Optimal spacecraft rendezvous by minimum velocity change and wait time

An optimization problem is investigated in this paper to obtain a minimum velocity change, sometimes called as minimum-energy, to rendezvous a target spacecraft. The problem formulation starts with known initial positions and velocity vectors of two spacecraft, so-called target and chaser, respectively. The Kepler's time-of-flight equation in terms of the universal variables and the relationship between final position vectors of the two spacecraft are posed as constraints. Three-dimensional orbital information is obtained by using the f and g solution that called the Lagrange coefficients. One of advantages for the universal variables is that it provides total orbital information valid for all conic orbits without much numerical difficulty. The wait time concept is also employed to release the magnitude of velocity changes by minimizing the performance index. Finally, these techniques are demonstrated using numerical simulations.