Near-Optimal Low-Thrust Earth-Mars Trajectories via a Genetic Algorithm

Abstract

A genetic algorithm is used to determine several types of Earth‐Mars trajectories, with the objective of maximizing payload delivered to Mars. The trajectories have three phases: Earth escape, heliocentric flight, and arrival into low Martian orbit. The actual planetary orbits are used with one approximation: Mars’s very small orbit inclination to the ecliptic plane is ignored. Impulses provided by chemical rockets are used for Earth departure and capture into orbit about Mars. The optimizer chooses the magnitude and direction of the impulse explicitly for the departure from Earth and implicitly, by choosing the hyperbolic excess velocity vector, for the arrival at Mars. The heliocentric flight uses low-thrust nuclear‐electric propulsion; cases with continuous thrust and cases in which a coasting, that is, a no-thrust phase, is allowed are both considered. The continuous time history of the thrust pointing angle is modeled using a sequence of cubic polynomials whose coefficients become parameters of the genetic algorithm’s chromosome. The fitness function of the genetic algorithm is dynamic; it first forces the spacecraft to arrive within the Martian sphere of influence. With that accomplished, it then emphasizes optimizing final mass.