Multi-Revolution Low-Thrust Trajectory Optimization Using Symplectic Methods. (arXiv:1901.02881v1 [physics.space-ph])

<a href="http://arxiv.org/find/physics/1/au:+E_Z/0/1/0/all/0/1">Zhibo E</a>, <a href="http://arxiv.org/find/physics/1/au:+Guzzetti_D/0/1/0/all/0/1">Davide Guzzetti</a>

Optimization of low-thrust trajectories that involve a larger number of orbit

revolutions is considered a challenging problem. This paper describes a

high-precision symplectic method and optimization techniques to solve the

minimum-energy low-thrust multi-revolution orbit transfer problem. First, the

optimal orbit transfer problem is posed as a constrained nonlinear optimal

control problem. Then, the constrained nonlinear optimal control problem is

converted into an equivalent linear quadratic form near a reference solution.

The reference solution is updated iteratively by solving a sequence of

linear-quadratic optimal control sub-problems, until convergence. Each

sub-problem is solved via a symplectic method in discrete form. To facilitate

the convergence of the algorithm, the spacecraft dynamics are expressed via

modified equinoctial elements. Interpolating the non-singular equinoctial

orbital elements and the spacecraft mass between the initial point and end

point is proven beneficial to accelerate the convergence process. Numerical

examples reveal that the proposed method displays high accuracy and efficiency.

Optimization of low-thrust trajectories that involve a larger number of orbit

revolutions is considered a challenging problem. This paper describes a

high-precision symplectic method and optimization techniques to solve the

minimum-energy low-thrust multi-revolution orbit transfer problem. First, the

optimal orbit transfer problem is posed as a constrained nonlinear optimal

control problem. Then, the constrained nonlinear optimal control problem is

converted into an equivalent linear quadratic form near a reference solution.

The reference solution is updated iteratively by solving a sequence of

linear-quadratic optimal control sub-problems, until convergence. Each

sub-problem is solved via a symplectic method in discrete form. To facilitate

the convergence of the algorithm, the spacecraft dynamics are expressed via

modified equinoctial elements. Interpolating the non-singular equinoctial

orbital elements and the spacecraft mass between the initial point and end

point is proven beneficial to accelerate the convergence process. Numerical

examples reveal that the proposed method displays high accuracy and efficiency.

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