TWISTOR BASED 6-DOF DISTRIBUTED ADAPTIVE LEADER-FOLLOWING CONTROL FOR MULTIPLE RIGID SPACECRAFT FORMATION

In the recently developed twistor framework, the distributed control of six-degree-of-freedom (6-DOF) multiple spacecraft leader-following formation is investigated in the presence of unknown external disturbances. A distributed adaptive controller is proposed under an undirected communication graph to guarantee that the formation flying and consensus of the attitudes of the leader and followers is reached simultaneously. Firstly, the 6-DOF dynamics of a rigid spacecraft modeled by twistors is presented, and the distributed control problem is formulated. Then, a distributed sliding surface is established for the system composed of the kinematics of the spacecraft. Based on the sliding surface, a sliding mode controller for the 6-DOF formation is proposed. For the unknown disturbances, an adaptive law is developed to estimate the upper bounds to substitute for the unknowns in the sliding mode controller. The stability of the closed-loop system is proved via Lyapunov stability theory. Finally, the effectiveness of the proposed protocol is demonstrated by numerical simulations.