Lyapunov Optimal Touchless Electrostatic Detumbling of Space Debris in GEO Using a Surface Multisphere Model

Abstract

High tumbling rates of uncooperative target pose strong technical challenges and collision risks that can prevent removal of the debris using contact, such as with robotic arms or capture nets. Electrostatic touchless detumbling is a promising technology that can be used to decrease the rotational velocity of an uncooperative object in geosynchronous orbit, from a safe distance. This paper demonstrates the advantages of applying a Lyapunov optimal control in conjunction with a surface multisphere model. This approach allows for the analysis of general shapes, eliminating the need for analytical approximations on debris shape and expected torque, employed by previous work. Moreover, using this model, the robustness of the system to uncertainties to the debris center of mass position is tested. This analysis uncovers an unstable phenomenon that was previously not captured using simpler models. An active disturbance rejection control ensures robustness of the system in the cases analyzed, also granting an increase in its effectiveness. It is shown in simulation that the system can exploit deviations in the center of mass to achieve a higher level of controllability and completely detumble all components of angular velocity.