Low-thrust trajectory design as a constrained global optimization problem

Abstract

The design of a spacecraft trajectory can be formulated as a global optimization task. The complexity of the resulting problem depends greatly on the final target planet, the chosen spacecraft intermediate route, and the type of engine and power system available on-board. Few attempts have been made to directly use a global optimization framework to design trajectories that make use of low-thrust propulsion because of the large scale and extreme complexity of the resulting non-linear programming problem. The presence of non-convex constraints, in particular, requires the use of solvers able to deal with such an added complexity. Here, the Sims–Flanagan transcription method is proposed to model the low-thrust trajectory design as a constrained global optimization problem. Then, two different solvers are applied: basin hopping and simulated annealing with adaptive neighbourhood. Both algorithms are hybridized with a local search. Two different interplanetary trajectories are considered: an Earth–Earth–Jupiter transfer with a nuclear electric propulsion spacecraft inspired by the Jupiter Icy Moons Orbiter and a transfer to Mercury inspired by the BepiColombo mission. For both problems, the proposed approach proves to be able to explore automatically the vast solution space, producing a large number of trajectories in a large range of final mass and flight times, proving the possibility to apply global optimization techniques directly to the low-thrust problem.

Automated Interplanetary Trajectory Planning

“…Vavrina and Howell [16] used a GA to choose initial values for their GALLOP program, which uses the Sims-Flanagan transcription method along with an NLP solver. Most recently, Yam, Di Lorenzo, and Izzo [17] used monotonic basin hopping (MBH) along with the Sims-Flanagan transcription to quickly and reliably solve low-thrust problems.…”

“…As in the original EMTG, an integer genetic algorithm is used to choose the sequence of planets to use for gravity assist maneuvers. The trajectory is then modelled using the Sims-Flanagan transcription, and a variant of monotonic basin hopping similar to that used in [17] is used to find the optimal trajectory for each candidate flyby sequence.…”

Automated Solution of the Low-Thrust Interplanetary Trajectory Problem

“…Recent research in low-thrust trajectory optimization has led to the creation of stochastic search methods that do not require an initial guess [32,33,34,28,17,11,35,18,36,37,38,19]. These methods are naturally suited for use in an HOCP framework.…”

“…The first example case is a low-thrust mission to Mercury, based on a version of ESA's Bepi-Colombo mission [43,44,17]. BepiColombo will use low-thrust electric propulsion and flybys of Venus and Mercury to reach its final orbit about Mercury.…”

“…A problem may have several such funnels. MBH was originally developed to solve molecular conformation problems in computational chemistry, but has been demonstrated to be effective on various types of interplanetary trajectory problems [16,17,40,35,18,36,41]. MBH is a two-stage solver that alternates back and forth between a stochastic global search stage and a deterministic NLP stage.…”