Revision as of 13:23, 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 the moments of inertia

The yaw arm is modeled with the moment of inertia

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.

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 )

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

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

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.

@@ Line 1: / Line 1: @@
-Moments of Inertia
+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.
-https://en.wikipedia.org/wiki/Moment_of_inertia
+For the underlying theory see [http://www.olliw.eu/2018/camera-gimbals-a-robotics-approach/ Camera Gimbals: A Robotics Approach].
-https://en.wikipedia.org/wiki/List_of_moments_of_inertia
+The camera is described by the three main moments of inertia
+* I_pitch, I_roll, I_yaw
-Solid cuboid
+The roll arm is modeled with the moments of inertia
-I = 1/12 M ( a^2 + b^2 )
+* I2_roll, I2_yaw
+The yaw arm is modeled with the moment of inertia
+* I3_yaw
+= Ideal Camera Design =
-=== Ideal ===
+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 idael from the perspective of PID control/axis coupling.
+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 ===