A hybrid control framework for impulsive control of satellite rendezvous

We focus on the problem of satellite rendezvous between two spacecraft in elliptic orbits. Using a linearized model of the relative dynamics, we first propose a periodic similarity transformation based on 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 trade-offs between computational complexity and fuel consumption. The adopted hybrid formalism allows us to prove suitable stability properties of the proposed controllers. The results are comparatively illustrated on simulation examples.