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.
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.
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).
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
> 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.
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?
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[ 5.5 ms ] story [ 45.2 ms ] threadIn 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.
Which I think is a good thing :)
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
Having familiarity with all 3, as soon as I read this sentence I knew it was all down hill for me.