Drone Control and the Complementary Filter

Find all of my other videos here: engineeringmedia.com/videos
Get the map of control theory: www.redbubble.com/shop/ap/550...
Download eBook on the fundamentals of control theory (in progress): engineeringmedia.com
Let's talk about the complementary filter and how we can use it to estimate the attitude of a drone using an IMU. It is such a dead simple filter, which is a good reason to learn it, but it’s also practical because it produces nice results when blending measurements from two different sensors.
Check out my videos on Drone Simulation and Control: bit.ly/2OnlW5m
Website - www.engineeringmedia.com
Patreon - / briandouglas
Twitter - @brianbdouglas
Email - [e-mail]
Errata:
~2:23 - I state that the accelerometer is measuring the acceleration due to gravity, when in fact it's measuring the acceleration caused by the normal force from the ground. So it's directly up and the exact opposite direction of gravity! Whereas, an accelerometer in free fall would measure no acceleration at all even though it would be accelerating. So the "convert to angle" block would also take care of this sign flip.
Don't forget to subscribe!
If you have any questions on it leave them in the comment section below or on Twitter and I'll try my best to answer them.
I will be loading a new video whenever I can and welcome suggestions for new topics. Please leave a comment or question below and I will do my best to address it. Thanks for watching!

[@masroor20]

Brian please also give comprehensive lecture on kalman filter.

[@GoxXxLB]

kzbin.info/aero/PLn8PRpmsu08pzi6EMiYnR-076Mh-q3tWr Its not Brian but you might find it useful.

[@iliasilisparrow]

YES, please.

[@sedjaiabdelbasset1566]

+1

[@manuel56354]

Yes please!!

[@brianballewsr20]

Dido

[@DaeHan2321]

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!

[@AI-ro2bm]

THE KING IS BACK!!!

[@CharlesStaffeld]

excellent blend of theory and practical application. more of this!

[@peterfistin8584]

Excellent explanation. I am happy to see how you havd managed to summarise the topic and show a practical (discrete) implementation

[@chrismusix5669]

"I like the direction you're going with this!" ~DSF "Thanks for the complement!" ~Drone

[@johncgibson4720]

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.

[@AfdhalAtiffTan]

A very clear explanation, thank you, Brian!

[@dasuberedward]

Glad to see these again!

[@meelimorenoo]

Just in time.... I am currently working on my digital control project, this is perfect ... Thanks a lot... Keep going!!!! :) :)

[@power-max]

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]

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]

For some difficulties, Kalman filter is discontinued in Betaflight and CC3D. Most drone development favors the traditional Fourier spectrum analysis.

[@grapix1184]

Finally a comprehensive explanation, thank you very much !

[@toniprahasto1137]

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!

[@wataruimahayashi5937]

Thank you for your comprehensive explanation about complementary filter

[@manuel56354]

Awesome video, thank you! I will use this shortly!

[@10e999]

Always a pleasure to watch your content Brain, even on the MATLAB channel ! ;) Btw, how's your book ? Have a great day !

[@beto5adani]

Thank you man it is so understanble , it'll very well see a implemantation in some embbeed system like arduino or other

[@Mainstream818]

Dude you are awesome. control theory in school is so bad at applying real world examples. Definitely subscribing and getting your ebook

[@Fintan2578]

I had applied this filter for three years in my projects,but I ultimately figure it out .thank u!

[@tuha3524]

very useful. Long for further lectures!

[@harshitsoni2718]

what an explanation 😍🤘🤘now i have very good feeling about my drone project

[@destructionindustries7485]

Absolutely excellent visualization on minute 4. Thanks

[@eng-emre-avci]

This just saved our lives. Thanks a lot.

[@tseckwr3783]

thanks for the explanation and excellent video, Dr. Brian

[@MhmBura]

Brilliant as ever! lecturers be taking notes!

[@evandromaf]

This is the guy. Thank so much professor

[@PANKAJSHARMA-eu7hz]

i love it.. great work Brian

[@yogeshkurade5720]

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).

[@TheGhost13X]

Hi Brian! We are waiting for the next video! :D

[@wailkerjack7979]

It doesn't get any more intuitive than that，thanks!!

[@harshdobariya1030]

Best explanation on complementary filter. Thanks

[@fauzansyauqi2815]

Thank you so much sir, your video really help me to understand how to complementary works.

[@Aniruddhabiswas94]

I am really greatful to have you as my Guru....Happy Gurupurnima🙏

[@jbenitez3669]

excellent explanation!

[@realcygnus]

superb content

[@TheAbhro]

It will be great if you make a video on kalman filter. Thanks for all the videos

[@hp90582]

Kral geri döndü.

[@neilchen2570]

Great lecture! Really appreciate your work 🙌🙌🙌 May I ask which software you use for making this video?

[@monirmahbub3838]

A lecture on sensor using something like the Kalman filter would be very useful :)

[@meysamsaeedian4735]

Thanks for your interesting video! Could you please create a lecture regarding model predictive control systems?

[@harrypotter1155]

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

[@njdk7796]

it would be great if you implement such algorithm in a code, matlab perhaps as in the past :)

[@vivekjebaraj]

Hi brian, I'm eagerly waiting for the 3rd part in drone simulation. Is there any videos coming up with the continuation?

[@BrianBDouglas]

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.

[@Xylos144]

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]

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!

[@jonask4650]

Brian, i love you

[@MusaYmc]

thanks a bunch

[@AllElectronicsGr]

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]

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.

[@AliAli-vo3fp]

great thank you

[@Bruder_chill]

awesome

[@zakariafadli9383]

Great video as used to.

[@tomonsterheard]

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.

[@mindthomas]

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]

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.

[@CuriousHuman_Channel]

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.

[@yousefedris3701]

Awesome

[@raychou8719]

if only roll can be calculated? Or pitch and yaw can be obtained in same way? Thanks for sharing the video.

[@hungtuan9347]

Your videos are great. I wonder which software you used to design the lectures? Appreciate if you could share it.

[@BrianBDouglas]

Check it out here! engineeringmedia.com/my-setup

[@suryaj2810]

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]

Vinayak Dan nope.

[@martinrasmussen5898]

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.

[@robokishan]

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

[@lejF88]

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]

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.

[@AliHassan-xt1xb]

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

[@taufikrahmadani8252]

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 :)

[@xXKM4UXx]

is there an implementation of this on simulink?

[@solitary062ak]

If compare to UKF, which one is better for aerial navigation system?

[@lamiafarah506]

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

[@samrajanr4908]

Can u plse make a video on uav collision avoidance simulink model

[@tobilgs]

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...

[@hhiii7277]

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.

[@ASDFAHED1985]

Please what is the program used to prepare that nice video?

[@ruturajyellurkar9588]

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?

[@sebve9399]

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?

[@akshayrao1484]

can someone explain what is the meaning of stable over long term in accelerometer?

[@mohammedmasiullah5201]

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.

[@mnada72]

Is there a continuation for this topic?

[@debasismohapatra627]

Sir please make vehicle control videos. Thanks

[@abhijitmajee6754]

Why did you stop uploading videos? Please do some complex control sys projects of possible. From scratch with conception, design and modelling.

[@signature445]

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.

[@kushalgowdan6906]

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???

[@ashikkhan2840]

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]

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]

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]

@@liobundury thanks !! yeah i understand

[@ndeligiannis]

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???

[@prithiviraj6853]

bro if i implemented to mobile sensors means which method is more accurate ?

[@nirbhay_raghav]

If only my control systems faculty was like him.

[@berkayylmaz2527]

i dont understood that 1/z ? Is it equals to 1/DeltaTime? so frequent? thx:)

[@phillipmaser132]

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.

[@gabrielogungbure5785]

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

[@RickJankowski92]

Is it possible to get your e book FUNDAMENTALS OF CONTROL THEORY for free ?

[@TimeFadesMemoryLasts]

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.

[@i3130002]

I cannot get how can you use accelerameter of a moving object with this!!

[@rasmusjensen9035]

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]

Unfortunately I cannot understand this passage either. I would also be very happy about an explanation Brian.

[@jonask4650]

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!

[@zdenekhurak]

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.

[@jeffersonpimentamelo]

Omg, he don't left us!!

[@AV1461]

Give us homework! Or some suggestion of how to further put the topic into practice.

[@user-yv6oq2cp2g]

what does 1/Z mean ?

[@mnada72]

one sample delay

[@manuel56354]

This is where Brian talks about how to implement a z-domain transfer function in code: kzbin.info/www/bejne/pJzUZYqhjZx2fLc

[@robokishan]

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]

9:10 What is 1/z? Or what is that z?

[@leonardoflss]

In discrete systems instead of Laplace's domain we use the Z-transform, so 1/z is a delay in discrete time

[@jacksonsmith2955]

@@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]

@@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]

@@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]

@@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...

[@itsover6668]

Are you the real batman?

[@donmed2]

could you speak slowly nixt time please

[@shiqiai2881]

great explanation!