Summary In this article, a complete modelling, synthesis, and analysis methodology of control compensators for descent and landing (D&L) on small planetary bodies is presented. These missions are scientifically very rewarding but technically extremely challenging due to the complex and poorly known environment around those bodies, which calls for the ability to manage competing robustness and performance requirements. While this issue is typically addressed via the redefinition of D&L guidance strategies, here, it is tackled through the augmentation with a simple yet robust control compensator. This compensator is designed using linear fractional transformation modelling to capture the interplay with uncertain gravity fields and the recently developed structured H∞ optimisation framework, which has been proved particularly suitable for industry‐oriented applications. The proposed approach is completely generic but uses the scenario of a landing on the Martian moon Phobos as an illustrative example. Different compensators are then verified and compared analytically via the structured singular value μ and through high‐fidelity Monte Carlo simulation.
The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.
Abstract. The orbital dynamics around the Libration points of the classical circular restricted three-body problem (CR3BP) have been investigated in detail: in the last few decades, dynamical systems theory has provided invaluable analytical and numerical tools for understanding the dynamics of Libration Point Orbits (LPOs). The aim of this paper is to extend the model of the CR3BP to derive the LPOs in the vicinity of the Martian moon Phobos, which is becoming an appealing destination for scientific missions. The case of Phobos is particularly extreme, since the combination of both small mass-ratio and length-scale moves the collinear Libration manifold close to the moon's surface. Thus, a model of this system must consider additional dynamical perturbations, in particular the complete gravity field of Phobos, which is highly-inhomogeneous. This is accomplished using a spherical harmonics series expansion, deriving an enhanced elliptic three-body model. In this paper, we show how methodologies from dynamical systems theory are applied in differential correction continuation schemes to this proposed nonlinear model of the dynamics near Phobos, to derive the structure of the dynamical substitutes of the LPOs in this new system. Results obtained show that the structure of the LPOs differs substantially from the classical case without harmonics. The proposed methodology allows us to identify natural periodic and quasi-periodic orbits that would provide unique low-cost opportunities for close-range observations around Phobos and high-performance landing/take-off pathways to and from Phobos' surface, which could be exploited in upcoming missions targeting the exploration of this Martian moon.
One of the paramount stepping stones towards NASA's long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. Since a precursor mission to Phobos would be easier than landing on Mars itself, NASA is targeting this moon for future exploration, and ESA has also announced Phootprint as a candidate Phobos sample-and-return mission. Orbital dynamics around small planetary satellites are particularly complex because many strong perturbations are involved, and the classical circular restricted three-body problem (R3BP) does not provide an accurate approximation to describe the system's dynamics. Phobos is a special case, since the combination of a small mass-ratio and length-scale means that the sphere-of-influence of the moon moves very close to its surface. Thus, an accurate nonlinear model of a spacecraft's motion in the vicinity of this moon must consider the additional perturbations due to the orbital eccentricity and the complete gravity field of Phobos, which is far from a spherical-shaped body, and it is incorporated into an elliptic R3BP using the gravity harmonics series-expansion (ER3BP-GH). In this paper, a showcase of various classes of non-keplerian orbits is identified and a number of potential mission applications in the Mars-Phobos system are proposed: these results could be exploited in upcoming unmanned missions targeting the exploration of this Martian moon. These applications include: low-thrust hovering and orbits around Phobos for close-range observations; the dynamical substitutes of periodic and quasi-periodic Libration Point Orbits in the ER3BP-GH to enable unique low-cost operations for space missions in the proximity of Phobos; their manifold structure for high-performance landing/take-off maneuvers to and from Phobos' surface and for transfers from and to Martian orbits; Quasi-Satellite Orbits for long-period station-keeping and maintenance. In particular, these orbits could exploit Phobos' occulting bulk and shadowing wake as a passive radiation shield during future manned flights to Mars to reduce human exposure to radiation, and the latter orbits can be used as an orbital garage, requiring no orbital maintenance, where a spacecraft could make planned pit-stops during a round-trip mission to Mars
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