The paper studies the two-body coupling dynamics between the space platform and server while launching process, as well as energy saving optimization of the double pulse control of the server during rendezvousing and docking to the target satellite. Firstly, the space platform forms an orbiting relationship with the target satellite, keeping its launch tube axis aiming at the target satellite. After receiving the launch command, the server shoots out from the launch tube. The Kane method is used to establish the platform-server two-body dynamics model. Due to the effect of the coupling of the two-bodies, the attitude of the platform is perturbed, causing the server unable to accurately aim at the target satellite while separating the tube. Two velocity pulses are applied to the server through its small rocket engine. The initial pulse occurs at the moment when the server is separating the tube, changing its course to ensure accurate rendezvous with the target satellite; the end pulse occurs at the moment when the server rendezvous to the target satellite, reducing its relative velocity to zero to achieve soft docking. The optimization index is the least energy-efficient, that is to minimize the sum of the squares of the two pulse amplitudes. The paper summarizes it as a nonlinear programming problem. Under the condition that the rendezvous flight time is small compared to the period of the platform orbiting the target satellite, the average angular velocity of the orbiting flight can be regarded as a small parameter, and the canonical perturbation method can be used to obtain the first-order approximate solution of the nonlinear programming. Then the optimizing iteration process is started from the approximate solution as its initial guess. Finally, a numerical simulation verification is carried out.