Optimal low-thrust linearized elliptic orbit rendezvous considering the communication window

The optimal low-thrust linearized elliptic orbit rendezvous problems are studied for both continuous thrust and piecewise constant thrust considering the communication window constraint. Based on the analytical state propagation expressions for linear relative motion under on–off constant thrust, the analytical energy-optimal solution using piecewise constant thrust is derived by the Lagrange multiplier method for given switching time points. This solution is further extended to obtain the analytical energy-optimal solution using continuous thrust. For the piecewise constant thrust with free switching time points, the fuel-optimal problem is formulated as a nonlinear programming problem, which is solved by a modified differential evolution algorithm. In addition, the derived analytical energy-optimal solution for given switching time points is used to reduce the number of optimization variables, and it is numerically proven to effectively reduce the optimization time. Several examples are presented to show the effectiveness of the proposed method for the low-thrust orbit rendezvous problem considering the communication window constraint.