Model-based Control: Difference between revisions

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For a homogeneous, solid cuboid holds
For a homogeneous, solid cuboid holds


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


* https://en.wikipedia.org/wiki/Moment_of_inertia
* https://en.wikipedia.org/wiki/Moment_of_inertia
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!relative ratio
!relative ratio
|-  
|-  
| pitch || I &prop; 2.5^2 + 5.5^2 = 36.5 ||  1
| pitch || I &prop; 2.5<sup>2</sup> + 5.5<sup>2</sup> = 36.5 ||  1
|-  
|-  
| roll || I &prop; 5.5^2 + 9^2 = 111.25 ||  3.05
| roll || I &prop; 5.5<sup>2</sup> + 9<sup>2</sup> = 111.25 ||  3.05
|-  
|-  
| yaw || I &prop; 2.5^2 + 9^2 = 87.25 ||  2.39
| yaw || I &prop; 2.5<sup>2</sup> + 9<sup>2</sup> = 87.25 ||  2.39
|}
|}


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!relative ratio
!relative ratio
|-  
|-  
| pitch || I &prop; 2.5^2 + 4.5^2 = 26.5 ||  1
| pitch || I &prop; 2.5<sup>2</sup> + 4.5<sup>2</sup> = 26.5 ||  1
|-  
|-  
| roll || I &prop; 4.5^2 + 6.3^2 = 59.94 || 2.26
| roll || I &prop; 4.5<sup>2</sup> + 6.3<sup>2</sup> = 59.94 || 2.26
|-  
|-  
| yaw || I &prop; 2.5^2 + 6.3^2 = 45.94 ||  1.73
| yaw || I &prop; 2.5<sup>2</sup> + 6.3<sup>2</sup> = 45.94 ||  1.73
|}
|}


Line 97: Line 97:
!relative ratio
!relative ratio
|-  
|-  
| pitch || I &prop; 6^2 + 2^2 = 40 || 1
| pitch || I &prop; 6<sup>2</sup> + 2<sup>2</sup> = 40 || 1
|-  
|-  
| roll || I &prop; 2^2 + 3^2 = 13 ||  0.325
| roll || I &prop; 2<sup>2</sup> + 3<sup>2</sup> = 13 ||  0.325
|-  
|-  
| yaw || I &prop; 6^2 + 3^2 = 45 || 1.125
| yaw || I &prop; 6<sup>2</sup> + 3<sup>2</sup> = 45 || 1.125
|}
|}


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

Revision as of 19:17, 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.

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


The camera is described by the three main moments of inertia

  • Ipitch, Iroll, Iyaw

The roll arm is modeled with these moments of inertia

  • I2roll, I2yaw

and the yaw arm with

  • I3yaw


Ideal Camera Design

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

  • Iroll ≈ Iyaw
  • Ipitch << Iroll, Iyaw

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 ( a2 + b2 )

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

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

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