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Autonomous spacecraft control via Shielded Deep Reinforcement Learning (SDRL) has become a rapidly growing research area. However, the construction of shields and the definition of tasking remains informal, resulting in policies with no guarantees on safety and ambiguous goals for the RL agent. In this paper, we first explore the use of formal languages, namely Linear Temporal Logic (LTL), to formalize spacecraft tasks and safety requirements. We then define a manner in which to construct a reward function from a co-safe LTL specification automatically for effective training in SDRL framework. We also investigate methods for constructing a shield from a safe LTL specification for spacecraft applications and propose three designs that provide probabilistic guarantees. We show how these shields interact with different policies and the flexibility of the reward structure through several experiments., Comment: 9 pages, 2 figures, 2 tables, ACC 2024

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling problem -- learning convenient representations of the gravitational potential from position and acceleration data. These PINN gravity models, or PINN-GMs, have demonstrated advantages in model compactness, robustness to noise, and sample efficiency when compared to popular alternatives; however, further investigation has revealed various failure modes for these and other machine learning gravity models which this manuscript aims to address. Specifically, this paper introduces the third generation Physics-Informed Neural Network Gravity Model (PINN-GM-III) which includes design changes that solve the problems of feature divergence, bias towards low-altitude samples, numerical instability, and extrapolation error. Six evaluation metrics are proposed to expose these past pitfalls and illustrate the PINN-GM-III's robustness to them. This study concludes by evaluating the PINN-GM-III modeling accuracy on a heterogeneous density asteroid, and comparing its performance to other analytic and machine learning gravity models., Comment: 40 pages, 10 figures, submitted to The Journal of Astronautical Sciences

This manuscript develops a simultaneous navigation and gravity estimation strategy around a small body. The scheme combines dynamical model compensation with a mascon gravity fit. Dynamical compensation adds the unmodeled acceleration to the filter state. Consequently, the navigation filter is able to generate an on-orbit position-unmodeled acceleration dataset. The available measurements correspond to the landmarks-based navigation technique. Accordingly, an on-board camera is able to provide landmark pixels. The aforementioned position-unmodeled acceleration dataset serves to train a mascon gravity model on-board while in flight. The training algorithm finds the optimal mass values and locations using Adam gradient descent. By a careful choice of the mascon variables and constraints projection, the masses are ensured to be positive and within the small body shape. The numerical results provide a comprehensive analysis on the global gravity accuracy for different estimation scenarios.

This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of fundamental and geometrically insightful motions. These fundamental motions are obtained using Lyapunov-Floquet theory. In the case that the dynamics are perturbed by the action of a controller or by unmodeled dynamics, the weights on each fundamental solution are allowed to vary as in a variation-of-parameters approach, and in this manner function as state variables. This methodology reveals interesting insights about satellite relative motion and also enables elegant control approaches. This approach can be applied in any dynamical environment as long as the chief orbit is periodic, and this is demonstrated with results for relative motion analysis and control in the eccentric Keplerian problem and in the circular restricted three-body problem (CR3BP). Some commentary on extension of the methodology beyond the periodic chief orbit case is also provided. This is a promising and widely applicable new approach to the close-proximity satellite relative motion problem.

Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite relative motion solutions for linearization about a closed chief orbit. By identifying the analytic relationship between Lyapunov-Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration of the types of close-proximity natural relative motion available in various applications. The approach is demonstrated for the Keplerian relative motion problem with general eccentricities in multiple coordinate representations. The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.

This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for the orbit radius and other elements. The conservation of the Jacobi integral is used to make the problem solvable to first-order in the perturbations. The solutions are characterized as small deviations from an unperturbed circular orbit. The approximations are developed for near-circular orbits with initial mean motion $n_{0}$ around a body with rotation rate $c$. The approximations are shown to be valid for values of angular rate ratio $\Gamma = c/n_{0} > 1$, with accuracy decreasing as $\Gamma \rightarrow 1$, and singularities at and near $\Gamma = 1$. Extensions of the methodology to eccentric orbits are discussed, with commentary on the challenges of obtaining generally valid solutions for both near-circular and eccentric orbits.