Trajectory Optimization Using Global Methods

This paper compares three different global indirect approaches for solving the problem of finding optimal trajectories for low thrust spacecraft. The three methods tested were downhill simplex, genetic algorithms and simulated annealing. Two problems are analyzed. The first is a planar low thrust problem. This is the problem of finding a minimum time trajectory from Earth to Mars orbit using a fixed thrust electric propulsion system. The second problem is the 3 dimensional problem of orbit transfer into an inclined heliocentric orbit. Global optimization methods have the advantage of not requiring a good initial guess for the costates, or for the controls, and having some ability to avoid falling into local minima. In addition because they employ the costate equations, only a small number of parameters are needed to determine the trajectory. This paper explores the use of global methods and introduces a methodology for evaluating global methods for use in optimization. Details such as the creation of scalar cost functionals and termination conditions for numerical integration are discussed. The results show that with a reasonable amount of work by the analyst all of the global methods employed in this paper can be used successfully to obtain solutions to 2D and 3D trajectory optimization problems.