Optimal short-range rendezvous using on-off constant thrust

A control parameter direct optimization method for the optimal short-range elliptic orbit rendezvous problem using on-off constant thrust is proposed. This method is based on analytical state propagation expressions for linear relative motion under on-off constant control acceleration. This avoids numerical integration for the orbit dynamic equations. Normalized optimization variables are introduced to replace switching times. Then this problem is transformed into a nonlinear programming problem with bound constraints on the optimization variables and terminal equality constraints. The along-track and cross-track thrusts are used for the in-plane and out-of-plane motions, respectively. Both the minimum-fuel and minimum-time solutions are obtained by using the Matlab function fmincon. Numerical examples are provided to verify the proposed method. The results indicate that the proposed method is accurate and fast.