Study on two methods for tethered satellites' punctual transfer to the release position

Two ways to make a tethered satellite reach the desired position at the specified time are proposed. One is based on the planning method using a polynomial function, and the other is based on the method using the Gauss Pseudospectral. The former plans the state trajectory by using a polynomial function, which can make the satellite reach the desired position at the specified time and make the transfer trajectory more smooth. The latter plans the state and control trajectory by using the Gauss Pseudospectral, which can make the satellite reach the desired position at the specified time and make the power optimal. The proposed method can not only be used to implementation of geostationary, cislunar, or deep space exploration transfer orbits, but also it can be used in the specified orbit capture. The simulation results verify the validity of the proposed approaches.