# Safety-Aware Optimal Attitude Pointing for Low-Thrust Satellites
## 4 Discussion and Conclusions  
This paper presented a method to obtain optimal attitude guidance controls for a spacecraft in geostationary orbit, avoiding pointing sensitive instrumentation towards the Sun during an attitude maneuver while maintaining the direction of a beam pencil. This method used RL to produce an optimal trajectory that reacted to the presence of obstacles to maintain the configuration in the pointing set. The simulations carried out demonstrated that the trajectory that we designed avoided the forbidden pointing direction while maintaining the antenna in the operational pointing direction for two classes of paths, one that violated the bright-spot condition and a second that violated the antenna-pointing condition. When comparing the average CPU times for the two classes of solutions shown here (Path 1, 1.437 s, and Path 2, 2.113 s) with those determined in [5], which perform Lie group-based pointing while avoiding a bright spot (between 0.36 and 0.406 s), the comparison seems unfavorable: however, in their method, the user is required to firstrun the program with a \"guessed\" \(c_{i}\) value and then increment the \(c_{i}\) values manually, each time running and then visually confirming that the trajectory avoids the forbidden region, a process that is certainly less efficient even if it is less computationally demanding. Therefore, a comparison of CPU times between the two papers is not entirely meaningful, and in terms of the ease of operation, ours is certainly preferable. A possible drawback of our method is that we assumed the attitude to be precisely known. However, in a real mission, there will be delays in the pose estimation. We also assumed that the initial and final orientations were chosen such that the Sun-avoidant and beam pencil vectors fell in the pointing set at the initial and final position, which is reasonable, but a refinement could be to select a suitable orientation to replace the initial and final orientations if they are chosen to fall outside of the pointing set. Another weakness is the \"black box\" nature of the policy function neural network; also, we constructed a simple reward function and did not perform any reward shaping: it was seen as preferable since a poorly shaped reward function can cause a solution that is not ideal even if it provides the highest reward. This can be seen particularly in the fact that the vehicle passes the obstacle relatively closely and then overcompensates through the rest of the trajectory. Refining of the reward function and the inclusion of time and sensor delays are areas to be addressed in future work. [PERSON] carried out the research during her Postdoc with [PERSON] on attitude control for satellites and developed a novel geometric method for motion planning on the frame bundle of connected surfaces of arbitrary constant cross-sectional curvature. [PERSON] and [PERSON] noticed that an improvement could be made to the constrained planning approach used by [PERSON] in the paper [5] by combining this geometric method with reinforcement learning. [PERSON] developed the concept, wrote the paper, and carried out the simulations, and [PERSON] and [PERSON] provided constructive criticism and technical input. All authors read and agreed to the published version of the manuscript. This work was sponsored by the European Regional Development Fund (FiRST Lab Project #FESR 1084). Not applicable. The lead author can be contacted for the data generated during the simulations. No external data sets were used. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results. The following abbreviations are used in this manuscript:  
R. Reinforcement learning  
[PERSON]'s Maximum Principle  
L.L.