# Generating Low-Earth Orbit Satellite Attitude Maneuver Profiles Using Deep Neural Networks
## 3 Proposed Technique for Generating Attitude Reference Profiles  
Section 2 described the difficulty in obtaining a maneuver profile in a short time, considering all the limiting factors. This occurs because the satellite's attitude kinematics model is nonlinear, and previous research-derived solutions used optimal control theory [24; 25; 26; 27]. However, in this approach, the initial guesses influence the quality of the potential solutions. Therefore, we proposed a technique that uses a data-driven deep neural network (DNN) to obtain the initial guesses and then is optimized to minimize the pointing error and maneuvering time as the satellite points to its new target. First, the upload profile of the LEO satellite was created using angular acceleration and time data, as mentioned in Section 2. The values of the angular acceleration generated for each time, shown in Figure 2, are defined as  
\[\mathrm{a(t)}=a_{0}+\mathrm{J}\cdot t,\quad 0<t<t_{1},\]  
Finally, the angles for duration are given by  
\[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]  
\[\theta_{1}=\frac{1}{2}a_{0}\cdot t_{1}+\frac{1}{6}J\cdot t_{1}, \tag{22}\]  
\[\theta(t)=\theta_{1}+\omega_{1}(t-t_{1})+\frac{1}{2}a_{12}\cdot(t-t_{1})^{2}, \ t_{1}<t<t_{2}, \tag{23}\]  
\[\theta_{2}=\theta_{1}+\omega_{1}(t_{2}-t_{1})+\frac{1}{2}a_{12}\cdot(t_{2}-t_{ 1})^{2}, \tag{24}\]  
\[\theta(t)=\theta_{2}+\omega_{2}(t-t_{2})+\frac{1}{2}a_{12}\cdot(t-t_{2})^{2}- \frac{1}{6}J\cdot(t-t_{2})^{3},\ t_{2}<t<t_{3}, \tag{25}\]  
\[\theta_{3}=\theta_{2}+\omega_{2}(t_{3}-t_{2})+\frac{1}{2}a_{12}\cdot(t_{3}-t_ {2})^{2}-\frac{1}{6}J\cdot(t_{3}-t_{2})^{3}, \tag{26}\]  
\[\theta(t)=\theta_{3}+\omega_{3}(t-t_{3})+\frac{1}{2}a_{34}\cdot(t-t_{3})^{2}, \quad t_{3}<t<t_{4}, \tag{27}\]  
\[\theta_{4}=\theta_{3}+\omega_{3}(t_{4}-t_{3})+\frac{1}{2}a_{34}\cdot(t_{4}-t_ {3})^{2}, \tag{28}\]  
\[\theta(t)=\theta_{4}+\omega_{4}(t-t_{4})+\frac{1}{2}a_{34}\cdot(t-t_{4})^{2}- \frac{1}{6}J\cdot(t-t_{4})^{3},\quad t_{4}<t<t_{5}, \tag{29}\]  
\[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]0  
\[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]1  
\[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]2  
\[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]3  
The attitude and angular rate profile of the satellite up to \(t_{7}\) were generated onboard the satellite using the uploaded acceleration and time data. The commands for satellite attitude maneuvering were provided in quaternion form instead of Euler angles to avoid gimbal locks and other issues. The attitude profile for the maneuvering segment was converted into a quaternion form for training using a direction cosine matrix (DCM). The format of the data uploaded to the LEO satellites and used for maneuvering between target pointings is shown in \[\theta(t)=\frac{1}{2}a_{0}\cdot t+\frac{1}{6}J\cdot t^{3},\ 0<t<t_{1}, \tag{21}\]4 Table 1 shows that the maximum and minimum acceleration values (\(a\), \(b\)) and time duration data (\(t_{1}\) to \(t_{7}\)) are used for each axis. The value of \(t_{8}\) was determined at the start of the mission according to the mission design requirements for the satellite, and it was defined as the difference between the user-controlled maneuver time and the time interval from \(t_{1}\) to \(t_{7}\). To account for the size of the uploaded data, the same time (\(t_{1}\) to \(t_{8}\)) values were used for the roll, pitch, and yaw axes. In other words, all three axes had the same timeline, and only the acceleration values were generated differently. The proposed technique that employs DNN-based prediction uses data-based learning to obtain the initial guess for optimization. To perform data-based learning, it was necessary to preprocess the data, separate the data for training and validation, design the network and optimize it for learning, and validate the predictions. In the preprocessing stage, the input and output features must be selected.