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 those of the roll and yaw arms. For the underlying theory see Camera Gimbals: A Robotics Approach.

The camera is described by the three principal moments of inertia

• I_pitch, I_roll, I_yaw

The roll arm is modeled with these moments of inertia

• I2_roll, I2_yaw

and the yaw arm with

• I3_yaw

The model-based PID controller can also take into account different KV values of the pitch, roll and yaw motors via the K parameters.

Ideal Camera Design

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

• I_roll ≈ I_yaw
• I_pitch ≈ I_roll, I_yaw or I_pitch << I_roll, I_yaw

The first condition is however more important than the second, and should be approached if possible.

A similar condition I2_yaw ≈ I2_pitch would ideally be also fulfilled for the roll arm, which is however unrealistic in practical builds.

Moments of Inertia

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

For a homogeneous solid cuboid it holds

I = 1/12 M ( a² + b² )

• 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 ∝ 2.52 + 5.52 = 36.5	1
roll	I ∝ 5.52 + 92 = 111.25	3.05
yaw	I ∝ 2.52 + 92 = 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 ∝ 2.52 + 4.52 = 26.5	1
roll	I ∝ 4.52 + 6.32 = 59.94	2.26
yaw	I ∝ 2.52 + 6.32 = 45.94	1.73

Camera Mobius

width	height	length
6 cm	2 cm	3 cm

axis	approximate moment of inertia	relative ratio
pitch	I ∝ 62 + 22 = 40	1
roll	I ∝ 22 + 32 = 13	0.325
yaw	I ∝ 62 + 32 = 45	1.125

As evidenced by these estimates, the shape of the Mobius camera is not ideal from a gimbal control perpsective, and this camera is thus more difficult to stabilize than others.