Global Finite-Time Velocity-Free Hybrid Pose Control for Dual-Spacecraft Formation via Twistor Formulation

This article addresses the global finite-time pose control problem of a leader-following dual-spacecraft six-degree-of-freedom formation in the twistor framework, where velocity measurements of the follower spacecraft are not available. First, twistors are employed to describe the coupled pose motion of the follower spacecraft to eliminate redundant parameters and normalization constraints. Second, a uniformly globally finite-time stable controller without velocity measurement for the follower spacecraft is proposed by employing homogeneous theory, in which a hysteretic switching strategy is introduced based on a hybrid control method to avoid unwinding phenomena and enhance robustness to measurement noise. Subsequently, a hybrid filter is designed to provide damping for the controller due to the absence of velocity feedback. Finally, the uniform global finite-time stability is rigorously proved. The effectiveness of the proposed method is demonstrated by numerical simulations, and the results show that the position and attitude integral time-weighted absolute errors of the hybrid controller reduce by 3.34% and 29.74%, respectively, compared to those of the similar continuous controller.