Fixed-Wing UAV Pose Estimation Using a Self-Organizing Map and Deep Learning
<p>Standard mission profile (<b>left</b>) and typical trajectory state machine (<b>right</b>) [<a href="#B24-robotics-13-00114" class="html-bibr">24</a>].</p> "> Figure 2
<p>Simplified system architecture.</p> "> Figure 3
<p>System architecture with a representation of the used variables.</p> "> Figure 4
<p>Used UAV CAD model illustration.</p> "> Figure 5
<p>Camera and UAV reference frames.</p> "> Figure 6
<p>Example of generated UAV binary images.</p> "> Figure 7
<p>Example I of obtained clustering maps using SOM after 250 iterations: <math display="inline"><semantics> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </semantics></math> grid (<b>left</b>), <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics></math> grid (<b>center</b>) and <math display="inline"><semantics> <mrow> <mn>4</mn> <mo>×</mo> <mn>4</mn> </mrow> </semantics></math> grid (<b>right</b>). The dots represent the neuron positions according to their weights <math display="inline"><semantics> <mi mathvariant="bold">W</mi> </semantics></math> (output space).</p> "> Figure 8
<p>Example II of obtained clustering maps using SOM after 250 iterations: <math display="inline"><semantics> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </semantics></math> grid (<b>left</b>), <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics></math> grid (<b>center</b>) and <math display="inline"><semantics> <mrow> <mn>4</mn> <mo>×</mo> <mn>4</mn> </mrow> </semantics></math> grid (<b>right</b>). The dots represent the neuron positions according to their weights <math display="inline"><semantics> <mi mathvariant="bold">W</mi> </semantics></math> (output space).</p> "> Figure 9
<p>Example of the obtained sample hits (<b>left</b>), where the numbers indicate the number of input vectors, and neighbor distances (<b>right</b>), where the red lines depict the connections between neighboring neurons for the <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics></math> grid shown in <a href="#robotics-13-00114-f007" class="html-fig">Figure 7</a> center. The colors indicate the distances, with darker colors representing larger distances and lighter colors representing smaller distances.</p> "> Figure 10
<p>Used translation estimation DNN structure.</p> "> Figure 11
<p>Used orientation estimation DNN structure.</p> "> Figure 12
<p>Example of a similar topology shown by a UAV symmetric pose.</p> "> Figure 13
<p>Translation error boxplot in meters.</p> "> Figure 14
<p>Orientation error histogram in degrees.</p> "> Figure 15
<p>Examples of pose estimation using the proposed architecture—Original image (<b>left</b>), SOM output (<b>center</b>), and pose estimation (<b>right</b>). The orientation error for (A3) was 30.6 degrees, for (B3) 3.3 degrees, for (C3) 22.2 degrees, and for (D3) 14.4 degrees.</p> "> Figure 16
<p>Orientation error histogram at 5 m when varying the Gaussian noise SD (degrees).</p> "> Figure 17
<p>Obtained loss during the translation DNN training when removing network layers, as described in <a href="#robotics-13-00114-t007" class="html-table">Table 7</a>.</p> "> Figure 18
<p>Obtained loss during the orientation DNN training when removing network layers, as described in <a href="#robotics-13-00114-t008" class="html-table">Table 8</a>.</p> "> Figure 19
<p>Qualitative analysis example: Real captured frame (<b>left</b>) and BS obtained frame (<b>right</b>).</p> "> Figure 20
<p>Real captured frames obtained clustering maps using SOM with 9 neurons (<math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics></math> grid) after 250 iterations (<b>left</b>) and obtained estimation pose rendering using the network trained after 50,000 iterations (<b>right</b>).</p> ">
Abstract
:1. Introduction
2. Related Work
2.1. Unmanned Aerial Vehicles (UAVs)
2.2. Background Subtraction (BS)
2.3. Self-Organizing Maps (SOMs)
2.4. Deep Neural Networks (DNNs)
2.5. General Analysis
3. Problem Formulation & Methodologies
3.1. Synthetic Data Generation
3.2. Clustering Using a Self-Organizing Map (SOM)
Algorithm 1 Self-Organizing Map (SOM) [32,33,93] |
|
3.3. Pose Estimation Using Deep Neural Networks (DNNs)
3.3.1. General Description
Algorithm 2 Self-Attention Layer [95,96] |
|
3.3.2. Translation Estimation
3.3.3. Orientation Estimation
4. Experimental Results
4.1. Datasets, Network Training & Parameters
4.2. Performance Metrics
4.3. Pose Estimation Error
4.3.1. Comparison with Other Methods
4.3.2. Noise Robustness
4.4. Ablation Studies: Network Structure
4.5. Qualitative Analysis of Real Data
4.6. Overall Analysis & Discussion
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Deep Neural Network (DNN)—Translation: Additional Information
Layer (Type) | Output Shape | Parameters | Notes | Label |
---|---|---|---|---|
Input | (3, 3, 2) | - | - | Input |
2D Convolution | (3, 3, 64) | 1216 | - | Conv1 |
Batch Normalization | (3, 3, 64) | 256 | - | BN1 |
Activation (ReLU) | (3, 3, 64) | - | - | ReLU1 |
Self Attention | (3, 3, 64) | 4689 | - | Attn1 |
2D Convolution | (3, 3, 64) | 36,928 | - | Conv2 |
Batch Normalization | (3, 3, 64) | 256 | - | BN2 |
Activation (ReLU) | (3, 3, 64) | - | - | ReLU2 |
Self Attention | (3, 3, 64) | 4689 | - | Attn2 |
2D Convolution | (3, 3, 64) | 36,928 | - | Conv3 |
Batch Normalization | (3, 3, 64) | 256 | - | BN3 |
Activation (ReLU) | (3, 3, 64) | - | - | ReLU3 |
Self Attention | (3, 3, 64) | 4689 | - | Attn3 |
Dropout | (3, 3, 64) | - | 0.5 | Dout1 |
Self Attention | (3, 3, 64) | 4689 | - | Attn4 |
2D Convolution | (3, 3, 128) | 73,856 | - | Conv4 |
Batch Normalization | (3, 3, 128) | 512 | - | BN4 |
Activation (ReLU) | (3, 3, 128) | - | - | ReLU4 |
Self Attention | (3, 3, 128) | 18,593 | - | Attn5 |
2D Convolution | (3, 3, 128) | 147,584 | - | Conv5 |
Batch Normalization | (3, 3, 128) | 512 | - | BN5 |
Activation (ReLU) | (3, 3, 128) | - | - | ReLU5 |
Self Attention | (3, 3, 128) | 18,593 | - | Attn6 |
Dropout | (3, 3, 128) | - | 0.5 | Dout2 |
2D Convolution | (3, 3, 256) | 295,168 | - | Conv6 |
Batch Normalization | (3, 3, 256) | 1024 | - | BN6 |
Activation (ReLU) | (3, 3, 256) | - | - | ReLU6 |
2D Convolution | (3, 3, 256) | 590,080 | - | Conv7 |
Batch Normalization | (3, 3, 256) | 1024 | - | BN7 |
Activation (ReLU) | (3, 3, 256) | - | - | ReLU7 |
2D Convolution | (3, 3, 256) | 590,080 | - | Conv8 |
Batch Normalization | (3, 3, 256) | 1024 | - | BN8 |
Activation (ReLU) | (3, 3, 256) | - | - | ReLU8 |
Dropout | (3, 3, 256) | - | 0.5 | Dout3 |
Flatten | 2304 | - | - | Flatten |
Fully Connected | 512 | 1,180,160 | ReLU, L2 () | FC1 |
Dropout | 512 | - | 0.5 | Dout4 |
Fully Connected | 256 | 131,328 | ReLU, L2 () | FC2 |
Dropout | 256 | - | 0.5 | Dout5 |
Fully Connected | 3 | 771 | Linear | Output |
Appendix B. Deep Neural Network (DNN)—Orientation: Additional Information
Layer (Type) | Output Shape | Parameters | Notes | Label |
---|---|---|---|---|
Input | (3, 3, 2) | - | - | Input |
2D Convolution | (3, 3, 64) | 1216 | - | Conv1 |
Batch Normalization | (3, 3, 64) | 256 | - | BN1 |
Activation (ReLU) | (3, 3, 64) | - | - | ReLU1 |
Self Attention | (3, 3, 64) | 4689 | - | Attn1 |
2D Convolution | (3, 3, 64) | 36,928 | - | Conv2 |
Batch Normalization | (3, 3, 64) | 256 | - | BN2 |
Activation (ReLU) | (3, 3, 64) | - | - | ReLU2 |
Self Attention | (3, 3, 64) | 4689 | - | Attn2 |
2D Convolution | (3, 3, 64) | 36,928 | - | Conv3 |
Batch Normalization | (3, 3, 64) | 256 | - | BN3 |
Activation (ReLU) | (3, 3, 64) | - | - | ReLU3 |
Self Attention | (3, 3, 64) | 4689 | - | Attn3 |
Dropout | (3, 3, 64) | - | 0.5 | Dout1 |
2D Convolution | (3, 3, 128) | 73,856 | - | Conv4 |
Batch Normalization | (3, 3, 128) | 512 | - | BN4 |
Activation (ReLU) | (3, 3, 128) | - | - | ReLU4 |
Self Attention | (3, 3, 128) | 18,593 | - | Attn4 |
2D Convolution | (3, 3, 128) | 147,584 | - | Conv5 |
Batch Normalization | (3, 3, 128) | 512 | - | BN5 |
Activation (ReLU) | (3, 3, 128) | - | - | ReLU5 |
Self Attention | (3, 3, 128) | 18,593 | - | Attn5 |
Dropout | (3, 3, 128) | - | 0.5 | Dout2 |
2D Convolution | (3, 3, 256) | 295,168 | - | Conv6 |
Batch Normalization | (3, 3, 256) | 1024 | - | BN6 |
Activation (ReLU) | (3, 3, 256) | - | - | ReLU6 |
2D Convolution | (3, 3, 256) | 590,080 | - | Conv7 |
Batch Normalization | (3, 3, 256) | 1024 | - | BN7 |
Activation (ReLU) | (3, 3, 256) | - | - | ReLU7 |
2D Convolution | (3, 3, 256) | 590,080 | - | Conv8 |
Batch Normalization | (3, 3, 256) | 1024 | - | BN8 |
Activation (ReLU) | (3, 3, 256) | - | - | ReLU8 |
Dropout | (3, 3, 256) | - | 0.5 | Dout3 |
Flatten | 2304 | - | - | Flatten |
Fully Connected | 512 | 1,180,160 | - | FC1 |
Activation (QReLU) | 512 | - | - | QReLU1 |
Dropout | 512 | - | 0.5 | Dout4 |
Fully Connected | 256 | 131,328 | - | FC2 |
Activation (QReLU) | 256 | - | - | QReLU2 |
Dropout | 256 | - | 0.5 | Dout5 |
Fully Connected | 4 | 1028 | - | - |
Normalization | 4 | - | Quaternion Normalization | Output |
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Distance | Minimum | Median | Maximum | MAE | RMSE | SD |
---|---|---|---|---|---|---|
5 | 0.10 | 0.28 | 1.25 | 0.32 | 0.34 | 0.14 |
7.5 | 0.02 | 0.25 | 1.93 | 0.33 | 0.42 | 0.26 |
10 | 0.14 | 0.42 | 2.34 | 0.49 | 0.56 | 0.27 |
Distance | Minimum | Median | Maximum | MAE | RMSE | SD |
---|---|---|---|---|---|---|
5 | 0.77 | 14.77 | 179.8 | 29.26 | 47.44 | 37.37 |
7.5 | 1.81 | 14.31 | 178.7 | 28.34 | 45.98 | 36.23 |
10 | 0.98 | 19.88 | 178.1 | 39.71 | 59.01 | 43.68 |
Method | Median | MAE |
---|---|---|
SOM + DNN (Ours) | 0.28 | 0.32 |
GAbF [26] | 0.27 | 0.19 |
PFO [27] | 0.00 | 0.21 |
Modified PSO [27] | 0.00 | 0.18 |
GAbF [27] | 0.01 | 0.09 |
Method | Median | MAE |
---|---|---|
SOM + DNN (Ours) | 14.77 | 29.26 |
GAbF [26] | 14.6 | 37.2 |
PFO [27] | 1.47 | 94.26 |
Modified PSO [27] | 0.30 | 97.37 |
GAbF [27] | 2.71 | 89.22 |
Noise SD | Minimum | Median | Maximum | MAE | RMSE | SD |
---|---|---|---|---|---|---|
1 | 0.10 | 0.28 | 1.29 | 0.32 | 0.34 | 0.14 |
5 | 0.09 | 0.28 | 1.17 | 0.32 | 0.35 | 0.15 |
10 | 0.09 | 0.28 | 1.66 | 0.33 | 0.37 | 0.16 |
15 | 0.11 | 0.28 | 1.69 | 0.34 | 0.39 | 0.19 |
30 | 0.09 | 0.29 | 2.04 | 0.37 | 0.45 | 0.25 |
50 | 0.09 | 0.32 | 3.37 | 0.41 | 0.50 | 0.28 |
100 | 0.13 | 0.52 | 3.82 | 0.66 | 0.82 | 0.49 |
200 | 0.17 | 0.91 | 4.04 | 1.10 | 1.25 | 0.60 |
Noise SD | Minimum | Median | Maximum | MAE | RMSE | SD |
---|---|---|---|---|---|---|
1 | 1.54 | 14.68 | 179.20 | 29.29 | 47.44 | 37.34 |
5 | 1.86 | 15.67 | 179.40 | 32.60 | 51.93 | 40.45 |
10 | 1.52 | 21.85 | 179.86 | 41.72 | 61.00 | 44.53 |
15 | 2.19 | 30.93 | 179.79 | 54.37 | 73.83 | 49.97 |
30 | 2.86 | 86.07 | 179.89 | 90.74 | 106.04 | 54.92 |
50 | 7.76 | 120.26 | 179.70 | 110.77 | 121.11 | 48.99 |
100 | 12.56 | 132.39 | 179.82 | 125.64 | 131.95 | 40.36 |
200 | 6.77 | 134.47 | 180.00 | 126.00 | 132.12 | 39.80 |
Name | Variant |
---|---|
DNN-T1 | Considered DNN for translation estimation without any change |
DNN-T2 | Removing the SA layers |
DNN-T3 | Removing the SA layers & the kernel regularizers |
DNN-T4 | Removing the SA layers & the kernel regularizers & the batch normalization layers |
Name | Variant |
---|---|
DNN-O1 | Considered DNN for orientation estimation without any change |
DNN-O2 | Removing the SA layers |
DNN-O3 | Removing the SA layers & the kernel regularizers |
DNN-O4 | Removing the SA layers & the kernel regularizers & the batch normalization layers |
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Pessanha Santos, N. Fixed-Wing UAV Pose Estimation Using a Self-Organizing Map and Deep Learning. Robotics 2024, 13, 114. https://doi.org/10.3390/robotics13080114
Pessanha Santos N. Fixed-Wing UAV Pose Estimation Using a Self-Organizing Map and Deep Learning. Robotics. 2024; 13(8):114. https://doi.org/10.3390/robotics13080114
Chicago/Turabian StylePessanha Santos, Nuno. 2024. "Fixed-Wing UAV Pose Estimation Using a Self-Organizing Map and Deep Learning" Robotics 13, no. 8: 114. https://doi.org/10.3390/robotics13080114