Fuel-optimal space trajectories in the Euler-Hill frame represent a subject of great relevance in astrodynamics, in consideration of the related applications to formation flying and proximity maneuvers involving two or more spacecraft. This researchisbased uponemployinga Hamiltonianapproachtodetermining minimum-fuel trajectories of specified duration. The necessary conditions for optimality (that is, the Pontryagin minimum principle and the Euler-Lagrange equations) are derived for the problem at hand. A switching function is also defined, and it determines the optimal sequence and durations of thrust and coast arcs. The analytical natureof the adjoint variables conjugateto the dynamics equations leadstoestablishing useful properties of these trajectories, suchasthe maximum number of thrust arcs in a single orbital period and a remarkable symmetry property, which holds in the presence of certain boundary conditions. Furthermore, the necessary conditions allow translating the optimal control problem into aparameter optimization problem withafairly small parameter set composedofthe unknown initial valuesofthe adjoint variables. A simple swarming algorithm is chosen among the different available heuristic techniques as the numerical solving algorithm, with the intent of finding the optimal values of the unknown parameters. Five examples illustrate the effectiveness and numerical accuracy of the indirect heuristic method applied to optimizing orbital maneuvers in the Euler-Hill frame.
ASJC Scopus subject areas
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics