Rendezvous Guidance Trajectories via Multiple-Subarc Sequential Gradient-Restoration Algorithm

Abstract

We consider the three-dimensional rendezvous between a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and an initial separation velocity. We assume that the chaser spacecraft has variable mass and that its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We employ the Clohessy–Wiltshire equations, describing the relative motion of the chaser vis-a-vis the target, and the multiple-subarc sequential gradient-restoration algorithm to produce first optimal trajectories and then guidance trajectories for the following problems: P1—minimum time, fuel free; P2—minimum fuel, time free; P3—minimum time, fuel given; P4—minimum fuel, time given; and P5—minimum time×fuel , time and fuel free. Clearly, P1 and P2 are basic problems, while P3, P4, and P5 are compromise problems. Problem P1 leads to a two-subarc solution including a max-thrust subarc followed by another max-thrust subarc. Problem P2 ...