The purpose of this paper is to present a methodology and experimental results on using global optimization algorithms to determine the optimal orbit, based on the mission requirements, for a set of spacecraft flying in formation with an asteroid.
A behavioral‐based hybrid global optimization approach is used to first characterize the solution space and find families of orbits that are a fixed distance away from the asteroid. The same optimization approach is then used to find the set of Pareto optimal solutions that minimize both the distance from the asteroid and the variation of the Sun‐spacecraft‐asteroid angle. Two sample missions to asteroids, representing constrained single and multi‐objective problems, were selected to test the applicability of using an in‐house hybrid stochastic‐deterministic global optimization algorithm (Evolutionary Programming and Interval Computation (EPIC)) to find optimal orbits for a spacecraft flying in formation with an orbit. The Near Earth Asteroid 99942 Apophis (2004 MN4) is used as the case study due to a fly‐by of Earth in 2029 leading to two potential impacts in 2036 or 2037. Two black‐box optimization problems that model the orbital dynamics of the spacecraft were developed.
It was found for the two missions under test, that the optimized orbits fall into various distinct families, which can be used to design multi‐spacecraft missions with similar orbital characteristics.
The global optimization software, EPIC, was very effective at finding sets of orbits which met the required mission objectives and constraints for a formation of spacecraft in proximity of an asteroid. The hybridization of the stochastic search with the deterministic domain decomposition can greatly improve the intrinsic stochastic nature of the multi‐agent search process without the excessive computational cost of a full grid search. The stability of the discovered families of formation orbit is subject to the gravity perturbation of the asteroid and to the solar pressure. Their control, therefore, requires further investigation.
This paper contributes to both the field of space mission design for close‐proximity orbits and to the field of global optimization. In particular, suggests a common formulation for single and multi‐objective problems and a robust and effective hybrid search method based on behaviorism. This approach provides an effective way to identify families of optimal formation orbits.
Alisa Maddock, C. and Vasile, M. (2008), "Design of optimal spacecraft‐asteroid formations through a hybrid global optimization approach", International Journal of Intelligent Computing and Cybernetics, Vol. 1 No. 2, pp. 239-268. https://doi.org/10.1108/17563780810874735
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