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An eigenaxis tracking control algorithm is presented to provide rapid attitude tracking and synchronized rotation for on-orbit-servicing spacecraft. Based on the relative motion error dynamic equation, the algorithm uses the strategy similar with the move-to-rest attitude maneuver and imports a parameter describing the deviation degree from eigenaxis as feedback to ensure the whole tracking is an eigenaxis rotation. Finally, It carries out the simulation. And the results indicate the smooth maneuver process, high error accuracy, short tracking path and near optimal time are achieved after the whole tracking.