World's first video of 56 transition controls for a triple inverted pendulum.
2022 ж. 18 Там.
421 753 Рет қаралды
This is the world's first experimental video about 56 transition controls that occur in a triple inverted pendulum. The triple inverted system was developed by Embedded Control Lab. Control was implemented using LW-RCP02, which was developed by Embedded Control Lab, and Simulink. The sampling time is 1 ms.
* The triple inverted pendulum and LW-RCP02 can be purchased from Sungjin Techwin. For purchase inquiries, please contact sales@switch-vr.com.
3단 도립진자에서 발생하는 56가지 transition control을 실제로 구현한 세계 최초의 실험 영상입니다. 3단 도립진자는 Embedded Control Lab의 자체 기술로 개발하였으며 실시간 제어는 Embedded Control Lab에서 개발한 LW-RCP02와 Simulink를 이용하여 구현하였습니다. Sampling time은 1 ms 입니다.
* 3단도립진자와 LW-RCP02는 성진테크윈으로부터 구입할 수 있습니다. 구매문의는 sales@switch-vr.com로 해주세요.
This truly is the world's first video of 56 transition controls for a triple inverted pendulum.
And also one of the videos ever!
HAHAHAHAHAHAHA 😆
This video numbers among the other videos on youtube
Before seeing this video, I had never seen this video!
This is definitely a video of all time
Honestly, I would have been skeptical that this would even be possible. Just…wow.
The mathematics involved are being done … so fast …
I can do one of them
@@DSAK55 I can do 7 of them.
@@lostmykeys85 Well it says "1ms"
Congratulations.
I never thought that triple pendulum could be controlled. This video definitely needs more attention!!!
This is really impressive. I believe each axis has different weights, and also the distance between the axis of the connection in the very background is shorter than the other connections. This Setup with these different weights play probably a very important role to make these transitions possible. I wonder if these transitions would be still possible, if the weight on each axis would be the exact same or if it then would be near to impossible to control the pendulum like that.
Of course it's possible, that's the whole point of chaos theory
@@Alucard-gt1zf Yes but it's impressive cause although it is theoretically possible, it is close to impossible in reality.
In theory, it's possible to control an arbitrary number of pendulums - it's just that the difficulty goes up significantly with each additional pendulum added to the system.
@@bigmike- Yeah the margin for error goes down "exponentially" the more you add.
I feel like this is the engineer's version of the sorting algorithm video
1:35 the instant stop is incredible
I watched it a couple times because I thought it was a jump cut at first.
Advancing frame-by-frame you can really see how the control algorithm knows to "stack" each of the links vertically from bottom to top. Incredible!
Looks like a reversed video almost.
@@Roach_Dogg_JR all physics is technically reversible
@@melody3741 reverse my toast please
The fact that it can go from position 1 to any is already impressive as hell. Then it can go from ANY position to ANY other without returning to any other intermediate position is crazy to me. And from unstable positions to other unstable positions. Sooooooo freaking Impressive.
At 5:46, 8:15 it's maybe being a little bit cheeky on this front, but still... damn impressive.
Not taking anything away from how awesome this is but 2 to 6 and back goes through 5
Just a pedantic note: these positions are technically “marginally stable” But this in no way makes it any less impressive!
@@someonesomewhere1240 I think it's impossible to swing all three outstretched from bottom full extension to top full extension without it crossing another equilibrium position due to inertia. If they just full send it fully extended the entire swing, they'd be unable to correct without the thing collapsing back down, and wouldn't be able to stop it dead upright like that, this is probably the only way to do it (or shortest path at least). There are a few movements that fall to similar restraints, and some transitions are just going to have to pass through other equilibrium points. As long as they aren't fully stopping there I think it's unavoidable.
@@michaelanderson7924 why, because of the cart DoF? I think you can disregard that.
Holy crap this is probably one of the most amazing feats of engineering I've ever seen.
Holy crap! I haven't seen you since the G+ days...
If you like CNC machines you might enjoy this even more kzhead.info/sun/i8WRdbaXlp5_iGg/bejne.html
I feel like it's something that anyone can appreciate.
How about the SpaceX rockets returning to land?
lol
Any sufficiently advanced technology is indistinguishable from magic. - Arthur C. Clark
This is definitely witchcraft.
Exactly what I thinking right the way thru this video, and I programmed an inverted pendulum system in my engineering degree
Clarke*
Arthur magic
No it's called mathematics.
What I always love most about these kinds of things is when they transition back to the stable equilibrium; it's like, when they're going to any of the other states, it looks unnatural enough that my brain just takes it at face value, but when it's dropping back down suddenly my brain jumps in like "Hey, we've seen stuff like this (pendulums, rope, chain, etc.) dropping down and swinging around countless times, so we know what it'll look like here", and then it suddenly comes to a stop at the stable equilibrium with almost none of the usual swinging back and forth around it, and it just feels *wrong*
I love how simple the actual machine is; its the code and theory working the magic, not some particularly fancy machine itself
The precision capabilities of the machine also impresses me a lot. It probably has to perform such fine adjustments that we can't even see some of them.
@@DanielH212MC Yeah, but precision CNC machines can hold tolerance to below 1 micron. The equipment and pc controls have been around for quite some time. The coding is definitely the feat of engineering that was accomplished w/ this demonstration.
@@DanielH212MC Closed loop servos are amazing. The feedback is being used to balance the pendulums. This feature has recently been coming to steppers as well, which will be amazing for hobbiest who can't afford servos.
Not only the code itself does make it work. I believe each axis has different weights, and also the distance between the axis of the connection in the very background is shorter than the other connections. This physical Setup with these different weights play probably a very important role to make these transitions possible. I wonder if these transitions would be still possible, if the weight on each axis would be the exact same or if we then reach the limit in which it would not be impossible anymore to control the "triple inverted pendulum" like that.
@@RuLeZ1988 This demo is only possible due to the principle of inertia, which is a function of mass and force (a mass at rest will resist an applied force that attempts to move it in any direction, a mass in motion will resist any force that attempts to change the direction of that motion). The rig does not allow the designers to vary the force (torque) applied to the individual pendulum elements since they are free-swinging. Therefore, the only way this demonstration can work is if the pendulum elements all have a different mass, those masses being different enough to allow fine manipulation of input forces within the resolution of the control system/hardware so as to affect the elements individually and collectively with respect to their inertia within the bounds of some incredibly complex mathematical equations. The angular position/momentum feedback from each element (and the overall system) is then measured and corrected for at very high speed/resolution to arrive at the desired equilibrium. Of course, it should be possible to build such a machine with pendulum elements of the same length, as long as their masses were different enough to work within the resolution/frequency/tolerance confines of the hardware, control system and code. All of that said, I have absolutely no idea how bringing the masses/lengths of the elements closer together would affect the fiendishly complex calculations and coding required to make the machine reliably transition from any given equilibrium state to any other. That shit is just.... *boom* ... mind-blowing. :)
As a non-engineer/mathematician I can only admire how this looks like a simple task but understand how incredible this is.
I WANNA SEE FOUR
Heck it’s hard enough to balance a broom on my palm, I can’t image a broom with a hinge, let alone 2 hinges…
As an engineer who studied this kind of stuff, the real ass pain behind this is the funky math that went behind all of this...the theory is simple however. Once you solve for the equations though, SimuLink is a really powerful tool and really can just handle a lot of this with some clever usage of computer logic. The real impressive part isn't even the balancing. It's the ability to send the machine from 0 to any state. Dealing with the "swing-up" control was probably the worst part about developing this.
I dont know why KZhead would recommend this to me but it's sure nice it did. the first transitions were impressive enough on their own but being able to switch between any equilibrium is mind boggling to me.
In my last school year, 2018, my .ath teacher told us, if we could figure out how to predict/control a triple pendulum we would be (math-)famous. Well, he was right 😂
I love the swagger with which it goes to the stable equilibrium, just stopping the motor for a bit is not cool enough 😎
It is not the same as simply letting it go. The idea of control is that you have optimization parameter, which is transition time in this case. Without active control it it would swing for a long time. In the recommended there is this video kzhead.info/sun/oMmGh8qumF-AnKc/bejne.html , which shows the difference between controlled and uncontrolled transitions.
@@AlexTaradov oh yeah, I suppose the bearings would have to be super smooth, my brain imagined more of a dampening factor
@@AlexTaradov Their 0 to 7 looks so clean!
Holy shit, this is amazing. I once programmed a controll function for a single inverse pendulum and I was so very proud when I could get it to stand indefinitely and adjust to minor aoutside influences after working on it for several weeks. I can't begin to immagine how complex the function for this has to be. I really hope you didn't have to sacrifice too many virgins to some elder god to acchieve this.
If it was anything like my university engineering lab, there would have been plenty of spare virgins available.
This is highly under-rated fundamental robotic control. Very nicely done indeed.
Yes with this system you could make a robot that can balance much better than any human and walk and run and remain bipedal under nearly any circumstance.
@@VestigialHead I am guessing that the software was built using IK formulae and a lot of PID constants, with a lot of manual tuning. Have you considered trying a neural model, giving it an external monitor to observe its own results, and letting it attempt to train itself?
@@klerulothis is beyond simple PID control
@@yuukil5522 I recognize that. Like I said, my guess is that this is based on formulae that encode inverse kinematics--but those formulae would suggest desired behaviors, which in turn would require driving the actuator to achieve those goals, and that requires basic PID. It's one element of what is likely very many, in a classical higher-level control loop. What I'm curious about is, could the same results be achieved using a neural, self-trained control mechanism instead?
@@klerulo Theoretically speaking I’d say yeah it’s possible. I don’t know the details of this system but seems simple enough to represent mathematically and thus with sufficient design and training time would be possible to train a neural network to navigate.
I'm completely amazed and the rest of my family brushes it off thinking I'm weird and not seeing the magic. Oh well.
maybe you have the knack... kzhead.info/sun/d9xveNOig3Spoa8/bejne.html
Lols, you have to understand how difficult it is to appreciate it. And it doesn’t help that the video makes it “look easy”
It's like balancing 3 broomsticks on a finger.
This is very, very impressive! It even feels a little scary, and I can’t even put into words why…
Yes, exactly
The why is because these motors and systems are either currently or in the future will be what controls Boston Dynamics type robots. Spoiler alert they aren’t going to be dancing with them and they won’t be missing any shots like in the Terminator movies either.
It's profoundly, casually superhuman at a task you probably never considered just because it would be so ludicrously hard to do by hand, not just physically, like lifting something heavy, or intellectual, but both. And inverted pendulums are probably not the only thing it can do. Probably there are more practical applications that I also won't think of until I see them. For me it illuminates a gap in my imagination w.r.t the capabilities of robots.
I think it's because it reminds me of all the dancing skeleton cartoons I saw as a child! 😂
This should not be possible! Logically we understand that it should be "technically possible", but the problem seems so complex that it's hard to believe it can actually be done in reality.
What’s insane is you don’t see the man offshot while pulling the pulley ropes back and forth really quickly to make this all happen. Props to BTS rope guy.
I guess you could say you're a BTS stan
@@PronteCo not so much into Korean Pop music sorry.
@@PronteCo behind the scences
@@MV-vv7sg i know. It was a joke.
I would love to see this demonstration with lights on each pivot and a long exposure effect. That would look amazing!
Brilliant idea
You don't have to say everything you think
@@Connection-Lost Apply that to yourself
@@Connection-Lost I just thought about that!
@@salender4683 love this
Interesting how some transitions pass through intermediate equilibria. 6→2 and 2→6 are good examples of that.
yeah, it went through 5 briefly
The longer you watch, the more impressive you realize this is.
I'll be honest. Whenever I clicked on this video, I honestly didn't know what I was clicking on. And for the first minute or two, I was like "why is this video?" 😆. However, after a couple more minutes, I was LITERALLY blown away.!!!!
Well, there is a lot of math behind this. Loved it. This will definitely gather more attention in a close future.
Out of all of the triple inverted pendulum transitions, that was certainly all of them.
I’ve spent so much time admiring and simulating double pendulums, exploring their intricacies and visualizing their evolution- and here you are stabilizing a TRIPLE pendulum with some algorithm that I can’t even begin to comprehend. This is seriously on another level
I notice the pendulum segments are all different lengths - is that necessary for selective control of the individual segments? Like I notice in 2-> 5, the strategy relies on being able to swing the 3rd segment but not the first two
it is necessary, yes
The different frequencies from the respective lengths must be the basis for some independence in control. Brilliant.
A+, impressive!
It helps, but it's not strictly necessary. You can always disproportionately affect different arms even if they have identical dimensions.
@@joda7697 no, it is not necessary. These lengths do make it easier, though
Of all the 56 transition controls for a triple inverted pendulum videos out there, this is by far my favorite.
이 영상이 만들어지기까지 얼마나 많은 대학원생분들이 희생되었을지 상상조차 가지 않읍니다...
"Many Bothans^Wpost-docs died to bring us this information" kekeke
All of them. They didn't go out and see daylight for three years.
Translation: "I can't even imagine how many graduate students must have been sacrificed before this video was made..."
I may know of one 😉
6:55 that 5-3 was poetry
One of my favs too!
I didn't know what this video was gonna be, but it now certain feels like one of the best videos I'm gonna see in a while.
I don't know why 'the algorithm' sent me here, but it is truly wise and knows all our needs.
By far one of the best transitions is at 4:25, from 1 to 7, truly amazing
The most important to me: It has a limited and quite small platform, so it must not only perform those tricks, but also adjust the pieces to then go back to the center Just aatonishing!
from 6:55 - 7:30 are my favorite series of transitions
Those were very cool. Thanks for linking. I was about to leave early! 😀
yeah same
It's a sad day for the world's first video of 55 transition controls for a triple inverted pendulum. But I think they can, together, share joy in this accomplishment. In all seriousness though, this is fantastic. This is the kind of robotics work that allows for the craziest kind of innovation that one would never expect if someone didn't work out the math and physics behind this, put it to code, and build a practical rig to demonstrate it. All of which are enormously time-consuming for this tiny, sub-10 minute video that only got recognition because its uniqueness makes it a prime candidate for success in a system of algorithm-driven content promotion. Imagine the wonder and inspiration this has inspired now, reaching a third of a million people! The value must be immeasurable.
I'm not into engineering and I have no idea why this video was suggested, nor why I clicked on it. But I'm glad I did. That's truly incredible 👏
Reminiscent of an acrobat lifting up above their head and balancing a teammate on their hands, then letting them down again. Amazing how not just a double but a triple pendulum can be controlled with enough sensory feedback. Amazing!
The key is that each link is different length thus the natural swinging frequency is different for each link. By moving actuator at specific link resonant frequency it can move the desired link more than others. Nonetheless it’s incredible to see it in action working flawlessly.
That is not very likely how it works. It's a PID control system, using a feedback loop to constantly tune the position of the cart.
I've heard they use machine learning and chaos theory to achieve these what these machines do
@@eitanspuzzles ain’t no way this is just PID control
If you look closely you can see mass added to the ends of 1 and 2, I think this is really the key, since the inertia of each segment will be different.
@@stevelentz9458 I think those are resolvers (to measure the angular position of the joints).
Very impressive control performance. I wrote a Master Thesis for twenty five years ago for double inverted pendulum using Robust control, which was the hot topic at that time. The mechanic construction didn't aloud each pendulum to rotate fully around, so the start was done by hand to level both in upright position. The order for the controller went sky high and the loop shaping weight was designed for using the two eigenvalues for the pendulum otherwise the motor didn't have power enough.
That is just the biggest flex I've ever seen. Just wow.
This was absolutely mesmerising. It feels alive. Jovial. Mischievous. Those slow smooth slides maintaining balance? Damn. Phenomenally impressive. Bravo.
This is absolutely incredible! How hasn’t this video broken a million views?
Few people understand the achievement sadly..
I’m pretty sure it’s a reupload because I remember commenting on this a few years ago but now it’s not here and this was only from 7 months ago
1) The video name is incredibly complicated to decipher if you don't already know what this is so why bother watching something when you don't even understand the name. 2) it's 10 minutes long and most people nowadays aren't gonna invest that much time to watch something they've never heard of. And 3) it's a video about math, robotics, and physics so most normal people aren't interested (or actually hate in the case of math and physics) those topics. We obviously aren't most people lol Bonus answer: The thumbnail sucks
The mathematics and physics of this should be STRICTLY beautiful. But this is just more than math and physics. This is art found with hard science. This is simply beautiful.
Absolutely incredible. Glad the algorithm suggested it
This is some of the most beautiful motions I have ever seen
this is incredible mastery of control
As an engineer, just seeing this makes me wonder the level of numeric methods and computing processing that this took, truly amazing
This feels very much like a pre-2010 YT video. The title says what the video is about, no commentary, and the comments are filled with impressed people. Good stuff!
So impressive !
더 많은 공학도들이 이 영상을 보고 영감을 받으면 좋겠네요.
From description: “The sampling time is 1 ms” Wow, that’s not nearly as fine as I would have expected for a 3 pendulum control system, and yet it doesn’t seem to have any trouble at all.
This is the single most impressive control system I think I have ever seen. Absolutely outstanding.
Unbelievably cool. My mind is blown.
going from 6 to 7 is wild that's some damn precision
Feel like more people should be talking about this. Just beautiful and elegant.
The amount of transitions in these controls is impressive.
I’m don’t think the average person realizes how insane and amazing this actually is.
No! Everyone knows how insane that is! We all played at some point with a pendulum
Thank God the above average people like you can truly appreciate it
The insane person realizes how average and actually this amazing think do
@@swolleneyes I love you.
Can’t wait to see what six flags does with this technology
I have no clue why KZhead recommended this to me, but I can't stop watching. It's mesmerizing and absolutely genius.
With so man great transitions it's impossible to pick a favorite...! 😭😭💕
Simply astounding. My knowledge of control theory and design practice is pretty limited, but even at my layperson level I can understand how impressive this project is. I would love to know if this demo rig and its control software were developed by building a double pendulum iteration first, or whether the designers just decided to aim high and went straight for developing this Big Daddy version! Edit: I've just gone through the mental process of trying to figure out how to explain why this video is so cool to my family and friends, and the more I think it through the more mind-bendingly complex and impressive it gets. I've kinda sorta got a handle on how the various equilibrium states are achieved, on a theoretical level at least (no idea how the math would be translated into functional code though). But cleverly stringing subroutines together to go directly from any given state to any other without passing through a known stable equilibrium on the way is simply magic as far as I'm concerned.
영상 유익하네요!!
This amazing! I am smiling and in awe right now. Incredible work!
Truly incredible. Great work!
I find this strangely relaxing to watch. It also made me laugh out loud, probably because I imagined the machine to be sentient as it performed one feat of juggling after another. I could almost hear it saying "Huuu...UUP!!" I clapped at the end.
I am not that good in maths but I read how chaotic pendulum systems can be. Triple! This is incredible.
The title is exactly what is in the video. That is how all videos should be. This is incredible work (the video and the title).
I might be a nerd but this is more fascinating than 99% of the content I've seen in the past 5 years.
now this is some big brain stuff
This... Was one of the best thing i've ever seen There are three me that are wondering: 1) How do i construct a physics theory to properly describe when and how to give/remove energy from the system to make it do this? 2) How do i set up machines and sensor in a way that can give me feedback fast and acurate enough to properly balance it even when it's in his most unstable equilibrium spot? 3) How do i program a feedback loop that can automatically do small correction based on the points above? i'm a physics student and my friends are another physics students, an automation engineering student and a informatic student (not sure about specializations) so this was spectacular thinking about every part of our studies... I loved seeings this
The tools for this are called "control theory", they involve a good bit of physics and math from multiple domains. It's a very deep subject, and this triple pendulum is non-trivial to control the way they do. However, single "cart-pendulum system" (good thing to Google) are pretty standard control subjects that many university students do, and would definitely be both reasonably achievable and a great starting point for this if you wish to get more complex in future.
The simplest control strategy is something you've probably heard of, the PID controller. In essence it's saying "if I want something to go in X direction, I should apply X input", intuitive enough from Newton's Laws. PID is good enough to balance a single cart-pendulum. After that you can get into linear controls, which essentially generalizes the PID system and utilizes linear algebra to more formally describe and control a system. For a system as complex as the triple pendulum you almost certainly need more complex, non-linear/optimal control systems which are much more difficult to design.
@@chrisdonnell7200 thanks a lot, i will most certainly check it out... After i give my next exam that is almost a week from now
@@silver_3552 Basically, an inverted pendulum... a controlled rocket is very similar to an inverted pendulum.
@@scowell i see, that's an interesting analogy that i didn’t think of... There is so much to learn and i'm really glad i've written that message and to all that have responded giving me something to search
Living in the 21st century is learning about an unsolvable problem, waiting two weeks, then stumbling across people who solved it
Great work! This really is unbelievable
Is there a research paper or some simulink code I may view?
If I try really hard, I can sometimes balance a broom on my finger.... so, I got that going from me.... which is nice...
This is one of the coolest things I've ever seen. And I wouldn't have thought this was amazing until I started studying engineering. I can't even comprehend the physics needed to set up the control.
This is sooo cool! I always watch the triple pendulum vids thinking that micro movements would drastically change the outcome of the swing, but they are actually controllable to the point of being able to predict and balance them like you have! Sweet! The last few iterations were the most impressive (and I assume the hardest to get right too), really cool.
It's unstable at some of the positions, but the non-linearity of the geometry stabilizes it. Excellent work!
I'd imagine the majority of the stability is achieved through powered microcorrections, moving the base to adjust the angles of the pendulums relative to each other.
ALL of these except position 0 (all down) are unstable. The point of this thing is indeed that the apparatus counters, using motions of various magnitude and speed.
Amazing! Can you provide paper link?
We have not published a paper on this implementation yet. We will.
Absolute madness. Congratulations!
Remarkable. Thanks for sharing.
Fascinating.. But what do you do with this?
It's a benchmark plant for lots of control engineers. Furthermore, people who do research on reinforcement learning, this system is a great challenge. For classical control engineer, this system can be used for education purpose because, to swing this up, we need great amount of knowledge on control theory.
This is so amazing - is this is generic solution between any positions, or was each move planned out ahead of time?
It's 2-DOF(degrees-of-freedom) control. Feedforward+Feedback. Feedforward trajectory is calculated from the dynamic model offline. Feedback control compensates the error between the current trajectory and calculated feedforward trajectory.
Sorry my background is software and not really engineering so I'm not super familiar with some of these terms, but I guess I'm wondering about the commands and inputs from the sensors - are the commands and sensors based on the angle at each pivot, or is it a "pre-baked" set of moves to get between each position? As a better way to ask my question - if someone bumps the table in the middle of the movement that wouldn't be an issue right? Thanks for the reply!!
I'm also so curious now what would happen if it's stable at the "full upright" position and then someone comes and knocks it over, what does the recovery process look like? If there's a public repo for the code I'd love to see it!
@@joshgribbon8510 If the bump is small, it can remain stable. Big bump will break the stability.
@@urimiroo Ah ok, but assuming it's fully destabilized, doesn't it still have it's target position and know how to get there?
Amazing work!
And they said it couldn't be done!! Bravo!
Is it an encoder to measure at the joint, is it wireless, or is it a slip ring?
encoder + slip ring
@@urimiroo Thank you for your reply
Could you share some details about what hardware is being used here? Curious about the cart, rails, motor, and encoders.
We developed it as a commercialized product. Sorry for not giving the detailed answer.
@@Bobsmith-xq2pr Robot Shen Yun - The Broadway Musical
@@Bobsmith-xq2pr I was kidding but meant robot jugglers and robot performers w/o humans. but totally kidding.
@@Bobsmith-xq2pr there most likely is a use case, since such projects never get funding, if theres none.
@@Bobsmith-xq2pr Comeon Bob, Thats incredibly closed minded... There HAS to be at least one use
This is mind boggling. So impressive!
That's incredible. Bravo!
I'm a programmer and not an engineer but this is very cool. Some really neat behind the scenes stuff I bet and lots of hours.
Holy shit.
*Pinned comment*
@@andyhervert9650 If I show people this and they don't understand why this is impressive I know we'll never be friends. It's really handy to have this quick social filter, and explains at least 20 of your views.
Equally impressive and cool, well done!
Amazing transitions
I know the answer already, but is there a Github or anything? Maybe a link to a paper?!? I'd love to read more about this. The double pendulum is on my bucket list.
No github. No paper yet. We are supposed to write a paper on it.
@@urimiroo can you reply to this comment when the paper is shared?
@@TheSingleSurvivor Sorry for my laziness. We are working on the paper. But it will take some time till we submit it. Due to some funded projects, we have to spend most of our time to handle those projects.
Start here: kzhead.info/sun/g81wnJylhJyPiX0/bejne.html Then: kzhead.info/sun/kpV8pKWAjZeXa4E/bejne.html
During my automatic control studies in the 1990's I was still tought, that this is assumed be im possible due to the missing mathmatical proof. I like this demonstration of scientific development and progress. Congratulations.
I'll bet there's still no math proof either, and the PIC just assumes a solution exists and happens to work.
I was also taught this was impossible because of the lack of a proof, but watching it started to doubt I was taught that, so thanks for your comment.
truly, one of the videos of all time.
Absolutely amazing. I did some analogue electronic control stuff in the past. I would have been quite sure, that this was not possible.
Do you have sensor data being returned to the controller from the articulation points - or is this an analysis of linear feedback of the horizontal?
We measure all the angle data of each articulated joints. It's basically feedback control.
@@urimiroo Excellent, and thanks for the reply.. I had that expectation. Great work and content. Thank you for sharing your efforts. Another question - I'm guessing you used a micro controller or FPGA? Did processor speed ever become an issue? I'm just curious what your biggest bottleneck was when it came to the data acquisition and crunching, or if was simply never an issue.
@@AtomkeySinclair For the control, we use a lab-built RCP (Rapid control prototyping) environment. It acquires the sensor data and sends it to the PC on which Simulink is running. Simulink calculates the control value and send it back to the RCP unit. Then RCP unit generates the required signal for the actuator. PC and the RCP Hardware unit is interfaced through high-speed USB communication.
@@AtomkeySinclair kzhead.info/sun/oMmGh8qumF-AnKc/bejne.html Here's a video of someone with a similar setup pushing the pendulum. You can see it comes back to stability, which is pretty cool. However they only went between equilibriums 0 and 7, but none of the others.
This is excellent. However the numbers (start and target equilibrium, shown at top-right) are difficult to follow 'intuitively'. A better visualisation might be to keep the table (shown at 0:13 - 0:21) onscreen, and fill-in the boxes as the demonstration progresses. For example, using 'amber' to indicate which transition is about to be done (or is in progress), then 'green' once that transition has been achieved. (Or perhaps hashed- and then solid-colour, for the benefit of those who are colourblind.) I would also be interested to know how the relative-lengths of the pendulums affects the feasibility of this demonstration. I would guess that the three pendulums need to be different lengths, such that different frequencies of input motion will affect each pendulum differently. But is the order significant? ( 'Short-medium-long', versus 'long-medium-short', 'medium-long-short', etc.) I could also be wrong... is it possible with three pendulums of the same length?
Thank you for the suggestion. We will think about it later. For the length of the pendulum, we use the following rules: short-medium-long as shown in the video. Same length is not a good idea because the mechanical structure prevent it from happening.
iirc same length pendulums would mean you could get singularities, which are not desirable. Like imagine the first joint being at 0 degrees and the second at 180 degrees, then the third joint would be exactly in the same axis as the first joint and become uncontrollable. On the maths side it would make the equations to divide by zero or something similar in that point.
@@CatNolara If all the pendulums have same length, then they will collide while they are rotated. Remember that we have to install a rotary encoder at each joint. It means that it needs some space to avoid the collision.
@@urimiroo if the problem is purely structural, would it be a solution to have the pendulums offset from each other in the z direction (while they are laying flat)? As in, have the pendulums not almost touching but a bit more spaced apart in order to have room for the encoder? I guess this is going to require a lot extra work to mount them that way though. But anyway, the question I guess is, do the physical dimensions of the pendulums play a role into the model? Does the system need to be modelled differently if you put in different size pendulums (or different size order) than the ones you have now?
@@CatNolara what you're describing is irrelevant of the lengths of the vectors, but is an artifact of using Euler angles to describe rotations and it's called gimbal lock. That is why you don't use Euler angles to describe the rotations of 3 axis systems but you use quaternions (which are essentially vector representations of 3D rotations) and then you avoid this problem.
This is amazing.
Quite impressive. Nice work!