# A Multi-Step CNN-Based Estimation of Aircraft Landing Gear Angles

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## Abstract

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## 1. Introduction

- Object extraction and normalization modules are added to adapt to the change in aircraft target scale. The target detection module extracts the area of the aircraft, and the normalization module normalizes the area size. Then, the normalized area is inputted into the subsequent vector field regression network, voting for the key points of the fuselage. The normalization module could effectively avoid the error of the vector field network, which is caused by dramatic changes in the input image. The target detection module adopts an efficient YOLO-V4 model.
- The aircraft is divided into the landing gear and the fuselage to detect key points. The landing gears are movable, and the shape of the aircraft without the landing gear changes very little and can be regarded as a rigid body. Therefore, the aircraft as a whole can be divided into the landing gear and the two parts of the fuselage. Aircraft key points consist of landing gear key points and fuselage key points. The target detection module obtains the key points of the landing gears. The key points of the fuselage are acquired by a robust pixel-level voting network, which requires the model to be a rigid body. In addition, the distance-based coefficients are multiplied by the loss function to optimize the vector field;
- To resolve the difficulty of obtaining depth information, we propose a method to directly calculate the absolute angle between the landing gears and fuselage plane by using key positions in 2D images according to the constraints of aircraft, omitting the step of regaining 3D spatial coordinates;
- This article contributes a synthetic aircraft dataset of different camera views containing landing gears with different angles to verify the algorithm performance.

## 2. Related Works

## 3. Proposed Methods

#### 3.1. Norm Module

#### 3.2. Vector Field Loss Function Optimization

#### 3.3. CAL Module

- Find the right triangle between the landing gear and fuselage shown in Figure 3b. Because the aircraft’s vertical tail is perpendicular to the fuselage plane, in Figure 3a, the line that is parallel to the aircraft’s vertical line is perpendicular to the fuselage plane. Considering the rotating direction of the landing gear, the vertical foot of the nose landing gear is on the fuselage line, and the vertical foot of the rear landing gear is on the wing belonging to the fuselage plane.
- Given the aircraft model, the true length in the triangle is calculated from the ratio of the length of each side to the length of the fuselage, wing, and tail respectively.
- Then the sines and cosines is used to calculate the angle $\theta $ between the landing gears and fuselage plane.

#### 3.4. Synthetic Aircraft Datasets

## 4. Experiments

#### 4.1. Angle Measurement Results

#### 4.2. Normalized Module

#### 4.3. K Loss Function

#### 4.4. Experiment on Different Datasets

#### 4.5. Robustness

#### 4.6. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Principle of the angle estimation. Key points are abbreviated to kpts. We use YOLO-V4 to get two types of detection boxes, including the landing gear tires and the aircraft. Then the norm module gets the normalized central points of landing gear tires. At the same time, the norm module extracts the overall image inside the aircraft detection frame and normalizes the image to the PVNet network. In the PVNet network, vector fields are regressed to vote for the fuselage key points. Finally, CAL module is used to compute the landing gear angles according to key points and the aircraft model.

**Figure 2.**(

**a**) is the visual loss value, the higher the brightness, the greater the loss value. (

**b**) is the weight value K based on the distance between the pixel and key point when $\lambda $ = 5. The x-coordinate is the distance and the y-coordinate is the value of K.

**Figure 3.**(

**a**) is the mask image of the aircraft. The solid line is the key points of the fuselage, wing, and tail, the red dot is the key point of the landing gear, the pink dot is the connection point of the landing gear and the fuselage, the green dotted line is the straight line of the connection point parallel to the fuselage and wing, and the red dotted line is the straight line of the key point of the landing gear parallel to the vertical tail. (

**b**) is the triangle formed by the landing gear key points, connecting points, and dotted line intersection.

**Figure 4.**(

**a**) is the original image in the dataset. (

**b**) is the mask image, and (

**c**) is the mask image displaying labeled key points. The dataset contains about 40,000 images.

**Figure 5.**The figures above show the input data form of the vector field network model made by the dataset. In the top line, the first picture from left to right is the original image. The second picture in the top line is the mask with the labeled information of the displayed key points. The rest of the pictures are pixel vector field labels belonging to corresponding key points.

**Figure 6.**The input is the real pixel coordinates of key points, and the output is the curve of error threshold and the angle accuracy. (

**a**) is the accuracy of the different methods about the rear landing gear, and (

**b**) is the accuracy of the different methods about the nose landing gear.

**Figure 7.**The proposed method works on datasets; predicts key points in two parts, calculates angle with no depth information.

**Figure 9.**Parts of output images. The predicted angles are magenta font at the top of the graph. The number after the letter forward is for the nose landing gear angle. The number after the letter left is for the left rear landing gear angle, and the number after the letter right is for the right rear landing gear angle when facing the front. The number after the letter airframe represents the angle between the vertical tail and the airframe. The number after the letter wing indicates the angle between the vertical tail and the wing.

**Table 1.**The mean error of angles and accuracy rate with different measurement methods when threshold equals 10.

Method | The Nose Error | The Rear Error | Mean Angle Error | The Nose Accuracy | The Rear Accuracy |
---|---|---|---|---|---|

Sine | 18.7 | 12.4 | 12.2 | 33.8% | 52.5% |

Cosine | 15.8 | 10.2 | 11.8 | 71.2% | 77.5% |

Sine and cosine | 16.6 | 11.2 | 11.6 | 45.8% | 62.0% |

Combined method | 11.5 | 8.7 | 9.1 | 68.9% | 77.8% |

**Table 2.**The mean error and accuracy rate table with or without normalization. F means false, while T indicates true.

Normalize | The Nose Angle | The Rear Angle | Mean Angle Error | Kpt Fuselage | Kpt Landing Gear | The Nose Accuracy | The Rear Accuracy |
---|---|---|---|---|---|---|---|

F | 30.6 | 16.6 | 17.7 | 10.9 | 3.8 | 27.9% | 58.1% |

T | 11.5 | 8.7 | 9.1 | 3.6 | 3.7 | 68.7% | 78.0% |

**Table 3.**This is a mean error and accuracy rate table with different loss functions. F means false, while T means true.

K Loss | The Nose Angle | The Rear Angle | Mean Angle Error | Kpt Fuselage | Kpt Landing Gear | The Nose Accuracy | The Rear Accuracy |
---|---|---|---|---|---|---|---|

F | 11.8 | 8.1 | 8.9 | 4.5 | 3.8 | 66.7% | 79.9% |

T | 11.9 | 7.9 | 8.8 | 3.3 | 3.7 | 67.4% | 81.0% |

Datasets | The Nose Angle | The Rear Angle | Mean Angle Error | Kpt Fuselage | Kpt Landing Gear | The Nose Accuracy | The Rear Accuracy |
---|---|---|---|---|---|---|---|

Total | 18.3 | 8 | 11.7 | 5 | 4.6 | 49.0% | 82.2% |

Parallel | 11.5 | 8.7 | 9.1 | 3.6 | 3.7 | 68.9% | 77.8% |

Undercart down | 12.0 | 8.5 | 10.2 | 2.8 | 3.0 | 70.4% | 77.1% |

Within 10 degrees | 11.5 | 5.1 | 9.6 | 5 | 4.6 | 66.0% | 92.1% |

All meet | 8.3 | 4.8 | 7.2 | 3 | 3.1 | 81.9% | 91.9% |

Datasets | The Nose Angle | The Rear Angle | Mean Angle Error | Kpt Fuselage | Kpt Landing Gear | The Nose Accuracy | The Rear Accuracy |
---|---|---|---|---|---|---|---|

Overall | 64.0 | 59.9 | 60.8 | 54.8 | 13.5 | 9.4% | 5.3% |

Varying light | 6.7 | 4.5 | 4.6 | 3.7 | 3.3 | 84.8% | 91.4% |

Low resolution | 9.1 | 5.2 | 5.6 | 1.9 | 1.4 | 64.9% | 88.6% |

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**MDPI and ACS Style**

Li, F.; Wu, Z.; Li, J.; Lai, Z.; Zhao, B.; Min, C.
A Multi-Step CNN-Based Estimation of Aircraft Landing Gear Angles. *Sensors* **2021**, *21*, 8440.
https://doi.org/10.3390/s21248440

**AMA Style**

Li F, Wu Z, Li J, Lai Z, Zhao B, Min C.
A Multi-Step CNN-Based Estimation of Aircraft Landing Gear Angles. *Sensors*. 2021; 21(24):8440.
https://doi.org/10.3390/s21248440

**Chicago/Turabian Style**

Li, Fuyang, Zhiguo Wu, Jingyu Li, Zhitong Lai, Botong Zhao, and Chen Min.
2021. "A Multi-Step CNN-Based Estimation of Aircraft Landing Gear Angles" *Sensors* 21, no. 24: 8440.
https://doi.org/10.3390/s21248440