The paper presents an asymptotic stabilization strategy for the deployment of a controlled tethered satellite system in three-dimensional space, in which the tether length rate is taken as the control variable. Firstly, a rigid-rod tether model is employed to establish the nonlinear dynamic equations of in-plane and out-of-plane motions of the system. Then, by stability analysis of the linearized system at a preassigned direction to deploy, the control law and asymptotic stability condition for the deployment are obtained. The electrodynamic tethered satellite in equatorial plane is discussed. As a result, the large swing motions during deployment are stabilized asymptotically through reliance on the electrodynamic force and the tether length rate. The case studies in the paper well demonstrate the proposed stabilization control strategy.
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