@ErezI
When it comes to comparing the quadratic curve fits, it is difficult to look at just the coefficients and compare them. If you have multiple tests, you should plot the quadratic plots on the same figure and see how repeatable they are. What may seem like a noticeable variation in the coefficients, could still result in curves that are very similar.
By the way, you should not just average values of a0, a1, and a2 to get a0_average, a1_average, and a2_average, as this will result in wrong curve. If you would like to find an average of all 4 runs, then you can just create a quadratic fit of all the points from the 4 data sets - that is the proper way to do it. However, if after plotting the 4 curves they look very similar, you can use any of the 4 individual fits. The PI (Proportional Integral) controller on the ESC will compensate for minor deviations.
The error you saw with params not being valid was due to the latest version of voxl-esc tools using new parameter structure. So the solution is (which is what you already figured out) to update the firmware and params to latest. This type of change does not happen too often. We will add this to documentation to make this clear.
Alex