Optimal Low-Thrust Docking with a Constrained Approach Direction Using Two Intermediate Points

In this paper, a new optimal-control-based guidance law for a perfect rendezvous from a predetermined terminal approach direction, i.e., docking, is derived. The guidance law softly constrains the chaser to pass through two intermediate points located in the desired approach direction, in addition to the rendezvous soft constraint at the end of the scenario and the minimization of the control effort. As a result, the chaser tends to keep its motion in the desired approach direction. An analytical, open-loop solution is derived, and a closed-loop algorithm is presented as well. The designer determines the intermediate points’ locations, while the speeds at these points are obtained by a secondary minimization process whose performance index is also determined by the designer. This paper presents two secondary performance indexes: The original problem’s cost function and the minimum deviation indexes. Simulations demonstrate the performance of the proposed guidance law, showing small miss distances, velocity misses, and angle misses. It is concluded that the new proposed guidance law brings the chaser to a perfect rendezvous with the target in the desired approach direction. Moreover, the approach trajectory can be shaped via different secondary optimization criteria.