Fuel-optimal and low-thrust rendezvous in elliptical orbits with fixed terminal-approach direction

The bounded low-thrust, fuel-optimal, and fixed terminal-approach direction rendezvous in elliptical orbits is investigated. In a novel frame of reference, called the Docking coordinate system, a linearized dynamic model is established, which is suitable for rendezvous with fixed terminal-approach direction. Then, a two-stage maneuver is developed: in the first stage, the chaser moves from the initial point to an intermediate point, whose perpendicular projection onto the terminal-approach direction lies in the positive side of the target (the terminal-approach direction points in the negative side); in the second stage, the chaser transfers to the target with the fixed terminal-approach direction guaranteed. By a novel piecewise Legendre-Gauss-Radau pseudospectral method, the two-stage fuel-optimal rendezvous is transformed into a reduced-dimension quadratic programming. The overall fuel consumption as a function of the time proportion of the first stage with respect to the total rendezvous time is minimized. Numerical results prove the advantages of the proposed approach.