have anything better at the moment.
"Ja, Kalzium, das ist alles!" -Otto Loewi
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Pyro
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lol,
15 Mb for 4000 dollars, now you buy a tiny little stick with 16Gb for 30 bucks! and a dollar was worth a lot more then.
all above information is intellectual property of Pyro.  |
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franklyn
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http://www.sciencemadness.org/talk/viewthread.php?tid=17362&...
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