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.