Orbital rendezvous performance comparison of differential geometric and ZEM/ZEV feedback guidance algorithms

In this paper, the performance of two distinct classes of feedback guidance algorithms is evaluated for a spacecraft rendezvous problem utilizing a continuous low-thrust propulsion system. They are the DG (Differential Geometric) and ZEM/ZEV (Zero-Effort-Miss/Zero-Effort-Velocity) feedback guidance algorithms. Even though these two guidance algorithms do not attempt to minimize the onboard fuel consumption or $\mathrm{\Delta }V$ directly, the $\mathrm{\Delta }V$ requirement is used as a measure of their orbital rendezvous performance for various initial conditions and a wide range of the rendezvous time (within less than one orbital period of the target vehicle). For the DG guidance, the effects of its guidance parameter and terminal time on the closed-loop performance are evaluated by numerical simulations. For the ZEM/ZEV guidance, its near- fuel-optimality is further demonstrated for a rapid, short-range orbital rendezvous, in comparison with the corresponding open-loop optimal solutions. Furthermore, the poor $\mathrm{\Delta }V$ performance of the ZEM/ZEV guidance for a slow, long-range orbital rendezvous is remedied by simply adding an initial drift phase. The ZEM/ZEV feedback guidance algorithm and its appropriate variants are then shown to be a simple practical solution to a non-impulsive rendezvous problem, in comparison with the DG guidance as well as the open-loop optimal guidance.