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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 ...

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What you describe is probably due to cosine losses. Namely, when you pitch or roll your thrust vector points away from the vertical direction and thus not completely compensating gravity anymore. One way to compensate for this would be to scale your thrust by dividing by it by the cosine of angle of your thrust vector with the vertical direction.

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Extending the previous answer which describes how to compute a minimum-jerk trajectory given a consistent distance coordinate system. A simple way to do this is to treat the first coordinate as your origin then convert each other GPS point to meter distances from your first coordinate using one of the latitude and longitude equations here

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As reported for example in https://robotics.stackexchange.com/a/21571/6941, a minimum-jerk trajectory in one dimension is coded with respect to time $t$ as: $$x(t) = x_i + (x_f-x_i) \cdot \left( 10\left(\frac{t}{t_f}\right)^3 -15\left(\frac{t}{t_f}\right)^4 +6\left(\frac{t}{t_f}\right)^5\right),$$ where $t_f$ is the final time ($2\, \text{s}$ in your case),...

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We can solve this problem by using MATLAB and specifically by applying the partial fraction expansion by means of the function residue. The MATLAB code below [r, p] = residue([20 100], [1 13.5 41 80 100]); syms s; F1 = r(1) / (s - p(1)); F2 = r(2) / (s - p(2)); F3 = r(3) / (s - p(3)); F4 = r(4) / (s - p(4)); F34 = (2*real(r(3))*s - 2*real(r(3))*real(p(3)) -...

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You can operate the quadcopter with a poorly tuned attitude rate PID, log relevant quantities, build a model from the data, and finally use the model to tune the PID iteratively. Suppose that such an inner PID delivers voltage commands to the propellers. You could instruct the quadcopter to safely perform a bunch of maneuvers and at the same time log/acquire ...

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