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Multiobjective Earth-Moon Trajectory Optimization in the Restricted Four-Body Problem

Asadian, Nima | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39518 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Pourtakdoust, Hossein
  7. Abstract:
  8. Outer space mission design utilizing restricted four-body model for spacecrafts equipped with impulsive engines is investigated. Applied researches in the field of space mission design are typically based on two-body models and in some more advanced cases involve application of the restricted three-body models. As the general solution of the two-body problem is known (conic sections), the transfer trajectories are generally designed using simple Hohmann transfers. But, when considering three-body problem, there is no closed-form solution and low-energy transfer trajectories are designed through the use of stable/unstable manifolds of the corresponding halo orbits. In this way, some interesting spatial tunnels develop that are called Interplanetary Superhighways (ISP). The problem with ISPs is its limited utility and one can find low-energy transfers only for special cases. More importantly, one can not determine transfer trajectories that are optimal in a multiobjective sense, e.g. a trajectory that is optimized with respect to both the transfer time as well as the required ΔV maneuvers. In this dissertation, initially the available Restricted Four-Body Problems (R4BP) are introduced and subsequently a new R4BP called BiElliptic Problem (BEP) is developed. For the developed model, the effect of the Sun on the traditional Lagrange points of the Earth-Moon system is investigated. In this way, first, the quasi-periodic orbits replacing the collinear libration points L1 and L2 are computed using an innovative approach. Second, a parametric study is performed to detect the change in the structure of the quasi-equilibrium points of the BEP. Following the study of the dynamics of the quasi-equilibrium points for the Sun-Earth-Moon BEP system, optimal Earth-to-Moon transfer in the multi-gravitational field of the Sun, Earth as well as the Moon is investigated utilizing genetic algorithm. Due to the fact that it is usually desired to have optimal trajectories in the sense of optimal transfer time as well as minimum total impulse, the multiobjective optimization methodology of NSGA-II is introduced and applied. The optimization problem is formulated using the ballistic capture trajectories to the Moon. The trajectories require less energy due to elimination of some ΔV required to have the spacecraft captured by the Moon. To this end, a mid-course maneuver is introduced for which the time and required impulse are the key optimization parameters. Comparison of the pertinent results of this problem with the existing literature is promising and is an indication of good potential of the proposed parameterization and optimization scheme to extract more realistic and efficient outer space optimal transfer trajectories
  9. Keywords:
  10. Trajectory Optimization ; Multidisciplinary Optimization ; Restricted Four Body Problem (RFBP) ; Bielliptic Problem (BEP) ; Quasi Periodic Orbits ; Non-Coplanar Motion of Primaries ; Ballistic Capture ; Earth to Moon Transfer

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