A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of fly-by, descent-to-hover, and ascent-from-hover maneuvers.
This work was done by A. Bechet Acikmese and David Bayard of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free online at www.techbriefs.com/tsp under the Information Sciences category.
The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 395-2322. Refer to NPO-41322.
This Brief includes a Technical Support Package (TSP).
Algorithms for Maneuvering Spacecraft Around Small Bodies
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Overview
The document focuses on the development of optimal guidance algorithms for small body explorations, specifically asteroids and comets. These algorithms aim to compute fuel or energy optimal trajectories for maneuvers around small bodies by solving associated optimal control problems using a direct method based on convex programming. The research, supported by the Jet Propulsion Laboratory and NASA, addresses the challenges posed by long two-way light-time and mission durations in controlling spacecraft from the ground and minimizing fuel consumption during small body operations.
The key innovation lies in a novel solution approach where the optimal control problem is doubly discretized. By discretizing the time axis and spectrally discretizing the control input using Chebyshev basis functions, the infinite dimensional optimization problems associated with small body maneuvers are converted into finite dimensional ones. This approach allows for the formulation of convex programming problems or their convexification, leading to efficient and robust optimization algorithms with polynomial time convergence properties.
The document emphasizes the importance of formulating guidance problems for small body explorations as convex programming problems, highlighting this as a critical step in the research. By implementing these algorithms, the team demonstrates their effectiveness in solving guidance problems autonomously, paving the way for onboard implementation in future missions. The results of this research are directly applicable to sample return missions to asteroids and comets, showcasing the practical relevance of the work.
Furthermore, the document mentions the availability of additional technical support and resources through NASA's Commercial Technology Program and the NASA Scientific and Technical Information Program Office. It encourages further exploration of aerospace-related developments with wider technological, scientific, or commercial applications.
In summary, the document presents a significant advancement in autonomous guidance algorithms for small body explorations, offering a solution to the challenges posed by long mission durations and limited ground control. The research not only contributes to the field of space exploration but also holds promise for future NASA missions involving small bodies like asteroids and comets.
