An evolutionary discretized Lambert approach for optimal long-range rendezvous considering impulse limit

Abstract In this paper, an approach is presented for finding the optimal long-range space rendezvous in terms of fuel and time, considering limited impulse. In this approach, the Lambert problem is expanded towards a discretized multi-impulse transfer. Taking advantage of an analytical form of multi-impulse transfer, a feasible solution that satisfies the impulse limit is calculated. Next, the obtained feasible solution is utilized as a seed for generating individuals for a hybrid self-adaptive evolutionary algorithm to minimize the total time, without violating the impulse limit while keeping the overall fuel mass the same as or less than the one associated with the analytical solution. The algorithm eliminates similar individuals and regenerates them based on a combination of Gaussian and uniform distribution of solutions from the fuel-optimal region during the optimization process. Other enhancements are also applied to the algorithm to make it auto-tuned and robust to the initial and final orbits as well as the impulse limit. Several types of the proposed algorithm are tested considering varieties of rendezvous missions. Results reveal that the approach can successfully reduce the overall transfer time in the multi-impulse transfers while minimizing the fuel mass without violating the impulse limit. Furthermore, the proposed algorithm has superior performance over standard evolutionary algorithms in terms of convergence and optimality.