Tethered satellite retrieval based on subsatellite's movement arc and linear velocity

It is discovered that the new states, the subsatellite's movement arc and linear velocity that are composed by the tether's length and pitch angle, as well as their derivative, are subject to the ellipse equation in the phase plane that consists of the two new states. According to the property, during the retrieval process the new states are driven to transfer among some ellipses by thrusters installed on the subsatellite. In this way the new states can be driven to the vicinity of zero and made not leave the vicinity again. Then the corresponding original states, tether's length and pitch angle, as well as their derivative, will reach the expectative precision. The results of simulations illustrate that the control approach of tethered satellite retrieval is effective.