# Generating Low-Earth Orbit Satellite Attitude Maneuver Profiles Using Deep Neural Networks
## 5 Case Studies  
In this section, we examine the generated LEO satellite maneuver profiles that conform to various initial and final boundary conditions, minimize maneuver time, and satisfy the constraints described in this paper. As mentioned earlier, when generating maneuver profiles solely using a DNN, the quaternion is generated within the error range. Therefore, the satellite attitude and angular rate estimated at the end of the maneuver can be affected not only by the attitude and angular rate error at the end of the maneuver but also by the error throughout the maneuver duration, which can lead to more significant estimation errors. Additionally, performance degradation may occur for certain initial and final attitudes, angular velocities, and angular accelerations. Therefore, we analyzed the results of the second-stage optimization correction using the predicted value from the DNN that was constructed using data-based learning as an initial guess. Figures 8-10 show the maneuver profiles generated for the five missions. For the target-pointing segment, a maneuver range of 2-68\({}^{\circ}\) was assumed, and the angular velocities exhibited during the mission ranged from 0.01 to 0.25\({}^{\circ}\)/s. In the figures, the yaw maneuver for the mission duration was assumed to have the angle and angular rate of the pointing that was aimed at the same direction as the target, considering the Earth's rotation and the roll and pitch exhibited various angles and angular velocities to point at different targets. Figure 7: Quaternion prediction RMSE according to target pointing tilt angle. mission required a roll of 30.54\({}^{\circ}\), a pitch of 7.79\({}^{\circ}\), and a yaw of \(-\)0.01\({}^{\circ}\). At the start of the second mission, the initial angular velocities for the roll, pitch, and yaw axes were 0.03\({}^{\circ}\)/s, 0.01\({}^{\circ}\)/s, and 0.04\({}^{\circ}\)/s, respectively. The start of the third mission required a roll of 30.54\({}^{\circ}\), a pitch of 7.79\({}^{\circ}\), and a yaw of \(-\)0.01\({}^{\circ}\). At the start of the third mission, the initial angular velocities for the roll, pitch, and yaw axes were 0.04\({}^{\circ}\)/s, 0.03\({}^{\circ}\)/s, and 0.06\({}^{\circ}\)/s, respectively. The fourth mission required a roll of \(-\)35.00\({}^{\circ}\), a pitch of \(-\)17.45\({}^{\circ}\), and a yaw of \(-\)1.67\({}^{\circ}\). At the start of the fourth mission, the initial angular velocities for the roll, pitch, and yaw axes were 0.03\({}^{\circ}\)/s, 0.04\({}^{\circ}\)/s, and 0.08\({}^{\circ}\)/s, respectively. The final mission required a roll of 30.28\({}^{\circ}\), a pitch of \(-\)9.61\({}^{\circ}\), and a yaw of 0.63\({}^{\circ}\). At the start of the fifth mission, the initial angular velocities for the roll, pitch, and yaw axes were 0.25\({}^{\circ}\)/s, 0.09\({}^{\circ}\)/s, and 0.05\({}^{\circ}\)/s, respectively. Figure 8 shows the angular acceleration profiles generated using the proposed technique for generating maneuver profiles for each of the five missions. To reduce the upload burden on the LEO satellite, angular accelerations and segment-specific time data were used to create profiles on the ground. In Figure 8, the red, green, and blue lines represent the angular acceleration on the roll-, pitch-, and yaw-axes in the local vertical local horizontal (LVLH) frame, respectively. The generated profiles were used to verify the angular rate at the start of the mission and the quaternion attitude error. Figure 9 shows the angular rate profiles for the five target-pointing missions. The red, green, and blue lines represent the roll, pitch, and yaw rates in the LVLH frame, respectively. The angular velocities were generated by integrating the uploaded data, which included angular accelerations and time information. The error in each angular rate at the start of each target-pointing mission was less than 0.0001\({}^{\circ}\)/s, and significant discontinuities were not observed in the figure.