Optimal impulsive rendezvous for highly elliptical orbits using linear primer vector theory

In this paper, minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic. To this end, the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target. Lawden's primer vector theory is then applied on this linear but time-varying system. The analytical solution of the required primer vector for this problem is then derived by using a recently developed method. For the existing non-optimal solutions which don't satisfy the conditions, the methods are further designed to improve the performance by shifting impulses or adding a new one. Finally, two algorithms are developed for free-impulse time-fixed rendezvous problems. The first algorithm can determine the globally optimal trajectory with the optimal number of impulses. The second one enables for fast trajectory planning. The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.