Swing-up and Control of Linear Triple Inverted Pendulum
Ғылым және технология
Modular inverted pendulum, by default triple, easily adjusted to double or simple one. LQR time-varying controller implemented to 2-DOF control scheme both for the swing-up and stabilization in the upright position. Real setup equipped with a special fast FPGA-based PC with REX Control System. Reference trajectories computed by BvP. Designed due to cooperation between VSB-TUO, Department of Cybernetics and Biomedical Engineering. Powered by REXYGEN (www.regygen.com)
Public version of the paper "Closed-loop Swing-up and Stabilization of Inverted Pendulum by Finite-horizon LQR Applied in 2-DOF Concept": control.ibspan.waw.pl:3000/contents/export?filename=Docekal-et-al.pdf
or control.ibspan.waw.pl:3000/contents/show/202?year=2020.
Reference to my webpage: smartcontrols.cz/index.php?lang=EN
Пікірлер: 412
My jaw genuinely dropped at the first swing up and stayed open for most of the video
@StepanOzana
3 жыл бұрын
Thanks!
@lonelyspaceman4832
3 жыл бұрын
@@StepanOzana I'll second that. This is absolutely astounding!
@tristanandersen3974
3 жыл бұрын
For me the swing down was even more impressive. That’s some motion control where if really feels like the computer generated world is bleeding into the physical world.
@Not_me737
3 жыл бұрын
@@StepanOzana keep up the great work!
@Cyberdactyl
3 жыл бұрын
How do we know a swing up is just not a swing down with the video in reverse?
Mine works super stable in the down position.
@ilhamrahkmanriefda652
3 жыл бұрын
Gravity laugh
3 жыл бұрын
Also under perturbation? 😋
@leonardmilcin7798
3 жыл бұрын
@ Of course, it reliably becomes stable after any perturbation.
3 жыл бұрын
@@leonardmilcin7798 You could have messed up the control. 😉
@leonardmilcin7798
3 жыл бұрын
@ Fortunately, I am using best industry practices when it comes to my control loop. I can mathematically prove it contains no bugs and that is no small feat. The only problem my team of PhDs is observing is long period of oscillation after perturbation that suggests less than optimal control. Fortunately, we found breakthrough solution in the form of magic substance, iron oxide, which applied to our pendulums greatly reduces the problem. We are now registering a patent to generate this magic substance in situ, on our steel models, by a very ingenious process. I can't give much more information about it.
When you see the first downswing and think its not that impressive but then you see the uncontrolled one
@joshuakuehn
3 жыл бұрын
I was blown away the first up swing when it became clear it was balancing a 3 arm pendulum cause those are children of chaos
the swing up and down maneuvers are awesome
@freescape08
3 жыл бұрын
No joke, I can barely work out what's going on at 10% speed.
Holy crap even standing 2 pendulums is insane… but 3?!?! I don’t even want to know how much math went into this! Incredible!
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
@ibrahimtufekci512
2 жыл бұрын
so many differential equations it is totally an art
so you made a table with more talent than me great
@sayethwe8683
3 жыл бұрын
a table who's primary and possibly only function is to be good at this one thing. If you had thousands of hours of practice, you could probably do just as well. but you'd also be able to do other things too.
@2010ngojo
3 жыл бұрын
More brain power too.
@numbdigger9552
Ай бұрын
@@sayethwe8683 i mean even with a billion hours of practise you will never be as good at digging and lifting as an excavator. Some things cannot be learned.
The swing up is impressive but that swing down is just so satisfying.
I live for that triumphant 90s musac that begins when the pendulum swung up. That combined with the 90s aesthetics of the whole video is simply *chef's kiss*
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
I've worked on inverted pendulums and attempted double inverted pendulums, and seen them successfully done, but I've never even tried a triple and this is the first smoothly successful one I've seen! Absolutely wondrous
I didn't even know that was physically possible. I read that a double pendulum was chaotic, and this one is a triple ! Incredible work !
Searching for videos of random/chaos movement of triple pendulums. I didn't expect to see this, that's some great engineering!
That is some ninja grade control engineering 🤹 kudos
I can't express how amazed I am...
@StepanOzana
4 жыл бұрын
thank you so much!
@StepanOzana
4 жыл бұрын
A new paper on trajectory planning for inverted pendulums is out: www.mdpi.com/2073-8994/12/5/792
Fantastic demonstration. It's been quite a few years since I studied control engineering but I don't think I was ever equipt to manage this, it's probably a good thing I ended up working with databases :D
This machine should've controlled that suez canal ship's steering! :D
@StepanOzana
3 жыл бұрын
:-)
This should be scaled up and get seats. The new attraction in an amusementpark near you! THE GUTSPILLER!
@TheWizardGamez
3 жыл бұрын
have fun, with 30+G maneuvers where you can actually feel your blood rushing to one side of your body, and when you have to come down, that's right, you knock out, because your body cant take more than -2Gs of force, you weak person
@futureshit-glungis7202
3 жыл бұрын
@@TheWizardGamez well if its called THE GUTSPILLER the people should expect that
This is pure beauty! Nice Work!
@StepanOzana
4 жыл бұрын
thank you so much!
@StepanOzana
4 жыл бұрын
A new paper on trajectory planning for inverted pendulums is out: www.mdpi.com/2073-8994/12/5/792
what a fantastic algorithm and regulation ! congrats! This should be in shown in a kinetic art museum !
I know only a little about PID systems, but enough to know that is very, very impressive.... Congratulations and thanks for sharing :)
This helps explain self balancing wheels. Well done!
not single, not double, but triple pendulum... and swing up itself😲 thank you for great video and it’s most mind blowing, inspirating one in this year for me.
I came across this whilst doing a coursework in designing an observer-based LQR controller for a Furuta inverted pendulum.... It blows my mind that this demonstrations is possible!!!!
@stepanozana5928
3 жыл бұрын
Thanks for nice words! I appreciate this.
The uncontrolled swing down shows just how little friction is in the joints. Super impressive.
Very cool 👍 engineering like this always goes unappreciated. This tech is going to be awesome! 👌 those gyros are so sensitive and precise. Way cool
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
A new paper on trajectory planning for inverted pendulums is out: www.mdpi.com/2073-8994/12/5/792
@heatshield
3 жыл бұрын
I'm blown away. Can you confirm these are free bearings? No motors above platen?
@StepanOzana
3 жыл бұрын
@@heatshield Yes. All of these joints are free. The entire swingup is induced by a cart moving left and right. The cart is the only actuated component in the system.
@MaorAvni
3 жыл бұрын
What is the input to the system? Vision?
@liambohl
3 жыл бұрын
^ good question. Are there encoders on the joints?
@dextrosity7350
3 жыл бұрын
@@liambohl pretty sure it's vision since there are what looks like reference lines on the pendulum.
Truly Exceptional. Thanks for sharing this...jawdropping.
@StepanOzana
3 жыл бұрын
Thank you very much for support.
I never though it was possible to do something like this. Amazing tip of engineering.
You are the master of chaos ! Fantastic !
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
This looks straight up magical... holly crap.
Your channel is gold
yo what the heck how is this even possible, absolutely mind bending
The swing up is the most fascinating part holy moly
That was the coolest thing I've ever seen.
It's like arm-torso-leg of an acrobat; but with only one point of input. Amazing.
Advancement is striking thank u
this is mindblowing...
This is very impressive !
@StepanOzana
3 жыл бұрын
Thanks for nice words.
omg this is so impressive
Me clicking on the video: "Not sure what to expect. Let's see..." 0:10 "Ah yes, I think I get it" 0:17: (O_O) what, how? This was incredible. The speed paired with the stability... Just wow!
Amazing. I want to know what kind of bearings those are. Silky smooth movement holy crap.
probably the most amazing music i have ever seen on a video XD
@StepanOzana
3 жыл бұрын
Thanks.There were some comments saying it was terrible. My answer is: why bothering watching something one dislikes?
@sean63b
3 жыл бұрын
@@StepanOzana terrible? no way man - it was the best. also amazing motion control :)
That is absolutely amazing
@StepanOzana
13 күн бұрын
Thanks!
Just amazing! Chapeau!🎩 Now the only logic conclusion is to add an extra dimension... make ball-joints and move the cart in 2 dimensions in the plane! 👻
How does it interpret the location of the pendulum? This is some amazing control
@StepanOzana
3 жыл бұрын
Location of the pendulum is determined via 3 values from rotational incremental sensors located in the joints plus 1 linear incremental sensors describing position of the cart.
@ITpanda
3 жыл бұрын
@@StepanOzana If you are using a stepper motor to control the first arm would you not be able to know the position of the first arm without any sensors for it. Following this maths could be used to predict where the second arm is based on last input and time. If both of these things are true, as I believe them to be. Couldn't one use only one sensor placed on the third arm, maths, and knowledge of all previous to accomplish positioning?
@2000blobfish
3 жыл бұрын
@@ITpanda Only the cart is controlled, you could get a two-set solution (in non-degenerate cases) for the system given the cart position and 6-tuple space/orientation information of the third arm, but just the cart position and second bearing orientation isn't nearly enough data to create a useful inference.
@ITpanda
3 жыл бұрын
@@2000blobfish Right sir you are, two sensors should be possible for positioning information.
@MattKeveney
3 жыл бұрын
@@StepanOzana How are the outer encoders wired back to the main controller? ...slip rings?
A+, outstanding.
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
Great work!
@StepanOzana
13 күн бұрын
Thanks!
wow! amazing! cool technology)
Wow !!!! never imagined and seem before
@StepanOzana
3 жыл бұрын
Thank you for support.
Fantastic!!! . Its an anti- pendulum. Kills all oscillatory motion.
@StepanOzana
3 жыл бұрын
Thanks for nice words.
Actually insane
So you guys must be warlocks and have just used some kinda crazy warlock spell or something cause I just watched for the first time and I must say I am first of all impressed. I am also very well aware that I as a 41 years old have seen some things but that was pure wizardry! Or some really fun toys!!! Thanks!
Well, i was just about to teach the lagrangian equations of an inverted pendulum on cart, what are the odds 😁 but this is really amazing and i will read your paper in my free time.
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
So freaking cool
this is incredible
@StepanOzana
3 жыл бұрын
Thanks.
Hypnotizing
Those who took classical mechanics classes know that this should be impossible to be done, and yet someone did it!
There's so much going on in there, so much more than just a few sensors checking balance in real time and triggering motors to go to a certain direction until a certain parameter is met.
this is amazing
@StepanOzana
3 жыл бұрын
Thanks for support.
Very impressive.
@StepanOzana
13 күн бұрын
Thanks!
Awesome!! 👏👏👏👏👏👏
Amazing and educational
amazing!
Thank god it’s defined to just 2 dimensions of pivot
Im impressed
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
More than ALphaGo winning a match against the world champion, this here tells me how advanced AI has become. Truly a marvel!
Fascinating work. I'm curious: If I wanted this system to hold a stable pose with the first arm (closest to actuator) down, and the other two up, is that a simple change or are the control algorithms highly tailored to the specific stable poses of fully up/fully down? In other words, how much customization is required depending on the desired pose? Another question: How much of the mechanical configuration (arm length, arm mass, motor properties, encoder resolution, etc) is predefined (a priori vs. a posteriori)? I'm quite curious how fragile this control method is to changes like additional mass on the arms, or changes in the arm lengths. Does it learn based on the response of the system to perturbation or must it know the mechanical properties up front?
@filippetrovic7259
2 жыл бұрын
Interesting questions, indeed. Well, , i suppose you can predefine everything and get one movement configuration, to say like that. But if you change something a little bit, then it is completely different. As for the path you want to get or other specific charachteristics, you can define some things and later, depending on what you want to achieve, correct some things. For example, you have one lengths of two part pendulum. Then you calculate at what time you want for it to be full length with some angle, or whatever. Then, if you change the initial parameters, be it mass, angle or make it have initial velocity, then it will be different. But even with different initial parameters, you could ,,fit calculations" somewhat for your conditions to be met, at some point. xD
@veganjoy
Жыл бұрын
just in case you havent seen this recent video: kzread.info/dash/bejne/e2l72NmQe86onco.html
Excellent work, Stepan. I could have done without the corny music and instead heard you explain the demo and your work. This is brilliant stuff - you deserve a speaking part in this video.
amazing
Public version of the paper "Closed-loop Swing-up and Stabilization of Inverted Pendulum by Finite-horizon LQR Applied in 2-DOF Concept": control.ibspan.waw.pl:3000/contents/export?filename=Docekal-et-al.pdf or control.ibspan.waw.pl:3000/contents/show/202?year=2020
I may be alone in this but I'm more impressed with the swing down then the swing up.
Wow! 😱 Just wow.
this is me with a broom when I'm supposed to be sweeping superb control. how much of the control is maths and how much "feel"
This is amazing
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
Fascinating video. I wonder if casual viewers will appreciate just how astonishing this feat of control is. It's 100 times more impressive than it seems! :-) Just to lower the tone a bit: as an exceedingly top-heavy woman, I could really do with this technology in a bra.
@StepanOzana
3 жыл бұрын
Thank you very much for your support.
I'd love to see a printed version of the arms rotational patterns
The KZread algorithim god has blessed this video.
amazing. Is there any constraint regarding the relative weight and weight distribution of the three pendulums?
soundtrack is 100% appropriate
@StepanOzana
3 жыл бұрын
Thanks.
Please make an amusement park ride based on this!!!
AWESOMEEEEEEE
Seal : finally, a worthy opponent!!!
Oh my god wow, talk about tuned PID control lol
@ferronzomeren2733
3 жыл бұрын
I doubt a PID controller is applied to this system tho
@Jeremy.Bearemy
3 жыл бұрын
Yeah PID would be an oversimplification. Something like this you can easily model the system or "plant" that needs to be controlled and use Laplace transforms to create the exact control algorithms needed for a theoretically perfectly built triple pendulum. No tuning needed.
@emlmm88
3 жыл бұрын
The description says it used an LQR time-varying controller. I don't know enough about process control to know exactly what that is, but I doubt that it's something as simple as a tuned PID controller.
I wonder if you could try a table with 2 axes of motion, and rotate the top pendulum 90 degrees. Wouldn’t be able to swing up/down anymore but would be neat to see the wide range of motion to keep it up. Nice work!
@emiliaolfelt6370
7 ай бұрын
that would actually make the problem significantly easier
Next challenges if it is. first arm up, second down. And vice versa Over and under the translation.
So how does this work? Does each joint contain a potentiometer so the computer knows the position or is it sensing where the net weight is shifted to
I love you!
I'd like to see it bring control starting at initially chaotic conditions. How long does it take to get to balanced position from chaotic initial conditions?
You could this as security systems the trespasser would either back off after seeing it or get so entrance by it that he stay still for a while for a camera to capture his face
Does the swing up works as well as in this video, at each time ? This is so impressive !
@StepanOzana
3 жыл бұрын
yes. the same behavior each time.
I wonder how far you could push it? Imagine if you had a much longer track, I am unaware of what type of drives it my have i.e. (the capabilities of them) But say you smacked it intending to force them down, how quickly would it react and could it recover?
Awesome!!!
@StepanOzana
3 жыл бұрын
Thank you.
What are you using to collect position data, and or angular momentum data for the pendulums to determine the direction and speed the cart needs to travel to balance the pendulum?
@StepanOzana
2 жыл бұрын
We use encoders placed in the joints. The data are transferred wirelessly.
You only control the translation right? How do you get the inputs? With rotation sensor or visually with the colored arm? Cool stuff
@poodle5421
3 жыл бұрын
they said in another comment that there are sensors in the joints
Awesome work! I can't wait to read your paper. Is your method comparable to a Gain scheduling method with an infinite amount of controllers? Isn't a LQR time-varying controller very computationally expensive? Why choose this method over a nonlinear control method (Lyapunov redesign, feedback linearization) ? Thanks for the video.
@StepanOzana
4 жыл бұрын
Theoretically, it is comparable in that way. Practically, there is a finite numbers of controllers because a fixed sample period is used (1ms or 2ms). You basically pre-compute controller K(t) for t=0:0.001:Tf for a given planned reference trajectory. In each point of the trajectory, nonlinear system is considered as LTV system. I used this method because it is really elegant. It allows you to use one controller both for swingup and stabilization, no switching (so the swingup is done in the closed-loop). Altogether it does not require much of computational performance, you can even use older RPi to run the algorithm. We use faster FPGA-based computer due to need to handle wireless data transfer and other stuff. BTW, the paper will be focused on the design for a single inverted pendulum, but the approach is the same for a triple one. I will write a comment here once the paper is published, expected publication is spring 2020 but you never can tall for sure until you have a hardcopy proof :-)
@Haellsigh
4 жыл бұрын
@@StepanOzana Thanks for the detailed answer!
@StepanOzana
4 жыл бұрын
The paper on LQR design is accepted and will be out in a few weeks. I will let you know. But I also have a new paper on trajectory planning for inverted pendulums is out: www.mdpi.com/2073-8994/12/5/792
What's the input for the computer? Is it visual, forces, somehing else? Could be said in the description but I don't know any of these abbreviations.
Very impressive! What happens if there is a large disturbance? Will it recover?
@StepanOzana
3 жыл бұрын
No. It will break the closed-loop control and will swing down uncontrolled.
this is very cool! how much more complex would a 2-axis version be to control?
@StepanOzana
3 жыл бұрын
This would become a robotic sea lion: www.kky.zcu.cz/cs/video-lachtan-2
How do you even program that Because it needs to get more and more aggressive as it gets closer to the sides and work it’s way back to the middle or else it won’t have room to counter balance but it can’t get too aggressive or else it’ll fall It’s like when I would balance a broom on my finger tip as a kid TIMES 2
😳😳 What kind of mathematics went into controlling the system so precisely when the Friction in pendulum is So low!!!!
@StepanOzana
2 жыл бұрын
Time-variant LQR does the trick.
Great!!