Model-based Control: Difference between revisions
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The camera is described by the three principal moments of inertia | The camera is described by the three principal moments of inertia | ||
* I<sub>pitch</sub>, I<sub>roll</sub>, I<sub>yaw</sub> | * <i>I<sub>pitch</sub></i>, <i>I<sub>roll</sub></i>, <i>I<sub>yaw</sub></i> | ||
:[[File:Gimbal-model-camera-inertias.jpg|none|280px]] | |||
The roll arm is modeled with these moments of inertia | The roll arm is modeled with these moments of inertia | ||
* I<sup>(2)</sup><sub>roll</sub>, I<sup>(2)</sup><sub>yaw</sub> | * <i>I<sup>(2)</sup><sub>roll</sub></i>, <i>I<sup>(2)</sup><sub>yaw</sub></i> | ||
and the yaw arm with | and the yaw arm with | ||
* I<sup>(3)</sup><sub>yaw</sub> | * <i>I<sup>(3)</sup><sub>yaw</sub></i> | ||
In the GUI they are accessible as the {{PARAMNAME|T}} parameters. The model-based PID controller can also take into account different KV values of the pitch, roll and yaw motors via the {{PARAMNAME|K}} parameters. | In the GUI they are accessible as the {{PARAMNAME|T}} parameters. The model-based PID controller can also take into account different KV values of the pitch, roll and yaw motors via the {{PARAMNAME|K}} parameters. | ||
<div class="toclimit-2">__TOC__</div> | <div class="toclimit-2">__TOC__</div> | ||
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From the perspective of PID control and gimbal axis coupling, the camera should ideally have these properties: | From the perspective of PID control and gimbal axis coupling, the camera should ideally have these properties: | ||
* I<sub>roll</sub> ≈ I<sub>yaw</sub> | * <i>I<sub>roll</sub></i> ≈ <i>I<sub>yaw</sub></i> | ||
* I<sub>pitch</sub> ≈ I<sub>roll</sub>, I<sub>yaw</sub> or I<sub>pitch</sub> << I<sub>roll</sub>, I<sub>yaw</sub> | * <i>I<sub>pitch</sub></i> ≈ <i>I<sub>roll</sub></i>, <i>I<sub>yaw</sub></i> or <i>I<sub>pitch</sub></i> << <i>I<sub>roll</sub></i>, <i>I<sub>yaw</sub></i> | ||
The first condition is however more important than the second, and should be approached if possible. | The first condition is however more important than the second, and should be approached if possible. | ||
A similar condition I<sup>(2)</sup><sub>yaw</sub> ≈ I<sup>(2)</sup><sub>pitch</sub> would ideally be also fulfilled for the roll arm, which is however unrealistic in practical builds. | A similar condition <i>I<sup>(2)</sup><sub>yaw</sub></i> ≈ <i>I<sup>(2)</sup><sub>pitch</sub></i> would ideally be also fulfilled for the roll arm, which is however unrealistic in practical builds. | ||
= Moments of Inertia = | = Moments of Inertia = | ||
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For a homogeneous solid cuboid it holds | For a homogeneous solid cuboid it holds | ||
I = 1/12 M ( a<sup>2</sup> + b<sup>2</sup> ) | <i>I</i> = 1/12 <i>M</i> ( <i>a</i><sup>2</sup> + <i>b</i><sup>2</sup> ) | ||
Links: | |||
* https://en.wikipedia.org/wiki/Moment_of_inertia | * https://en.wikipedia.org/wiki/Moment_of_inertia | ||
* https://en.wikipedia.org/wiki/List_of_moments_of_inertia | * https://en.wikipedia.org/wiki/List_of_moments_of_inertia | ||
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!relative ratio | !relative ratio | ||
|- | |- | ||
| pitch || I ∝ 2.5<sup>2</sup> + 5.5<sup>2</sup> = 36.5 || 1 | | pitch || <i>I</i> ∝ 2.5<sup>2</sup> + 5.5<sup>2</sup> = 36.5 || 1 | ||
|- | |- | ||
| roll || I ∝ 5.5<sup>2</sup> + 9<sup>2</sup> = 111.25 || 3.05 | | roll || <i>I</i> ∝ 5.5<sup>2</sup> + 9<sup>2</sup> = 111.25 || 3.05 | ||
|- | |- | ||
| yaw || I ∝ 2.5<sup>2</sup> + 9<sup>2</sup> = 87.25 || 2.39 | | yaw || <i>I</i> ∝ 2.5<sup>2</sup> + 9<sup>2</sup> = 87.25 || 2.39 | ||
|} | |} | ||
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!relative ratio | !relative ratio | ||
|- | |- | ||
| pitch || I ∝ 2.5<sup>2</sup> + 4.5<sup>2</sup> = 26.5 || 1 | | pitch || <i>I</i> ∝ 2.5<sup>2</sup> + 4.5<sup>2</sup> = 26.5 || 1 | ||
|- | |- | ||
| roll || I ∝ 4.5<sup>2</sup> + 6.3<sup>2</sup> = 59.94 || 2.26 | | roll || <i>I</i> ∝ 4.5<sup>2</sup> + 6.3<sup>2</sup> = 59.94 || 2.26 | ||
|- | |- | ||
| yaw || I ∝ 2.5<sup>2</sup> + 6.3<sup>2</sup> = 45.94 || 1.73 | | yaw || <i>I</i> ∝ 2.5<sup>2</sup> + 6.3<sup>2</sup> = 45.94 || 1.73 | ||
|} | |} | ||
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!relative ratio | !relative ratio | ||
|- | |- | ||
| pitch || I ∝ 6<sup>2</sup> + 2<sup>2</sup> = 40 || 1 | | pitch || <i>I</i> ∝ 6<sup>2</sup> + 2<sup>2</sup> = 40 || 1 | ||
|- | |- | ||
| roll || I ∝ 2<sup>2</sup> + 3<sup>2</sup> = 13 || 0.325 | | roll || <i>I</i> ∝ 2<sup>2</sup> + 3<sup>2</sup> = 13 || 0.325 | ||
|- | |- | ||
| yaw || I ∝ 6<sup>2</sup> + 3<sup>2</sup> = 45 || 1.125 | | yaw || <i>I</i> ∝ 6<sup>2</sup> + 3<sup>2</sup> = 45 || 1.125 | ||
|} | |} | ||
As evidenced by these estimates, the shape of the Mobius camera is not ideal from a gimbal control perspective, and this camera is thus more difficult to stabilize than others. | As evidenced by these estimates, the shape of the Mobius camera is not ideal from a gimbal control perspective, and this camera is thus more difficult to stabilize than others. | ||
Revision as of 10:54, 1 October 2019
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
- Ipitch, Iroll, Iyaw
The roll arm is modeled with these moments of inertia
- I(2)roll, I(2)yaw
and the yaw arm with
- I(3)yaw
In the GUI they are accessible as the T parameters. 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:
- Iroll ≈ Iyaw
- Ipitch ≈ Iroll, Iyaw or Ipitch << Iroll, Iyaw
The first condition is however more important than the second, and should be approached if possible.
A similar condition I(2)yaw ≈ I(2)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 )
Links:
- 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 perspective, and this camera is thus more difficult to stabilize than others.