Distributed Control of 6-DOF Leader-Following Multi-Spacecraft Formation near an Asteroid Based on Scaled Twistors
Bo Zhang, Jing Chen, Binxing Hu
Abstract
This paper addresses the distributed six-degree-of-freedom (6-DOF) control problem of translation-rotation coupled spacecraft formation in the vicinity of an asteroid. Due to the complicated gravity field of an asteroid, there exist no circular or elliptic orbits for the spacecraft, which renders the control schemes designed for the spacecraft formation near the Earth inapplicable. In the framework of twistors, a distributed leader-following control scheme is proposed by combining the dynamic surface technique and consensus theory under an undirected communication topology. First, a scaled-twistor-based position-attitude coupled dynamic model of the spacecraft near an asteroid is established to circumvent numerical difficulty. Since the state of the leader can only be accessed by a subset of the followers, an observer is integrated into the control scheme to estimate the state of the leader for each follower. Then, the pose error between each follower and its desired pose is represented by the scaled twistor. Based on the error dynamics, virtual control is designed according to the consensus theory, and a distributed control law is proposed via the dynamic surface method. To eliminate the large control effort and aggressive transient in the initial phase, adaptive gains are introduced into the control scheme. Furthermore, neural networks (NNs) are used to compensate for not only the external disturbances but also the filter errors resulting from the dynamic surface method. By virtue of the Lyapunov theory, it is proved that the pose errors of the followers are ensured to converge to the neighborhood of the origin, and all the adaptive gains and weights of the NNs are bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.