Genetic Algorithm and Calculus of Variations-Based Trajectory Optimization Technique

Abstract

A genetic algorithm is used cooperatively with the Davidon‐Fletcher‐Powell penalty function method and the calculus of variations to optimize low-thrust, Mars-to-Earth trajectories for the Mars Sample Return Mission. The return trajectory is chosen thrust-coast-thrust a priori, has a fixed time of flight, and is subject to initial and final position and velocity equality constraints. The global search properties of the genetic algorithm combine with the local search capabilities of the calculus of variations to produce solutions that are superior to those generated with the calculus of variations alone, and these solutions are obtained more quickly and require less user interaction than previously possible. The genetic algorithm is not hampered by ill-behaved gradients and is relatively insensitive to problems with a small radius of convergence, allowing it to optimize trajectories for which solutions had not yet been obtained. The use of the calculus of variations within the genetic algorithm optimization routine increased the precision of the final solutions to levels uncommon for a genetic algorithm.