Easy engineering technique of optimal electric propulsion trajectory estimation
- Paper number
IAC-06-C4.4.06
- Author
Prof. Mikhail S. Konstantinov, Moscow Aviation Institute (MAI), Russia
- Coauthor
Dr. Vyacheslav Petukhov, Khrunichev State Research & Production Space Center, Russia
- Year
2006
- Abstract
It is considered spacecraft transfer between non-coplanar elliptical and circular orbits using electric propulsion and, as an option, conventional high-thrust engines. Generally, it is considered the combined flight profile consisting of two phases. During high-thrust phase spacecraft is delivered from given parking orbit into an intermediate orbit. Goal of low-thrust phase is spacecraft insertion from this intermediate orbit into a target orbit. The circular target orbits are under consideration, but both parking and intermediate orbits can be arbitrary. Taking into account symmetry reasons, it can be proved that apsidal line of intermediate orbit should belong to the plane of target orbit. Therefore only 3 parameters of intermediate orbit have significance, namely there are apogee/perigee altitudes and its inclination with respect to target orbit. So, the trajectory optimization problem divides into two sub-problems: 1) optimization of high-thrust transfer from the parking orbit into an intermediate orbit, and 2) optimization of low-thrust transfer from the intermediate orbit into the target orbit. This decomposed problem has 3 free parameters (perigee/apogee altitudes and inclination of intermediate orbit), which should be optimized also. While the first sub-problem is trivial, the optimization of low-thrust phase remains quite difficult. But due to novel numerical techniques and new developed software it becomes feasible to carry out optimization of numerous low-thrust trajectories on the relatively dense grid of above enumerated parameters of intermediate orbit. As result the table of required characteristic velocity on this grid was computed. Low-thrust trajectories were optimized using Pontrjagin maximum principle and averaging technique. Due to averaging, the computed optimal trajectories are asymptotic. Therefore these results are correct for any spacecraft parameters while averaging assumptions are held true. Moreover, these trajectories could be scaled for a given target orbit altitude, and the primary gravitational parameter. Such a way it was constructed the universal table of non-dimensional characteristic velocities corresponding to optimal transfers between non-coplanar elliptical and circular orbits in the inverse-square gravity field. So, considered optimization problem reduces to final spacecraft mass maximization with respect to apogee/perigee altitudes, and inclination of intermediate orbit while high-thrust phase is optimized using well-known patched-conics technique, and parameters of optimal low-thrust phase are interpolated from pre-computed 3D-grid. Both universal table and practical optimization technique is presented. These results were used for feasibility study of various space missions. Especially, considered technique is recommended to feasibility study of advanced missions to GEO using electric propulsion.
- Abstract document
- Manuscript document
IAC-06-C4.4.06.pdf (🔒 authorized access only).
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