Parallel optimization of trajectory planning and tracking for three-body tethered space system

This paper develops a new piecewise parallel optimal control scheme to suppress the libration of a three-body tethered system in circular orbits with a climber. Optimal control is achieved by controlling the tension in tether via regulation of tether length at the end body and the climber speed to minimize the Coriolis' effect. Thus, the total tether length of the system is no longer constant, which is different from the classical three-body tethered system and more effective in libration suppression. To facilitate the space implementation, the original optimal control scheme is split into two parallel phases on a dual-CPU system to reduce computational burden. Phase I predicts an optimal reference state trajectory for the next time interval piecewise by an open-loop optimization with a grossly simplified three-body tethered system model. Phase II tracks the predicted reference trajectory at the current time interval simultaneously by a closed-loop receding horizon control using a full dynamic model. The simulation results reveal that the newly proposed parallel optimal control scheme is able to suppress the libration of the three-body tethered system by controlling tether tension only. Moreover, by controlling the climber's speed adaptively, the libration angles of the tethered system can be suppressed with a shorter transfer period compared with the constant climber speed.