Optimal power-limited rendezvous of a spacecraft with bounded thrust and general linear equations of motion

The solution of the fixed-time optimal power-limited rendezvous with a general linear system of ordinary differential equations and a bound on the magnitude of the applied thrust is presented. Necessary and sufficient conditions for thrust saturation in an optimal solution are included. Because of the generality of the linear system of equations of motion, controllability considerations are required for a complete solution of this problem. It is shown that the condition of controllability can be defined completely in terms of a class of primer vectors associated with this problem. Moreover, it is shown that two distinct versions of the primer vector appear in this problem. Therefore, there is not a unique primer vector associated with every rendezvous problem. The work is applied to the problem of the rendezvous of a spacecraft near a satellite in circular orbit. The optimal rendezvous trajectory is determined by the interaction of a primer vector and the bound on the thrust magnitude. The results of computer simulations are presented graphically.