# Safety-Aware Optimal Attitude Pointing for Low-Thrust Satellites  
[PERSON]  
1 Facolta di Scienze e Tecnologie, Free University of Bozen-Bolzano, Piazza Universitat\({}^{*}\) 5, 39100 Bolzano, Italy; [PERSON]ipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy; [EMAIL_ADDRESS]  
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[PERSON]  
2 Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy; [EMAIL_ADDRESS]  
[PERSON]  
1 Facolta di Scienze e Tecnologie, Free University of Bozen-Bolzano, Piazza Universitat\({}^{*}\) 5, 39100 Bolzano, Italy; [PERSON]#### Abstract  
In geostationary orbit, long eclipses and the seasonal variations in the direction and intensity of the solar input can cause damage to sensitive equipment during attitude maneuvers, which may inadvertently point the equipment towards the Sun. The requirement that transmitting and receiving antennae remain pointed towards the Earth creates further restrictions to pointing directions. The aim of the study is to construct a novel geometric and reinforcement-learning-based method to determine attitude guidance maneuvers that maintain the equipment in safe and operational orientations throughout an attitude maneuver. The attitude trajectory is computed numerically using the geometric framing of Pontryagin's maximum principle applied to the vehicle kinematics using the global matrix Lie group representation on \(SO(3)\), and the angular velocities are shaped using free parameters. The values of these free parameters are determined by a reinforcement learning algorithm to avoid the forbidden areas while maintaining the pointing in operational areas (modeled as subsets of the two-sphere of all possible pointing directions of a particular axis). The method is applied to a model geosynchronous satellite and demonstrated in a simulation. title=false, roundcorner=0 pt,  
most other methods in the literature, [PERSON] [4] treated the matter directly on the special orthogonal group \(SO(3)\). Using \(SO(3)\) to represent the spacecraft's rotation allows pointing constraints to be imposed on multiple body-fixed directions. [PERSON] [5] found reference motions for reorienting a spinning satellite. The path-planning problem with pointing constraints was addressed using optimization of an analytically defined cost function, which includes these parameters. The analytical expression was expressed explicitly on the special orthogonal group \(SO(3)\) (instead of employing a local parameterization like Euler angles). However, no explicit way of determining the parameters to respect the pointing constraints was presented. One way of determining the parameters required is to preserve the pointing set is to \"teach\" the satellite's guidance system via a learning algorithm to respect the boundaries of the pointing set. In reinforcement learning (RL), an agent (the vehicle) maps observations (states) to actions via a policy function, which can generally be expressed as a neural network to maximize its reward, a scalar feedback signal. The goal of RL is to determine actions that generate a desired system behavior. The application of RL in obstacle avoidance is not new; the study [6] used an artificial potential field to design the positive rewards of the RL algorithm. According to the different requirements of the task, rewards were modified in the training process to obtain different paths. A control strategy with learning capabilities for unknown environments was demonstrated in [7] using RL with only sparse reward information. A discrete coding of the input space using a neural network structure was presented, which enabled a faster and more efficient convergence of the RL process. Preservation of a safe set is the fundamental concept of motion planning, which avoids catastrophic outcomes by maintaining motion within certain constraints defined by safety. Collision avoidance is the most commonly applied example of this kind of motion planning.