Robust Optimal Control of Spacecraft Translational-Rotational Coupled Motion under Uncertainty

The mysteries of our Earth, life, and future are intricately linked with primitive bodies like asteroids and comets. These celestial bodies are vital targets for exploration as outlined in the 2022 Planetary Decadal Survey. These destinations, however, present unique challenges due to their complex dynamics and the inherent uncertainties of their unpredictable nature. The intricacies of modern and future space missions, encompassing sophisticated technologies such as solar sails, asteroid/comet landings, and deep space rendezvous & docking, necessitate a refined approach to control. The coupled interaction between translational and rotational motion, referred to as 6DOF (six degrees of freedom), is crucial in managing the constraints posed by these mission scenarios. For example, the attitude of a spacecraft during solar sail operations directly impacts thrust direction, and the 6DOF paradigm is exemplified in primitive body landing and rendezvous & docking operations, given the need to balance line-of-sight and glideslope constraints. Moreover, the brevity of the landing phase on a primitive body does not allow for the decoupling of rotational and translational inputs, underscoring the need for a comprehensive 6DOF control framework. Addressing the complexities of 6DOF control in the face of uncertainties posed by a lack of knowledge of primitive bodies and the environment in deep space regions requires a methodology that is both robust and optimal, striking a balance between mission efficacy and cost-effectiveness. This research project aims to develop an innovative 6DOF control framework capable of optimizing maneuvers, thereby reducing mission costs, while simultaneously providing the flexibility necessary to adapt to a variety of space mission scenarios. The proposed 6DOF control framework will ensure safety and optimal maneuverability in the face of uncertainties through robust control techniques. The proposed research focuses on advancing the state-of-the-art of 6DOF control framework, leveraging cutting-edge technologies and methodologies such as Special Euclidean group SE(3) and its Tangent Bundle TSE(3) for 6DOF control, chance-constrained optimization, and machine learning algorithms. TSE(3) provides a geometrically sound approach to handling the combined complexities of attitude and position, while chance-constrained optimization ensures that the spacecraft can navigate uncertainties with a defined level of confidence. The incorporation of machine learning algorithms adds an adaptive layer to the framework, enabling it to learn from the environment and further improve its robustness over time. The proposed 6DOF control framework will directly address the challenges outlined in the Strategic Framework Envisioned Futures by the Space Technology Mission Directorate by ensuring optimal maneuverability under uncertainties, and the research outcome will significantly contribute to the success of NASA's future missions and support its objectives in advancing space technologies. In conclusion, the outcome of this research, a robust and optimal 6DOF control framework, will significantly benefit NASA's future deep-space endeavors. The proposed novel 6DOF control framework will not only reduce the costs associated with complex space missions but will also ensure that these missions are conducted safely and effectively, ultimately unlocking the secrets held by asteroids, comets, and other destinations calling for exploration.

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