Successive Convexification for Tethered Debris Deorbiting

Tether-based debris removal methods present a promising option for the mitigation of large space debris in the near Earth orbital regime. A necessary component of these methods is the deorbiting phase, where the debris is removed from its initial orbit by the action of an active spacecraft. However, further development of onboard guidance and control for tethered satellite system (TSS) is required. For this purpose, a planar model of the system is constructed which includes the chaser and target as point masses connected by a flexible tether. Then, a minimum-time optimal control problem for this model is developed and discretized to fit the requirements of a sequential convex programming algorithm – specifically successive convexification (SCvx). An additional problem, in which the minimum-time cost is augmented with a term that penalizes the libration rate, is introduced to reduce the oscillatory motion present in the libration angle and tether length. The resulting augmented problem converged in less iterations and with less oscillatory libration motion compared to the original problem. The time of flight for the augmented problem solution amounted to only a few seconds more than the original problem, indicating that the SCvx algorithm can be used effectively for the tethered debris deorbiting problem.