Drone Physics

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• Hacker News
• I would have liked to understand this, but the math behind it is overkill. One may need a PhD in aerospace to digest it.
  by huqedato
• Hello, blog author here. I agree the math appears overkill. I wrote this as a learning aid for myself with the benefit of hindsight of having worked with some drone sims. I wanted to dispel any doubt in my mind that I could derive drone physics from basic principles, instead of copy-pasting state equations. I went further and tried to motivate transport theorem, rotational analog of F=ma etc from scratch.

  In summary: I take F=ma and extend it for rotational motion. (1) Calculating linear motion when the vehicle containing sensors is rotating. (2) Calculating rotation of the vehicle itself due to thrust/yaw force acting about its center of mass.

  I'll echo what the other commenter said: this is no way PhD math. It may appear so - but I'm only being verbose with simpler concepts like cross products and rotation matrices.

  by hazrmard
• Yes and no. The math here is useful, albeit not required. It is not specialized PhD material; it's linear algebra. (And not the abstract quantum mechanics/chem kind!)

  What I mean by not required is, I've written drone firmware and didn't directly use this; the core can be done with a PID for rate controls (Compare measured rate along each axis with commanded; nudge motor power proportional to the diff), and commanding attitudes can be done with fundamental quaternion operations, as a slower outer loop.

  I would skip the Tait-Bryan stuff in the article, in favor of pure quaternions. Actually, I'm kind of floored the word "quaternion" doesn't appear in the article.

  by the__alchemist
• Previously: https://news.ycombinator.com/item?id=48781539
  by tolerance
• I wrote something similar (though admittedly more in depth) some time ago: https://www.cggonzalez.com/blog/index.html
  by cgg1
• I was looking for an explanation of how you deal with the fact that quad rotors are under-actuated, and therefore you lack the complete control authority to do any arbitrary motion in space. So path planning has to take this into account, but how is this described?
  by Isamu
• Pitch and roll are coupled to fwd/back and Left/right respectively. So, you can make it move however you want, but its attitude can't be set independently of its motion. That's a simplification. One consequence is, for example, if you have a fixed camera mounted fwd etc, the angle it looks will correlate with the speed you have it move.

  If you are just concerned with moving the center of mass to different locations in space, or have it travel with a specific velocity, you're fine.

  This sort of limitation is common vehicles of all sorts; having 4 independent DOF is above average!

  by the__alchemist
• This feels very https://ciechanow.ski/

  Which I think is a good thing :)

  by too_root
• It's my blog. Bartosz Ciechanowski's work was my inspiration!
  by hazrmard
• I studied this subject when I was building FPV sim from scratch. I noticed that yaw action is often misunderstood, falsely believing that it's caused by a change in angular momentum (think reaction wheels).

  There is a good SE answer about deriving net torques given each props' thrust force in less PhD language than this article: https://drones.stackexchange.com/a/416/11402

  If anyone is interested in tackling UAV simulation, make sure to check out this prop/motor performance database, helped me a lot building a virtual drone with realistic properties (mainly motor thrust & torque): https://database.tytorobotics.com/tests

  by ivanjermakov
• Why does four seem optimal? Why not three or five? or eight?
  by fragmede
• If you're into simulators then you may try applying forces directly rather than integrating ODE. If sim's has tiny numerical instabilities or integrator schedule is wrong the whole thing gonna fall spectacularly. The interest is with running large-scale simulations where along with ODE you need to handle collisions and deformations. The best one currently is MuJoCo.
  by cwiz
• > This article describes drone physics. Audience should have familiarity with introductory linear algebra, introductory calculus, and introductory classical mechanics.

  Having familiarity with all 3, as soon as I read this sentence I knew it was all down hill for me.

  by katzgrau
• Going down hill is easy, right?
  by dmd