Computation of optimal Mars trajectories via combined chemical/electrical propulsion, part 1: baseline solutions for deep interplanetary space

Abstract

The success of the solar-electric ion engine powering the DS1 spacecraft has paved the way toward the use of low-thrust electrical engines in future planetary/interplanetary missions. Vis-à-vis a chemical engine, an electrical engine has a higher specific impulse, implying a decrease in propellant mass; however, the low-thrust aspect discourages the use of an electrical engine in the near-planet phases of a trip, since this might result in an increase in flight time. Therefore, a fundamental design problem is to find the best combination of chemical propulsion and electrical propulsion for a given mission, for example a mission from Earth to Mars. With this in mind, this paper is the first of a series dealing with the optimization of Earth–Mars missions via the use of hybrid engines, namely the combination of high-thrust chemical engines for planetary flight and low-thrust electrical engines for interplanetary flight. We look at the deep-space interplanetary portion of the trajectory under rather idealized conditions. The direct objective is to minimize the propellant consumption while containing the flight time; the indirect objective is to generate a nominal trajectory of easy implementation for guidance. We study the trajectory of a spacecraft controlled via the thrust direction and magnitude. We consider four control models. In Model 1, the thrust magnitude is set at the maximum value and the thrust direction is optimized. This results in a continuously varying thrust direction and a two-subarc trajectory. While the tangential component of the thrust is mostly directed forward, the normal component is directed upward in the first subarc and downward in the second subarc. The switch from the first subarc to the second is needed to shorten the flight time, albeit at the expense of higher propellant consumption. In Model 2, the thrust direction is assumed tangent to the trajectory and the thrust magnitude is optimized. This results in a three-subarc trajectory having a bang-zero-bang thrust magnitude profile, of particular interest in guidance because of its simplicity. Vis-à-vis Model 1, the trajectory optimizing Model 2 exhibits a significant decrease in propellant consumption, albeit at the expense of an increase in flight time. In Model 3, the thrust direction and magnitude are simultaneously optimized. For the minimum time problem, the solution of Model 3 reduces to that of Model 1. For the minimum propellant consumption problem, the solution of Model 3 reduces to that of Model 2. In Model 4, which is a discrete version of Model 2, the thrust direction is assumed tangent to the trajectory and the thrust magnitude is optimized in the class of controls allowed to have only two values: maximum thrust and zero thrust. The solution of this problem is identical with that of Model 2. For Models 1–3, the optimization problems were solved with the sequential gradient-restoration algorithm in either single-subarc form or multiple-subarc form. For Model 4, due to the specific problem structure, the solution was found with the modified quasilinearization algorithm.