A Hybrid Control Framework for Impulsive Control of Satellite Rendezvous

We focus on the problem of satellite rendezvous between two spacecrafts in elliptic orbits. Using a linearized model of the relative dynamics, we first propose a periodic similarity transformation based on the Floquet-Lyapunov theory, leading to a set of coordinates under which the free motion is linear time-invariant. Then, we address the problem of impulsive control of satellite rendezvous as a hybrid dynamical system, and we show that the arising elegant representation enables designing impulsive control laws with different tradeoffs between computational complexity and fuel consumption. The adopted hybrid formalism allows to prove suitable stability properties induced by the proposed controllers. The results are comparatively illustrated on simulation examples.