Nonlinear suboptimal synchronized control for relative position and relative attitude tracking of spacecraft formation flying

This paper deals with the optimal tracking and synchronized control of leader-follower spacecraft formation flying, considering motion with 6 degree-of-freedom (6-DOF). The relative position and relative attitude between spacecrafts are required to track a desired time-dependent trajectory. Modeling of 6-DOF formation spacecraft is introduced firstly, applying dual quaternion in describing the coupled relative motion. A nonlinear suboptimal synchronized tracking controller is then proposed to perform two tasks: (1) to ensure globally asymptotic convergence of the translational and rotational tracking errors with parametric uncertainties and external disturbances considered, and (2) to minimize the predefined performance indices. In the proposed controller, the optimal control and the sliding mode control (SMC) operate in a complementary manner. A control Lyapunov function (CLF) is constructed to solve the nonlinear optimal control problem, whereas SMC is established to ensure robustness and achieve accurate control. A detailed stability analysis and proofs of the resulting closed-loop system using a Lyapunov framework are also included. Finally, illustrative numerical simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller.