Model-based Control

The STorM32's model-based gimbal control can take into account, to a certain extend, the moments of inertia of the camera and the roll and yaw arms.

For the underlying theory see Camera Gimbals: A Robotics Approach.

The camera is described by the three main moments of inertia

• I_pitch, I_roll, I_yaw

The roll arm is modeled with the moments of inertia

• I2_roll, I2_yaw

The yaw arm is modeled with the moment of inertia

• I3_yaw

Ideal Camera Design

From the perspective of PID control and axis coupling, the camera should ideally have these properties:

I_roll \approx I_yaw, I_pitch << I_roll, I_yaw

Interestingly, a sphere is not ideal, maybe in contrast to common believe.

Moments of Inertia

Estimates for the relative ratios of the moments of inertia of the camera can be obtained by approximating by a cuboid.

For a homogeneous, solid cuboid holds

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

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

Camera Panasonic

width	height	length
2.5 cm	5.5 cm	9 cm

axis	approximate moment of inertia	relative ratio
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

axis	approximate moment of inertia	relative ratio
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

axis	approximate moment of inertia	relative ratio
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

The Mobius camera style is not ideal, and thus more difficult to stabilize.