Optimal orbital rendezvous using genetic algorithms

This paper examines the rendezvous of spacecraft using a Genetic Algorithm (GA). The solution of the optimal rendezvous contains many local optima, along with discontinuities in the solution. This makes locating a global optimal solution difficult. The GA is effective in solving these kinds of problems. Conventional calculus-based optimization methods are not effective with these kinds of problems because the optima they seek are the best in the neighborhood of the current point and they depend upon the existence of derivatives, so it requires an accurate initial guess to identify promising trajectories. Unfortunately, it is not apparent how to determine the initial guess, resulting in the need for a great number of trials. The goal of the optimization is to find the thrust time history that includes the magnitude and direction of the velocity change and the burn position (expressed by the true anomaly), such that the boundary conditions are satisfied to an acceptable level and in a reasonable time. In addition, the number of thrust arcs and the maximum magnitude of the velocity change can be regulated. This method was used on three test cases: 1) the Hohmann transfer, 2) the bi-elliptic transfer and 3) rendezvous with two impulses. The results of the Hohmann and the bi-elliptic transfers almost match analytical solutions (within the resolution of the variables of the GA). Although the result from the rendezvous with two impulses is not exact, the configuration of the trajectory is similar to the analytical solution.