The Computation of Optimal Rendezvous Trajectories Using the Sequential Gradient-Restoration Algorithm

摘要

This paper describes the formulation and numerical investigation of the thrust function required to minimize time or fuel usage for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max thrust acceleration via the Sequential Gradient-Restoration Algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, two of which determine the thrust direction in space and one which determines the thrust magnitude.rnThe main conclusion is that the optimal control distribution can result in two, three, or four subarcs depending on the performance index and the constraints. The time-optimal case results in a two-subarc solution with max thrust. The fuel-optimal case results in a four subarc solution consisting of an initial coasting period, followed by a maximum thrust phase, followed by another coasting period, followed by another maximum thrust phase. Regardless of the number of resulting subarcs, the optimal thrust distribution requires the thrust magnitude to be either at the maximum value or at zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust.