Optimal impulsive relative orbit transfer along a circular orbit

The relative orbit transfer problem associated with the Hill-Clohessy-Wiltshire equations is considered, and the open-time minimum-fuel problem with impulsive control is formulated. In particular, between two elliptic relative orbits of the in-plane motion, optimal three-impulse controllers are constructed. For the out-of-plane motion, optimal single-impulse strategies are obtained. Based on these results and the null controllability with the vanishing energy of the Hill-Clohessy-Wiltshire equations, a design method of feedback controllers with a total velocity change close to the optimal one is proposed. It is shown by simulation results that asymptotic relative orbit transfer is fulfilled by the proposed feedback controllers.