The paper presents the initialization condition for chaser flying around target and optimal keeping control algorithm to satisfy the requirement of on-orbit-servicing in eccentric orbits. The necessary condition for chaser fly around is presented by detailed analyzing with the time variant linear relative motion formula and resolution. Then, the condition for target to locate at the center of fly around cycle and the method to determine the shape and aperture of cycle are also presented. Considering the effect of perturbation, the paper designs a discrete LQR optimal controller with constraint control vector to keep chaser in scheduled cycle. And three control error boxes, which enable the controller work in the reasonable error areas and avoid much fuel be wasted for the measure error are designed. Finally, example design and simulation are carried out. The results are analyzed, and it is shown that the design method and control algorithm are rational and valid.
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