Drone Control and the Complementary Filter

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Brian Douglas

Brian Douglas

Күн бұрын

Пікірлер: 132
@masroor20
@masroor20 6 жыл бұрын
Brian please also give comprehensive lecture on kalman filter.
@GoxXxLB
@GoxXxLB 6 жыл бұрын
kzbin.info/aero/PLn8PRpmsu08pzi6EMiYnR-076Mh-q3tWr Its not Brian but you might find it useful.
@iliasilisparrow
@iliasilisparrow 6 жыл бұрын
YES, please.
@sedjaiabdelbasset1566
@sedjaiabdelbasset1566 6 жыл бұрын
+1
@manuel_youtube_ttt
@manuel_youtube_ttt 6 жыл бұрын
Yes please!!
@brianballewsr20
@brianballewsr20 6 жыл бұрын
Dido
@Aniruddhabiswas94
@Aniruddhabiswas94 3 жыл бұрын
I am really greatful to have you as my Guru....Happy Gurupurnima🙏
@johncgibson4720
@johncgibson4720 2 жыл бұрын
This episode really hit a home run for me. I am FPV flying CC3D/Betaflight helicopter for terminal speed cliff diving in my channel. And this complementary filter is unique to CC3D that people coming from Betaflight didn't know before and didn't know how to configure it in CC3D. I am one of those people.
@toniprahasto1137
@toniprahasto1137 6 ай бұрын
Fantastic video! Your clear explanations and detailed examples made the complex topic of complimentary filters incredibly accessible. Your ability to break down the math and theory into understandable segments is truly impressive. Keep up the great work-looking forward to more insightful content from you!
@power-max
@power-max 6 жыл бұрын
Kalman flter would be great! Once I figure out Field Oriented Control for BLDC motors, I think this understanding of the Complementary filter is going to help me make a really nice camera gimbal! (Apparently knowing "which way is up" is a much harder problem then I thought!)
@SamB-lc9cn
@SamB-lc9cn 6 жыл бұрын
I did something similar a short while ago, it takes a while to get your head around everything (especially if its new to you) but its super satisfying once you've made something with it. Good luck!
@johncgibson4720
@johncgibson4720 2 жыл бұрын
For some difficulties, Kalman filter is discontinued in Betaflight and CC3D. Most drone development favors the traditional Fourier spectrum analysis.
@AI-ro2bm
@AI-ro2bm 6 жыл бұрын
THE KING IS BACK!!!
@peterfistin8584
@peterfistin8584 Жыл бұрын
Excellent explanation. I am happy to see how you havd managed to summarise the topic and show a practical (discrete) implementation
@dagrapix
@dagrapix 3 жыл бұрын
Finally a comprehensive explanation, thank you very much !
@wataruimahayashi5937
@wataruimahayashi5937 4 жыл бұрын
Thank you for your comprehensive explanation about complementary filter
@DaeHan2321
@DaeHan2321 6 жыл бұрын
Brian, glad to see you're still posting videos. They've helped tremendously to further understand the topics. I'd like to suggest video lectures on State Space. I found this to be very interesting in my course. The ability to go from LODE - TF - SS is beneficial. Thanks!
@chrismusix5669
@chrismusix5669 5 жыл бұрын
"I like the direction you're going with this!" ~DSF "Thanks for the complement!" ~Drone
@destructionindustries7485
@destructionindustries7485 2 жыл бұрын
Absolutely excellent visualization on minute 4. Thanks
@Xylos144
@Xylos144 6 жыл бұрын
One slight correction (that doesn't impact the point of the video) - a stationary accelerator will see a positive acceleration equal to gravity AWAY from the ground, not towards it, because it is a body force. The accelerometer really can't measure gravity. It's measuring a normal acceleration that counteracts gravity when it's not in free-fall. Great videos as always Brian.
@BrianBDouglas
@BrianBDouglas 6 жыл бұрын
Oh, you are correct and I led folks a bit astray in this video! Thanks for the clarification on the video and I'll add that to the errata list so it, hopefully, won't trip anyone up in the future. Thanks!
@Mainstream818
@Mainstream818 2 жыл бұрын
Dude you are awesome. control theory in school is so bad at applying real world examples. Definitely subscribing and getting your ebook
@harshdobariya1030
@harshdobariya1030 2 жыл бұрын
Best explanation on complementary filter. Thanks
@CharlesStaffeld
@CharlesStaffeld 6 жыл бұрын
excellent blend of theory and practical application. more of this!
@Fintan2578
@Fintan2578 2 жыл бұрын
I had applied this filter for three years in my projects,but I ultimately figure it out .thank u!
@eng-emre-avci
@eng-emre-avci 5 жыл бұрын
This just saved our lives. Thanks a lot.
@evandromaf
@evandromaf 6 жыл бұрын
This is the guy. Thank so much professor
@MhmBura
@MhmBura 5 жыл бұрын
Brilliant as ever! lecturers be taking notes!
@tseckwr3783
@tseckwr3783 Жыл бұрын
thanks for the explanation and excellent video, Dr. Brian
@fauzansyauqi2815
@fauzansyauqi2815 9 ай бұрын
Thank you so much sir, your video really help me to understand how to complementary works.
@manuel_youtube_ttt
@manuel_youtube_ttt 6 жыл бұрын
Awesome video, thank you! I will use this shortly!
@harshitsoni2718
@harshitsoni2718 4 жыл бұрын
what an explanation 😍🤘🤘now i have very good feeling about my drone project
@dasuberedward
@dasuberedward 6 жыл бұрын
Glad to see these again!
@tuha3524
@tuha3524 6 жыл бұрын
very useful. Long for further lectures!
@meelimorenoo
@meelimorenoo 6 жыл бұрын
Just in time.... I am currently working on my digital control project, this is perfect ... Thanks a lot... Keep going!!!! :) :)
@wailkerjack7979
@wailkerjack7979 4 жыл бұрын
It doesn't get any more intuitive than that,thanks!!
@monirmahbub3838
@monirmahbub3838 6 жыл бұрын
A lecture on sensor using something like the Kalman filter would be very useful :)
@AfdhalAtiffTan
@AfdhalAtiffTan 6 жыл бұрын
A very clear explanation, thank you, Brian!
@beto5adani
@beto5adani 4 жыл бұрын
Thank you man it is so understanble , it'll very well see a implemantation in some embbeed system like arduino or other
@10e999
@10e999 6 жыл бұрын
Always a pleasure to watch your content Brain, even on the MATLAB channel ! ;) Btw, how's your book ? Have a great day !
@mindthomas
@mindthomas 5 жыл бұрын
Please note that an accelerometer can not be used to determine which direction is down when the drone is in flight, since gravity will not affect the accelerometer in flight, since gravity is cancelled by the propellers/thrust to make the drone fly and hover. When the drone is flying it is therefore WRONG to assume that the accelerometer can be used to determine roll angle from the assumption of it measuring the gravity direction. A lot of people use the accelerometer and complementary incorrectly on drones due to this misunderstanding. What happens when the accelerometer is used in a complementary filter as shown in this video, is basically that you end up with a dead-reckoning based estimate, since your accelerometer measurements (in the local drone frame) will always point in the direction of the thrusters plus the actual acceleration of the drone. This makes the estimate very vulnerable to the gyro bias resulting in a drifting estimate. What saves you then would be any type of position feedback, e.g. GPS or optical flow, since this makes the gyro bias observable. But without position feedback you could rather just fly your drone with a gyroscope only! For more information, feel free to read Chapter 2.1 and Appendix B of this rapport: tkjelectronics.dk/uploads/autonomous_indoor_navigation_for_drones_using_vision-based_guidance.pdf
@michaeljohnward632
@michaeljohnward632 3 жыл бұрын
Thank you for this reply. I have been going around in circles in my head trying to get this straight after reading about the pendulum rocket fallacy. An accelerometer in freefall will not feel gravity, so why would it do so when the thrust is switched on? It only feels the direction of thrust.
@dungtran-kj2nz
@dungtran-kj2nz 12 күн бұрын
@@michaeljohnward632 @mindthomas Thanks for sharing the information!
@TheAbhro
@TheAbhro 5 жыл бұрын
It will be great if you make a video on kalman filter. Thanks for all the videos
@TheGhost13X
@TheGhost13X 5 жыл бұрын
Hi Brian! We are waiting for the next video! :D
@jbenitez3669
@jbenitez3669 6 жыл бұрын
excellent explanation!
@vivekjebaraj
@vivekjebaraj 6 жыл бұрын
Hi brian, I'm eagerly waiting for the 3rd part in drone simulation. Is there any videos coming up with the continuation?
@BrianBDouglas
@BrianBDouglas 6 жыл бұрын
vivek jebaraj thanks! There will be five videos total for the drone series. The third will post today and the next two will post each week after.
@yogeshkurade5720
@yogeshkurade5720 6 жыл бұрын
Thank you, Sir! Can you please make a video on how to model physical world Problems? (Such as writing equations & signal flow diagrams for Simulink).
@hp90582
@hp90582 6 жыл бұрын
Kral geri döndü.
@CuriousHuman_Channel
@CuriousHuman_Channel 4 жыл бұрын
Why don't professors explain this like you did. I am trying to figure out how to build flight controller by myself. Thanks for amazing explanation.
@PANKAJSHARMA-eu7hz
@PANKAJSHARMA-eu7hz 4 жыл бұрын
i love it.. great work Brian
@realcygnus
@realcygnus 6 жыл бұрын
superb content
@njdk7796
@njdk7796 6 жыл бұрын
it would be great if you implement such algorithm in a code, matlab perhaps as in the past :)
@hungtuan9347
@hungtuan9347 4 жыл бұрын
Your videos are great. I wonder which software you used to design the lectures? Appreciate if you could share it.
@BrianBDouglas
@BrianBDouglas 4 жыл бұрын
Check it out here! engineeringmedia.com/my-setup
@meysamsaeedian4735
@meysamsaeedian4735 4 жыл бұрын
Thanks for your interesting video! Could you please create a lecture regarding model predictive control systems?
@martinrasmussen5898
@martinrasmussen5898 6 жыл бұрын
What does the calculation for delta angle look like? I'm using your guide for a university project, and for delta angle i have "angle velocity measure - last angle velocity measure", but it doesn't seem to give the correct filteret output.
@suryaj2810
@suryaj2810 6 жыл бұрын
Great video. I wonder if same concept could be applied to yaw angle estimation with a magnetometer and a gyroscope. Is there any logical mistake in such a filter?
@suryaj2810
@suryaj2810 4 жыл бұрын
Vinayak Dan nope.
@hhiii7277
@hhiii7277 5 жыл бұрын
I think this filter only works when no large side acceleration present. Also, let's assume z is the up/down direction (where the gravity direction is), and assuming x and y are the two horizontal directions. i don't think this filter works for x and y direction estimations.
@abhijitmajee6754
@abhijitmajee6754 5 жыл бұрын
Why did you stop uploading videos? Please do some complex control sys projects of possible. From scratch with conception, design and modelling.
@ASDFAHED1985
@ASDFAHED1985 2 жыл бұрын
Please what is the program used to prepare that nice video?
@haniemaleki88
@haniemaleki88 3 ай бұрын
I recently started working with RL in navigating robots in a flow. I started working on double gyre flow as a benchmark and applied 5 RL methods to it. but the problem is that I need to compare which method could help the robot in terms of using less energy but I don't know which feature of the flow can talk about using energy. could you help me figure it out?
@harrypotter1155
@harrypotter1155 5 жыл бұрын
Hi Brian, Do you have any recommendation on further reading about filter design whether it is in continuous time or discrete time? I am currently trying to design 2nd-order low-pass filter to be applied on lidar sensor for my drone altitude control Thanks in advance
@ruturajyellurkar9588
@ruturajyellurkar9588 11 ай бұрын
Is it possible to implement the same filter for getting altitude from a barometer and an accelerometer? Since we have to double integrate the accelerometer values, there's gonna be more errors, so what are the filter gains you would suggest?
@zakariafadli9383
@zakariafadli9383 6 жыл бұрын
Great video as used to.
@nirbhay_raghav
@nirbhay_raghav 5 жыл бұрын
If only my control systems faculty was like him.
@raychou8719
@raychou8719 5 жыл бұрын
if only roll can be calculated? Or pitch and yaw can be obtained in same way? Thanks for sharing the video.
@neilchen2570
@neilchen2570 5 жыл бұрын
Great lecture! Really appreciate your work 🙌🙌🙌 May I ask which software you use for making this video?
@lejF88
@lejF88 6 жыл бұрын
I love your videos. Although, I would like to see more actual examples of how to implement the theory in practice. In this video you write the low pass filter in the z domain. How would I write that in arduino code for example?
@BrianBDouglas
@BrianBDouglas 6 жыл бұрын
That's a good suggestion. I'm working on a band stop / notch filter video right now and I'll append a section at the end that shows how to go from z-domain to arduino code.
@tobilgs
@tobilgs 4 жыл бұрын
If I want to calculate the orientation of a model rocket, should I relay in the gyro completly? I think there will never be an accurate accelerometer reading at all during the short time of flight so I wonder if a complementary filter would make the results even worse in this case...
@kushalgowdan6906
@kushalgowdan6906 4 жыл бұрын
Hey Brian, at 8:32 in the block diagram you have multiplied the gyro angle by 0.98 and the accelerometer angle by 0.02, doesn't it mean angle computed by complimentary filter should be close to what the gyro reads. But your java script animation shows the complete opposite , isn't it???
@mnada72
@mnada72 3 жыл бұрын
Is there a continuation for this topic?
@sebve9399
@sebve9399 3 жыл бұрын
I have a question: If for example I couple gyro_y (MPU9250) to pitch. Then what happens when roll is 90 degrees? Because at this point, the rotation on gyro_y should change the yaw, not the pitch. Another problem is, if the sensor is upside down, that means that the gyro_z has to be -gyro_z. How do I deal with those problems?
@mohammedmasiullah5201
@mohammedmasiullah5201 3 жыл бұрын
Sir the explanation is really well, but I am confused between one concept In the discreet implementation what is delta t and 1/z blocks. I under stand for example if my sampling frequency is 200HZ then delta t is 1/200 but what is 1/z . I would be really gratefull for any help.
@rasmusjensen9035
@rasmusjensen9035 5 жыл бұрын
There seems to be a error in the math shown at 9:36 or is it just me? The second equation does not give the third if moving the last part og it to the right of the summation point and hence, wouldn't give a discrete low pass filter. The third equation, if solving for the single "Roll angle", would then be: [roll angle] = [0.02*(accel angle)+0.98*(gyro angle* Delta t)] + [roll angle]*(0.98/z) or am i wrong Brian ?
@jonask4650
@jonask4650 4 жыл бұрын
Unfortunately I cannot understand this passage either. I would also be very happy about an explanation Brian.
@jonask4650
@jonask4650 4 жыл бұрын
Nevermind, i got it... You have to factor out the roll angle on the left side of the equation to roll angle * (1- (0.98/z)) and after that you can divide the equation by (1- (0.98/z))... that results in the third equation of the video... thank you for the great video Brian!
@tomonsterheard
@tomonsterheard 5 жыл бұрын
watched a few of your videos. this is pretty impressive. are you in academia? what are your credentials if you don't mind me asking.
@zdenekhurak
@zdenekhurak Жыл бұрын
When the drone is sitting on the ground, the accelerometer does NOT measure the "acceleration due to gravity" as stated at about 2:28 and drawn with the red arrow pointing DOWN (suggesting a positive value in that coordinate system). Accelerometers measure something called proper acceleration, which is the acceleration relative to the free fall. Loosely speaking, they measure all but gravitational acceleration... When placed on a surface with the positive direction of the accelerometer pointing up, accelerometer reads g(=9.8...). If the positive axis of the accelerometer is oriented towards the ground (as sketched in the video with the blue arrow), it should read -g. Besides "theoretical" discussions of the concepts such as proper acceleration elsewhere, this is also what data sheets for IMUs such as MPU-9250 (referred to in other videos) state.
@TimeFadesMemoryLasts
@TimeFadesMemoryLasts 3 жыл бұрын
You could add that this only works if the drone hovers steadily. The accelerometer will read all kinds of the drone's acceleration if it changes its movement. The acceleration vector won't point straight down towards earth.
@lamiafarah506
@lamiafarah506 3 жыл бұрын
Hi, um novice in filtering. i wanted your advice that, for gyro drift which filter is the best?kalman or complimentary? the gyro drift mostly happens when we repeats going forward and backward
@solitary062ak
@solitary062ak 5 жыл бұрын
If compare to UKF, which one is better for aerial navigation system?
@taufikrahmadani8252
@taufikrahmadani8252 5 жыл бұрын
Thank sir!, but how to calculate the gains of gyro and accelero that in video was determined the Kg = 0.98 and Ka = 0.02, was it just trial and error or any method to calculate the gains? Thanks :)
@MusaYmc
@MusaYmc 4 жыл бұрын
thanks a bunch
@AliHassan-xt1xb
@AliHassan-xt1xb 6 жыл бұрын
Hi Brian., This question might be unrelated to this video but can you make a video on how does control theory/systems relate with AI and Machine learning? I am interested in both of these fields and want to do a PhD in something involving both of them. but i dont know the inter-relation of these both. Thnaks
@berkayylmaz2527
@berkayylmaz2527 3 жыл бұрын
i dont understood that 1/z ? Is it equals to 1/DeltaTime? so frequent? thx:)
@Bruder_chill
@Bruder_chill 6 жыл бұрын
awesome
@prithiviraj6853
@prithiviraj6853 Жыл бұрын
bro if i implemented to mobile sensors means which method is more accurate ?
@AliAli-vo3fp
@AliAli-vo3fp 4 жыл бұрын
great thank you
@gabrielogungbure5785
@gabrielogungbure5785 Жыл бұрын
Hi Brian. I am working on a project using Matlab/Simulink aerospace blockset. i want to modify the example on Parrot mambo drone for implementation on the physical drone. please i need help urgently
@robokishan
@robokishan 6 жыл бұрын
please explain accelerometer and gps sensor fusion. i am trying to use integration of linear acceleration from accelerometer and then convert it into displacement and then i am trying to filter it using kalman and add gps input. but tje first step isn't working accurately. how can i get linear displacement i mean travelled distance using accelerometer. Sensor : MPU6050 Mcu : Arduino
@ashikkhan2840
@ashikkhan2840 6 жыл бұрын
thanks Brian Douglas it's just awesome !! you have done superb job ,keep it up but one thing i don't understand 1/(1--0.98/z) what is value of z, can i write 1/(1--0.98/1) instead of it???clarify pls
@liobundury
@liobundury 6 жыл бұрын
I have the same question. How is 1/Z delays, one step? I feel like is very simple and I will feel dump when we get the answer.
@liobundury
@liobundury 6 жыл бұрын
Ok, so I did some googling, (please accept I might be wrong in this). No you cannot just write 1/(1--0.98/1), although you might get something that looks right but it is not. Z is not a value but a transform, from discrete, to time domain, (transform similar to Laplace transforms). In this case 1/Z is holding the value for the last unit step of the roll angle. It's like a memory block that remember it's last iteration. So in the part of the equation that you see (0.98/Z), that's 0.98 *1/Z or (0.98 * the value of the roll angle from the Previous time step). Hope it helps.
@ashikkhan2840
@ashikkhan2840 6 жыл бұрын
@@liobundury thanks !! yeah i understand
@phillipmaser132
@phillipmaser132 5 жыл бұрын
I have two actuator problem with 3 sensors which I believe would be 3 states. I am looking to use PID and state space control this problem. I don't think I need PID if using SS design model. I am trying to get a hold of state space. most models I build fail. I need to go back to basics and build from this. State Space is used because of 3 inputs and two outputs. The simple system reads setpoint of pressure and has two pumps using two different control actions for a pump. One pump is fast and other is fine adjust. I have no models for this. Still working through this not sure how to model pumps and motors yet? System time response is slow so ramp and soak then one op in a PID hold value at temperature. It works but not very accurate.
@ndeligiannis
@ndeligiannis 5 жыл бұрын
On 9:25 shouldn't we have New_Roll_angle and Old_Roll_Angle? the Roll_angle / z isnt it the previous estimated? And what is z???
@signature445
@signature445 4 жыл бұрын
Hi Brian , I am sending data from arduino to MATLAB it is like Ax,Ay,Az,Gx,Gy,Gz (Comma after numbers),when i check how much samples are coming (The above set) i found that its around 216.But now i am little bit confused that whether i need to take the sample rate of each (Ax/Ay/Az..) be 216 samples/sec or 216*6 samples/sec or 216 *11 samples/sec(This includes comma also). because i need to pass Ax ...through Low pass filter there i need sample period.
@jonask4650
@jonask4650 3 жыл бұрын
Brian, i love you
@samrajanr4908
@samrajanr4908 5 жыл бұрын
Can u plse make a video on uav collision avoidance simulink model
@RickJankowski92
@RickJankowski92 5 жыл бұрын
Is it possible to get your e book FUNDAMENTALS OF CONTROL THEORY for free ?
@akshayrao1484
@akshayrao1484 3 жыл бұрын
can someone explain what is the meaning of stable over long term in accelerometer?
@jeffersonpimentamelo
@jeffersonpimentamelo 6 жыл бұрын
Omg, he don't left us!!
@xXKM4UXx
@xXKM4UXx 4 жыл бұрын
is there an implementation of this on simulink?
@AllElectronicsGr
@AllElectronicsGr 6 жыл бұрын
Can we say that the complementary filter is a simple kalman filter, where the output angle compose the filter state and the complentary constants wheights the state uptade? Because its very clear that we are using a 0.02 and 0.98 confiability. In the kalman this ratio would be updated by the sensors uncertanty.
@EMRLaboratories
@EMRLaboratories 3 жыл бұрын
I would say 'not really'. The Kalman filter has the ability to also track sensor bias/error, provides the ability to be informed by the system model (ie the sensor location on a vehicle can increase the accuracy of the estimate - if you put the accelerometer away from the center of rotation you can increase certainty of the estimate due to roll induced accelerations for example), finally the covariance matrix can tell you if the estimate can even be trusted at all. Kalman filter = very powerful.
@debasismohapatra627
@debasismohapatra627 5 жыл бұрын
Sir please make vehicle control videos. Thanks
@i3130002
@i3130002 5 жыл бұрын
I cannot get how can you use accelerameter of a moving object with this!!
@yousefedris3701
@yousefedris3701 4 жыл бұрын
Awesome
@林冠岑-k8e
@林冠岑-k8e 3 жыл бұрын
what does 1/Z mean ?
@mnada72
@mnada72 3 жыл бұрын
one sample delay
@AV1461
@AV1461 6 жыл бұрын
Give us homework! Or some suggestion of how to further put the topic into practice.
@robokishan
@robokishan 6 жыл бұрын
and yeah don't do tutorial on just theory of kalman filter do the detailed tutorial on gps and accelerometer sensor fusion using kalman because there are plenty of tutorial on kalman filter but none on them are on gps and accelerometer
@Pianogamerer
@Pianogamerer 5 жыл бұрын
9:10 What is 1/z? Or what is that z?
@leonardoflss
@leonardoflss 4 жыл бұрын
In discrete systems instead of Laplace's domain we use the Z-transform, so 1/z is a delay in discrete time
@jacksonsmith2955
@jacksonsmith2955 10 ай бұрын
@@leonardoflss Would it be possible to get a brief elaboration on what exactly it means to divide a value by Z? Does it have units? I looked at the wikipedia page for the Z-transform and understood absolutely nothing, a bit lost here.
@leonardoflss
@leonardoflss 10 ай бұрын
@@jacksonsmith2955 I recommend to check the book Feedback Control of Dynamic Systems, by G. Franklin, J. Powell, and A. Emami-Naeini. In specific the 8th chapter: "Digital Control". Plus, the own Brain's playlist, "Discrete Control" is really good to help you out.
@leonardoflss
@leonardoflss 10 ай бұрын
@@jacksonsmith2955 I was so concerned to point out references that I forget to actually answer your question, tldr: "divide by z" is, in a practical sense, use the previous sample of a signal. Then, z^-1 is the last sample, z^-2 is the second to last, and so on and on... On discrete control we should think in terms of computing/measurement cycles, a.k.a loops. The data from the previous loop are at the k-1 index of the signals "arrays", and the data at the running cycle are at the k-th index.
@leonardoflss
@leonardoflss 10 ай бұрын
@@jacksonsmith2955 the signals does have unit. Taking the previous sample of a signal is just a time wise operation, so the unit is preserved. For example, a velocity signal at time k, in m/s, is m/s whatever is the index k, k-1, k-2...
@manuel_youtube_ttt
@manuel_youtube_ttt 4 жыл бұрын
This is where Brian talks about how to implement a z-domain transfer function in code: kzbin.info/www/bejne/pJzUZYqhjZx2fLc
@itsover6668
@itsover6668 5 жыл бұрын
Are you the real batman?
@donmed2
@donmed2 5 жыл бұрын
could you speak slowly nixt time please
@shiqiai2881
@shiqiai2881 6 жыл бұрын
great explanation!
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