Optimal Continuous-Thrust Orbit Transfers

摘要

The minimum time orbital transfer problem for spacecraft with steerable,continuous thrust of constant magnitude may be solved using Euler-Lagrange theory, which leads to the optimal control law in terms of Lagrange multipliers. Using analytical and empirical results, the optimal initial costates are modeled as functions of the problem parameters which are the initial thrust acceleration, A, and the final orbit radius, H, in canonical units. For circle to circle, coplanar orbit transfers, these approximate initial costate models lead to convergence in the shooting method for all practical values of A and H. The models also lead to convergence for a wide rang of other problems, including circle to hyperbola transfers and non-coplanar transfers. To counter the extreme sensitivity to small changes in the initial costate conditions, a dynamic step limiter is introduced which improve the convergence properties.