Revision as of 19:16, 6 September 2019

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.

The camera is described by the three main moments of inertia

The roll arm is modeled with these moments of inertia

and the yaw arm with

Ideal Camera Design

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

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

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 ( a² + b^2 )

width	height	length
2.5 cm	5.5 cm	9 cm

axis	approximate moment of inertia	relative ratio
pitch	I ∝ 2.5^2 + 5.5^2 = 36.5	1
roll	I ∝ 5.5^2 + 9^2 = 111.25	3.05
yaw	I ∝ 2.5^2 + 9^2 = 87.25	2.39

width	height	length
2.5 cm	4.5 cm	6.3 cm

axis	approximate moment of inertia	relative ratio
pitch	I ∝ 2.5^2 + 4.5^2 = 26.5	1
roll	I ∝ 4.5^2 + 6.3^2 = 59.94	2.26
yaw	I ∝ 2.5^2 + 6.3^2 = 45.94	1.73

width	height	length
6 cm	2 cm	3 cm

axis	approximate moment of inertia	relative ratio
pitch	I ∝ 6^2 + 2^2 = 40	1
roll	I ∝ 2^2 + 3^2 = 13	0.325
yaw	I ∝ 6^2 + 3^2 = 45	1.125

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

@@ Line 6: / Line 6: @@
 The camera is described by the three main moments of inertia
-* I_pitch, I_roll, I_yaw
+* I<sub>pitch</sub>, I<sub>roll</sub>, I<sub>yaw</sub>
 The roll arm is modeled with these moments of inertia
-* I2_roll, I2_yaw
+* I2<sub>roll</sub>, I2<sub>yaw</sub>
 and the yaw arm with
-* I3_yaw
+* I3<sub>yaw</sub>
 __NOTOC__
@@ Line 32: / Line 33: @@
 For a homogeneous, solid cuboid holds
-I = 1/12 M ( a^2 + b^2 )
+I = 1/12 M ( a<sup>2</sup> + b^2 )
 * https://en.wikipedia.org/wiki/Moment_of_inertia