# Generating Low-Earth Orbit Satellite Attitude Maneuver Profiles Using Deep Neural Networks
## 3 Proposed Technique for Generating Attitude Reference Profiles
For this process, it was necessary to select features that correlated with the output feature. As mentioned in Section 2, to reduce the dimension of the features and improve the accuracy of the model, the next point quaternion (\(Q1_{next~{}point}\), \(Q2_{next~{}point}\), \(Q3_{next~{}point}\), \(Q4_{next~{}point}\)) was selected as the output feature. For the input feature, the Earth-centered, Earth-fixed (ECEF) frame's position and velocity, the current point quaternion (\(Q1_{current~{}point}\), \(Q2_{current~{}point}\), \(Q3_{current~{}point}\), \(Q4_{current~{}point}\)) of the satellite's orbital parameters, and the relative angle and rate difference between the target pointing's initial position for the next mission and the current time were selected. The selected features are presented in \[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]5  
Because the values of the selected features have different ranges, the values were normalized to optimize learning via the gradient descent. Preprocessing was executed using the min--max method to process each feature uniformly according to  
\[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]6  
where \(\min\Big{(}X_{\text{{training data}}}\Big{)}\) and \(\max\Big{(}X_{\text{{training data}}}\Big{)}\) are the minimum and maximum values of each training data, respectively. To proceed with the training, the dataset was generated and divided into four parts to train the modeling network, select the parameters and network, test the quaternion prediction performance, and verify the maneuver profiles. The dataset was generated using a satellite dynamic attitude simulator under the following conditions: the maximum jerk was 9 deg/s\({}^{3}\), the maximum angular acceleration was 0.9 deg/s\({}^{2}\), the maximum angular rate was 2.9 deg/s, and the MOI values of the satellite for each axis were assumed to be 2500 kg m\({}^{2}\), 2500 kg m\({}^{2}\), and 1000 kg m\({}^{2}\). The optimal maneuver quaternion time-series dataset was obtained by performing trial-and-error with dynamic simulations to achieve the minimum feasible maneuver time and error. The dataset was composed of 1000 time-series samples with different initial and final orientations and angular velocities, of which 60, 10, 10, and 20% were used for training, modeling the network, and selecting the parameters, testing the quaternion prediction \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Parameter**} \\ \hline Roll & Maximum acceleration, Minimum acceleration for roll axis \\ Pitch & Maximum acceleration, Minimum acceleration for pitch axis \\ Yaw & Maximum acceleration, Minimum acceleration for yaw axis \\ Time & Acceleration duration \\  & \(t_{1}\), \(t_{2}\), \(t_{3}\), \(t_{4}\), \(t_{5}\), \(t_{6}\), \(t_{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of proposed technique for generating the reference attitude between target pointings. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Number of Features** \\ \hline \multirow{4}{*}{Input features} & Current point quaternion & 4 \\  & Satellite position vector & 3 \\  & Satellite velocity vector & 3 \\  & Relative angle difference to target point & 3 \\  & Relative angular rate difference to target point & 3 \\ Output features & Next point quaternion & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input and output features for maneuver duration modeling of LEO satellites. performance based on the trained model, and verifying the performance of the generated profiles, respectively. The procedure for creating a quaternion prediction model for maneuvering is shown in Figure 3. The optimal network and parameters were selected using a genetic algorithm to minimize the error of the time-series prediction results during the maneuver period based on the training and parameter selection datasets.