PHYSICS-INFORMED NEURAL NETWORKS FOR OPTIMAL PROXIMITY MANEUVERS WITH COLLISION AVOIDANCE AROUND ASTEROIDS

Exploring small planetary bodies, such as asteroids, is essential in understanding our planetary evolution and formation. For this reason, space agencies design space missions to explore these bodies. Thus, it is necessary to develop tools to compute optimal proximity maneuvers and trajectories around asteroids accurately. However, one of the main difficulties when dealing with asteroids is their irregular shapes, which can eventually lead a spacecraft to unexpected impacts if its trajectory is not designed carefully. To this end, this paper shows how it is possible to design optimal trajectories with collision avoidance around asteroids so that the spacecraft can avoid impacts with the irregular shape of an asteroid. We do so by employing the Rapidly-Explored Random Tree (RRT*) technique, which allows us to connect multiple arches of trajectory to avoid obstacles. In particular, every single optimal arch is computed via the indirect method exploiting Physics-Informed Neural Networks (PINNs). This is done by learning the Two-Point Boundary Value Problem (TPBVP) solution arising from applying the Pontryagin Minimum Principle (PMP) to the optimal control problem. The Extreme Theory of Functional Connections (X-TFC) is employed among the PINN frameworks because it analytically satisfies the boundary constraints. The proposed method is tested to design optimal trajectories around asteroids Gaspra and Bennu while avoiding impacts with their surfaces.