Abstract

In this paper, we use differential evolution (DE), with best-evolved results refined using a Nelder–Mead optimization, to solve boundary-value complex problems in orbital mechanics relevant to low Earth orbits (LEO). A class of Lambert-type problems is examined to evaluate the performance of this evolutionary method in its application to solving nonlinear boundary value problems (BVP) arising in mission planning. In this method, we evolve impulsive initial velocity vectors giving rise to intercept trajectories that take a spacecraft from given initial position in space to specified target position. The positional error of the final position is minimized subject to time-of-flight and/or energy (fuel) constraints. The method is first validated by demonstrating its ability to recover known analytical solutions obtainable with the assumption of Keplerian motion; the method is then applied to more complex non-Keplerian problems incorporating trajectory perturbations arising in low Earth orbit (LEO) due to the Earth’s oblateness and rarefied atmospheric drag. The viable trajectories obtained for these challenging problems demonstrate the ability of this computational approach to handle Lambert-type problems with arbitrary perturbations, such as those occurring in realistic mission trajectory design.

Highlights

  • The planning of orbital maneuvers and/or trajectories for spacecraft represents a design optimization problem that is associated with multiple engineering constraints

  • Upon examination of the results, three types of results were apparent: (i) infeasible trajectories that ended up at P2 but that intersected the Earth, (ii) trajectories that ended up hundreds or thousands of km from P2

  • The focus of this study has been to investigate the utility of a differential evolution (DE)-based approach for spacecraft trajectory planning under the realistic orbital conditions that would be present in the low Earth orbits (LEO) and

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Summary

Introduction

The planning of orbital maneuvers and/or trajectories for spacecraft represents a design optimization problem that is associated with multiple engineering constraints (e.g., time of flight, fuel consumption, and positional accuracy). With the emergence of satellite formation-flying mission concepts, additional constraints are often required in order to achieve satisfactory performance. The satellite formation topology may be required to satisfy a specified criterion during a finite portion of the orbit for the purposes of coordinated measurements. Owing to the multiple objectives and system complexity, analytical approaches to trajectory optimization are generally not available and numerical optimization is required. To this end, various evolutionary approaches for trajectory optimization have been explored over the past two decades. Various evolutionary approaches for trajectory optimization have been explored over the past two decades. evolutionary computing (EC) and optimization has since emerged as a means for dealing with highly constrained mission profiles for primarily interplanetary trajectories

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