Quadrotor Attitude Dynamics Identification Based on Nonlinear Autoregressive Neural Network with Exogenous Inputs

Figures & data

Figure 1. Body axis coordinate system

Figure 2. Quadrotor

Figure 3. Spherical joint

Figure 4. Inputs/outputs diagram

Figure 5. Axis damping feedback loop

Figure 6. Pin diagram

Figure 7. Part of AM335x family memory map (AM335x ARM cortex – A8 microprocessors (MPUs) technical reference manual 2013, 176)

Figure 8. NARX series-parallel architecture (MATLAB 2013a. 2013. MathWorks)

Figure 9. NARX parallel architecture (MATLAB 2013a. 2013. MathWorks)

Figure 10. Modeling performance of pitch rate transfer function

Figure 11. Modeling performance of roll rate transfer function

Figure 12. Modeling performance of yaw rate transfer function

Table 1. CTTF results

Angle rate	MSE	VAF (%)	Correlation Coefficient	Outlier ratio
Pitch rate	0.0106	18.6	0.75	0.07
Roll rate	0.0054	65.1	0.77	0.04
Yaw rate	0.0772	5.33	0.61	0.04

Table 2. NARX results

Angle rate	MSE	VAF (%)	Correlation Coefficient	Outlier ratio
Pitch rate	0.0077	54.4	0.74	0.07
Roll rate	0.0047	72.9	0.87	0.04
Yaw rate	0.0112	69.3	0.86	0.08

Figure 13. Modeling performance of the NARX model of pitch rate during testing

Figure 14. Modeling performance of the NARX model of roll rate during testing

Figure 15. Modeling performance of the NARX model of yaw rate during testing

Table 3. NARX results

Angle rate	MSE	VAF (%)	Correlation Coefficient	Outlier ratio
Pitch rate	0.0064	54.17%	0.77	0.06
Roll rate	0.0048	73.8%	0.86	0.06
Yaw rate	0.0050	50.6%	0.72	0.07

Table 4. NARX MSE

Data Used	1250	2500	3750	5000	6250	7500
Pitch Rate	0.02	0.015	0.014	0.012	0.008	0.008
Roll Rate	0.014	0.011	0.007	0.005	0.004	0.004
Yaw Rate	0.024	0.013	0.012	0.012	0.007	0.006

Figure 16. Number of delays vs MSE for pitch rate

Figure 17. Number of delays vs MSE for roll rate

Figure 18. Number of delays vs MSE for yaw rate

Figure 19. MSE for yaw rate vs training set size

Figure 20. MSE for roll rate vs training set size

Figure 21. MSE for pitch rate vs training set size

MATLAB. 2013a. 2013. MathWorks.

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