Suboptimal power-limited rendezvous with fixed docking direction and collision avoidance

This paper investigates the optimal-fuel rendezvous with power-limited propulsion systems, fixed docking direction, and collision avoidance. A linearized dynamic model is established based on the Hill-Clohessy-Wiltshire equations. This model is effective for rendezvous in both circular and elliptical orbits. To guarantee the final docking direction, the rendezvous mission is divided into two stages. In the first stage, the chaser moves to an intermediate point that is on the docking direction; in the second stage, the chaser approaches the target along the opposite direction of the docking. Collisions are prevented through setting a lower bound upon the distance between the intermediate point and the target. Then, a two-stage Gauss pseudospectral method is proposed to transform the trajectory-optimization problem into a reduced-dimension quadratic programming problem. Numerical simulations show that the proposed method 1) can deal with both circular and elliptical cases, 2) can guarantee the docking direction without collisions, and 3) can generate the suboptimal trajectory rapidly.