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Assuming ideal environment/hardware flying conditions, is it possible that the autopilot loses the control of the quadcopter? What is the maximum tilt in roll and pitch that is allowed for the quadcopter to be under the control? How to drive that from the quadcopter dynamics model?

I do not have a strong mathematical/physics background. I had followed this report to understand the quadcopter dynamics. https://andrew.gibiansky.com/downloads/pdf/Quadcopter%20Dynamics,%20Simulation,%20and%20Control.pdf

Any insights would be appreciated!

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I suppose it depends on what you mean by "under control". If you mean the point where the flight controller will stop being able to correct for the error, then I'm not sure that it's well defined. It will depend a lot on how sophisticated the flight control software is and how much time it has to correct(how long it will take for it to crash).

If you mean the maximum roll/pitch that can be maintained while flying, then that will also vary widely based on weight and thrust. If the craft tilts more than 90 degrees then there will be no downward thrust and it will lose altitude, but the angle at which it can maintain its altitude will vary drastically. A lightweight high thrust racing drone might be able to maintain more than 45 degrees without dropping, whereas a larger and heavier craft might not be able to go past 20 degrees. If you know the maximum thrust then you can figure out how much downward thrust it will produce at a given angle using the equation:

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If the downward thrust is greater than or equal to the weight of your craft then it will be able to maintain it's altitude.

I hope that helps even if I can't give a precise answer.

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