Optimal rendezvous trajectory planning with time constraint

The problem of fuel-optimal rendezvous with time constraint was considered based on the linearized Clohessy-Wiltshire equations. The rendezvous time was either specified or restricted to be less than an upper limit. The specific boundary point, on that the optimal number of impulses would be changed or a terminal coast would be included or not, was analytically found. The necessary and sufficient conditions for the boundary points were derived. Furthermore, the iterative algorithm for the optimal fixed-time, multi-impulse solutions was developed. According to the necessary and sufficient conditions of the specific boundary points, either the relationship between the characteristic velocity and the rendezvous time or the range of the optimal solutions with different impulses can be easily obtained, only needs calculating the optimal solutions of the specific points. Several simulation examples with a variety of initial conditions demonstrate the method of this paper