Fuel-Optimal Multi-Impulse Orbit Transfer Using a Hybrid Optimization Method

For the <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-impulse transfer between two earth orbits, this paper introduces <inline-formula> <tex-math notation="LaTeX">$N - 1$ </tex-math></inline-formula> intermediate orbits to describe the orbit transfer scheme. The eccentricity vector of the intermediate orbits and the true anomalies corresponding to the impulsive points are chosen as the optimization variables. Based on the patched conic theory, candidate solution can be analytically derived, constraints are removed from the optimization model, and the original problem is converted to a parameter optimization problem. The only difficulty lies in the initialization because the number of optimization variables increases linearly with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>, which can be very large. This is settled by a hybrid optimization algorithm that comprises two searching methods. The problem is solved first by an improved particle swarm optimization method and, then, by an adaptive conjugate gradient method. The proposed method is adaptive to problems with any finite <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> and can calculate the optimal <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> in any transfer scenarios. The simulation validates the proposed method with some well-known cases and demonstrates its adaptation to <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>.

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