Computing Euler Angles: The Euler Kinematical Equations and Poisson’s Kinematical Equations

[@reesetaylor3506]

AE 512: I appreciate the physical demonstrations of how to interpret the difference between the rate gyro output and the euler angles, really helped solidify my understanding

[@ShivaShakerii]

AA 516: Excellent presentation, Professor Lum! I was particularly impressed by the way you derived the block diagrams of the processes. Great job!

[@ChristopherLum]

Glad it was helpful, let me know how the other videos go.

[@WalkingDeaDJ]

Jason-AE512: That simulink is good way to practice.

[@milesrobertroane955]

AA516: Great video as always! I love watching Mathematica chow down on some horrible equations that I would've gasped at when I was a freshman.

[@ChristopherLum]

Quick correction, in the future can you change from AA519 to AA516 so my scraper finds these comments, thanks.

[@milesrobertroane955]

@@ChristopherLum Oops! I'll edit it

[@BryanLiberman]

AE512: Hey Dr. Lum, thanks for making this video! Content like this can get very complicated, and you presented it in a way that made it (comparatively) easy to follow!

[@jordantriolo571]

AE512: Great video! I appreciated the Simulink portion, letting us see how the equations could actually be used.

[@ChristopherLum]

Glad it was helpful!

[@benjaminshipp9050]

You're an outstanding educator! I really appreciate your level of effort and care you put into ALL of your videos. Not only do you have a clear grasp on this tough subject, but you are able to communicate it with clarity and ease. You have a rare gift Sir!

[@ChristopherLum]

Ben, thanks for the kind words. I'm glad it was helpful. Please let me know what you think of any of the other videos as well. Thanks for watching!

[@benjaminshipp9050]

@@ChristopherLum I watched nearly all of your videos for control theory over the summer when I was taking Intro. to Auto Controls, and this semester I'm in Adv. Flight Mechanics and your playlist on that has been instrumental as well as my understanding of Simulink and how to utilize it! Still lots to learn, but your videos have been amazing! I did have a few questions regarding the Euler angle (Phi) checks on the output of the Phi_dot integrator or the output of the Poisson or Quat rotation matrix 'C' Phi extraction. I put a 'MATLAB function' block which inputs Phi and outputs, with 'if' statements that should be correcting the rotations. Linked are a few videos I exported (thank you for the 3D animation videos (discovered those late)) that display my problem. Two show 3D plots based on point vectors multiplied by the rotation matrix (good-ish ones) and two depict the 3D Animation of the Euler angles (don't work). Suggestions kzbin.info/www/bejne/iqqpqJt_eaqIrrc kzbin.info/www/bejne/bInTc2RqZZ53grc kzbin.info/www/bejne/nX25ZYV_fbmkbNk kzbin.info/www/bejne/l3ycZ2eFg9Bqb7c Thank you again for all of your videos!!! Benjamin

[@benjaminshipp9050]

@@ChristopherLum I got FlightGear installed and it TOTALLY WORKED!!! I don't know why the same Euler angles were not displaying correctly in MATLAB, but FlightGear managed to display it as expected! Thank you sooooo much for allllllllllll of your wonder help! You can't imagine how many days I've wasted trying to figure out where my understanding was broken, but it appears it may just have been the software! Thank you again! FlightGear video of the same Intermediate Axes Theorem simulation (finally looks right!!!): kzbin.info/www/bejne/b3O0lpp3g65le9U

[@sunnysarkar7643]

AE 512: Doing the simulink with us is extremely helpful and useful. I am glad that is being included.

[@prabhjeetsingharora]

It is totally worth spending time refreshing the basics of Flight mechanics taught in the BEST possible manner. Each day I am going through at least one video of this channel, which has greatly enhanced my knowledge. Once again, thankyou Dr. Lum for creating such a beautiful content.

[@ChristopherLum]

Hi, Thanks, if you have questions or would like to discuss any of these concepts further, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@yaffetbedru6612]

AA516: I enjoyed the examples and the you bringing physical hardware to show during the lecture. Really ties the ends together.

[@newschool050]

I spent weeks searching for how to convert IMU values to Euler and all I got was bunch of formulas and no explanation. Especially thank you for explaining difference between IMU values and Euler rate and Euler angles.

[@davidtelgen8114]

AE512: Great video with the simulink examples!

[@ChristopherLum]

Glad you liked it!

[@sethwhittington28]

AE512: the possibility to have an error occur in the model of the aircraft reaches certain attitudes makes me nervous. This is the thing I will always forget to take into account! 😮

[@kktousif]

Excellent lectures Mr. Christopher. Indeed easy to follow and fall in love with the subject.

[@ChristopherLum]

Hi Tousif, Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@charlesperry7300]

A very effective lecture. The explanation and the presentation of the relavant eauations are in sync. Unlike other video s on the same subject ,lecturers keep on talking without pointing to with eauations he is talking about. Many eauation and figures are.dumped all over the slide in one slide.

[@ChristopherLum]

Thanks for reaching out. If you have questions or would like to request a video, please consider supporting the channel via Patreon at www.patreon.com/christopherwlum. I interact personally with Patrons at all levels. Thanks for watching!

[@NicAqueous]

By far the best explanation on this topic. Great work!

[@ChristopherLum]

Hi Nic, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@AlexandraSurprise]

AA516: Allie S, I used Simulink this summer for creating a control and dynamics model of an aircraft. I may need to take another look at my calculations after watching this. Something may be amiss...

[@radoraan5272]

same for me but i'm working with a rocket 😅

[@mehmetsahin8261]

Great job my dear teacher😊 Your videos are excellent to give theorical background and real life implementation. This is the education system i admire. I also have a question. When i read gyro datas which is angular velocity of my rigid body respect to body frame, instead of to product with H matrix, i integrated it. The result confuses me. Is it directly euler angle or any trash set of angles.

[@ChristopherLum]

Hi, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@edwardmau5877]

AE 512 Thanks for the Simulink demonstration.

[@abdulrhmanseed]

You are a legend! I was searching for the derivation for a couple of hours. It is really not intuitive and there are a lot of notations, which sometimes make things missy. Thanks again.

[@rowellcastro2683]

AA516: Hello Professor! Another great lecture! You explained very well how a flight controller could take in IMU data expressed from the body frame and convert it to readable data expressed in the reference frame that we see in a telemetry screen from GUI software such as Ardupilot. Thank you very much.

[@matthewbajamundi8774]

AE 512 I found the Simulink portion very insightful to how the Kinematical equations can be implemented using actual data from a sensor.

[@rahulbball9395]

Great explanation! I am taking my qualifying exam in flight dynamics, and your videos are very helpful!

[@yuthika_sagarage]

you saved the day, i was struggling to understand this derivation

[@ChristopherLum]

Glad it was helpful, thanks for watching (there are a few other related videos on this topic)

[@ramenegg2016]

I could understand the stuff with this video clearly, which I have struggled with it multiple days.

[@geetbhatia204]

All your lectures are awesome and you are a excellent tutor. Thanks for providing all this high quality content without any cost. Can you please make videos on mechanics of stabilization of payloads, for example gimbal, in UAVs. Thank you so much. You are a gem.

[@dariusm_]

I love your videos! This helped me design my Kalman filter to track orientation for my senior project

[@yaswanth6329]

Hii Dr. Lum, excellent video I was looking for this kind of video from many days and understandstood most part of it but I had a doubt😢 at 46:02, so first we do a roll about x axis which make the body frame z axis into the board and then x and y axis in the board plane now by applying some yaw rate(imu data) and then we transform it, we see that it is pitch rate, we see for this angle (60 degree example one ) we should have rotated about the new y axis (in the board plane) but in video you rotated it about the old y axis (pointing out of the plane) can I why this is the case

[@SayedTorak]

AE512: I could be wrong but I think the label for the middle matrix should be C2/1 rather than C1/2. Time stamp 8:55 Edit: I see you fixed it later in the video. Great video professor Lum.

[@ChristopherLum]

You are totally correct, nice catch!

[@PatrickGalvin519]

AA 516: Nice, clear explanations and derivations-especially on the block diagrams and Simulink demos. Also, cool drone setup! Has it evolved at all since the filming of this video?

[@boeing797screamliner]

AA516: I'm very new to Simulink, and this lecture along with your Simulink series has been a great way to get into it

[@bwsensing5553]

i，，，see our IMU ! Great lesson! thank you, Christopher! so professional !

[@wiloberlies9598]

Oh this is so cool. Thank you Dr Lum.

[@sianhoan833]

AA516: I appreciated the visualization of the angles in the example, it gets confusing with so many symbols. It's been a while since I've looked at Simulink, and I'll definitely have to watch your videos for review.

[@ChristopherLum]

Let me know if you have any questions on simulink and I can go over it during office hours

[@aimeepak717]

AE512: Is there a simple way to correct that 2pi wrapping that happens with the Poisson method for psi?

[@ChristopherLum]

Matlab has a function called 'unwrap' that might be helpful.

[@grucha456]

Isn't output matrix from yaw, pitch, roll sequence (in this case our matrix P at 38:19) is different for each sequence? If yes, we can't use this one in practical application, right? (since we can use different rotation sequences)

[@ChristopherLum]

Hi John, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@serajsersawi5786]

this is ridiculously helpful !!! thanks a million

[@ChristopherLum]

Glad it was helpful. There are other similar videos on the channel (including one on quaternions). I hoe to see you at another video soon, thanks for watching!

[@ToanLuu158]

AE512: This remind me the joke Why don’t Euler and Poisson play hide and seek together? Because no matter where Euler hides, Poisson can always find him using his equations.

[@REN-fr2sm]

I remember some programme use quaternion instead of matrix to solve euler angle, is it possible in future make an episode to explain how does it work? Btw, your video is very clear and helpful thanks for your effort

[@ChristopherLum]

You are correct, you can use quaternions. In fact, I just released a video on this topic at kzbin.info/www/bejne/b2mwl5hji8uapZI. Please let me know what you think, thanks for watching!

[@alinematheus3644]

thank you for your explanation! very clear! :)

[@karthikmurthy2511]

Great Video. Thanks for sharing...

[@aaronwickenhagen6236]

AA 516: I thought the Simulink examples in this lecture were extremely helpful, both to introduce using Simulink but also to visually explain concepts from the lecture (That drone ground control setup is also very cool).

[@petermay6090]

AA516: Intuitive and easy to follow! Are the Euler kinematical equations almost never used then?

[@bsgove]

AE512: It's amazing how many ways there are to approach the fundamental problem here.

[@shavykashyap]

AA 516 Very Good Lecture. Thank you

[@abobakersharfi9722]

Hi U R good explainer thx for all the But i may miss this abou H matrix can i implement magnetometer value extend of gairo value ? And thx

[@willpope3151]

[AA516]: Interesting derivation to get all the rates into the body frame. You mentioned your IMU used rate gyros, is there a reason it doesn't use an accelerometer to determine the attitude?

[@ChristopherLum]

Will, good question. Accelerometers measure translational acceleration, not angular rates. You could use an accelerometer if the vehicle was not moving (in fact some wind tunnel models use an accelerometer to measure the pitch angle) but these are only valid for static cases.

[@Po-ChihHuang]

AA516: very good lecture. Po

[@EomjiKim]

AA 516: Thank you for giving me an answer of my curiosity. I was always wondering of the reasons that helicopters motion changes more than I expected whenever I control, but through this video, I got some ideas. I have one question which can be very basic. Why is the numerical integration expressed as 1/s in the block diagram?

[@ChristopherLum]

The Laplace transform of an integration operator is 1/s

[@ChristopherLum]

In case it is helpful, here are all the Flight Mechanics videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrEx3A6W94sQGClk6Q4YCg-h. You can support this channel via Patreon at www.patreon.com/christopherwlum or by clicking the 'THANKS' button underneath the video. Please let me know what you think in the comments. Thanks for watching!

[@olivergriffiths1996]

Christopher Lum fantastic series! Thank you so much

[@deepbluesee2213]

how can I find the "gyroData.mat" and slx files? Thank you

[@deepbluesee2213]

@@mirkomizzoni413 no

[@nihalsingh6419]

Awesome series sir

[@kennethwilsey6260]

AA516 How would we deal with the wrap around from atand2 in the psi angle for Poisson's Kinematical Equations? Thanks Dr. Lum!

[@ChristopherLum]

Hi Kenneth, can you elaborate? Wraparound is a big pain in the neck for a lot of applications and I want to make sure I understand your question.

[@kennethwilsey6260]

@@ChristopherLum At the end of the video, the graphs compare Poisson's and Euler Kinematical equation outputs, but the yaw angles between the two methods don't align likely due to the atan2 computation in Poisson's method. Is the way to deal with this as simple as adding in a factor of pi?

[@ChristopherLum]

@@kennethwilsey6260 Ah, I see. Yes, you can add 2*pi if you want the graphs to match up but really, it shouldn't matter as the only way that the yaw angle is used is as an argument to a cos or sin function which do not care if the yaw angle is wrapped around or not. In short, you can usually use a wrapped or unwrapped version of the yaw angle is it usually doesn't matter.

[@AliRaza19052]

great video, thanks

[@ChristopherLum]

Glad you liked it, thanks for watching!

[@hasanhorata8381]

AA 516 - Hi Dr. Lum, I am still kind of confused by what you mean by "yaw" rate and such with the p,q, r, and "yaw rate" with phi_dot, theta_dot, and psi_dot. What is the difference between the two?

[@ChristopherLum]

Hasan, the difference is quantified by the H(Phi) matrix. Often pilots refer to pitch rate (q) as the same thing as theta_dot but these are different quantities. Please remind me at office hours and we can chat.

[@jonathanalvarez3875]

Great vid! I liked and subscribed, but maybe can you include the Rate Gyro data file in the references so that those who want to see their models work in simulink are able to? Thanks! Wish I had you as a professor

[@Kumky605]

AA516: Thought this was very engaging

[@xxroco0418xx]

Could you please upload the Gyrodata.mat

[@ChristopherLum]

Hi Raul, If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris

[@princekeoki4603]

AA516 : I am a bit confused on how Omega was derived for Poissons kinematical equations

[@jalenreed5204]

where can i find the quaternions video?

[@jalenreed5204]

nevermind

[@alexzhen179]

AA 516: Isn't the Omega matrix in the Poisson's equation the cross product matrix of (p,q,r)?

[@prasadvaidya9563]

Are the kinametical equations for calculating rate of change of Euler Angles implemented inside the IMUs like in mpu6050/9250 ??? Cause for calculating the RPY(roll,pitch,yaw) it only requires to integrate the reading over time... kindly correct me if I am wrong..

[@Colin_Baxter_UW]

AA516: Is the term 'yaw' derived from the longer expression 'yeehaw?'

[@손민혁-x3v]

How to calculate Euler angle rate in 3-1-3 rotation? i already understand about 3-2-1 rotation

[@peterwoo2489]

You are AWESOME !!! 😂😂😂

[@ChristopherLum]

Hi Peter, thanks for the kind words. There are other similar videos on the channels (for example showing how to do the same thing but use quaternions). If you look at the pinned comment, there is a playlist with the videos. Please let me know what you think of these as well. Thanks for watching!

[@deepbluesee2213]

how can I find the "gyroData.mat" and slx files? Thank you

[@AndersonYuan-j7g]

AA 516: Celeste Yuan (Late due to name discrepancies discussed)

[@nihalsingh6419]

Sir please provide that GyroData.mat file

[@kaikim8402]

NOICE ONE

[@timproby7624]

[AE 512] UAV control station in a pelican box... how do you ever have time to sleep?

[@ojasvikamboj6083]

A A 516: Ojasvi Kamboj

[@edengebretsadik7793]

AE512

[@ibrahimallafi1460]

Hi prof, if you don't mind could you send me your email I have some questions about gyro and modeling ? Thank you