Model-based Control

Moments of Inertia

https://en.wikipedia.org/wiki/Moment_of_inertia

https://en.wikipedia.org/wiki/List_of_moments_of_inertia

Ideal:

I_roll \approx I_yaw, I_pitch << I_roll, I_yaw

Interestingly, a sphere is not idael from the perspective of PID control/axis coupling.

Solid cuboid

I = 1/12 M ( a^2 + b^2 )

Camera Panasonic:

width	height	length
2.5 cm	5.5 cm	9 cm

pitch: I \propto 2.5^2 + 5.5^2 = 36.5 -> 1

roll: I \propto 5.5^2 + 9^2 = 111.25 -> 3.05

yaw: I \propto 2.5^2 + 9^2 = 87.25 -> 2.39

Camera GoPro Hero5:

width	height	length
2.5 cm	4.5 cm	6.3 cm

pitch: I \propto 2.5^2 + 4.5^2 = 26.5 -> 1

roll: I \propto 4.5^2 + 6.3^2 = 59.94 -> 2.26

yaw: I \propto 2.5^2 + 6.3^2 = 45.94 -> 1.73

Camera Mobius:

width	height	length
6 cm	2 cm	3 cm

pitch: I \propto 6^2 + 2^2 = 40 -> 1

roll: I \propto 2^2 + 3^2 = 13 -> 0.325

yaw: I \propto 6^2 + 3^2 = 45 -> 1.125