Distributed 6-DOF Adaptive Control of Multi-spacecraft Formation Using Scaled Twistors

This paper addresses the control problem of six-degree-of-freedom (6-DOF) multi-spacecraft formation flying in the vicinity of an asteroid under an undirected communication topology in the presence of uncertainties and disturbances. To cope with the issue that the real and dual parts of the twistor that represents the pose of a spacecraft are not in the same order, a scaled-twistor-based dynamic model is established for each spacecraft to avoid numerical difficulties in computation. On the basis of the scaled twistor model, a new distributed sliding surface is devised for the multi-agent system with a connected undirected communication graph. Then, a distributed control scheme is developed by combining the backstepping technique and sliding mode control theory under the assumption that the inertial parameters of the spacecraft and the upper bound of the external disturbances are known. To adapt to the uncertain inertial character of the spacecraft and external disturbances, adaptive laws are designed to estimate the inertial parameters and the upper bound of the disturbances to substitute for the corresponding assumed values in the controller. Finally, the stability of the whole closed-loop system is proved via Lyapunov stability theory. Numerical simulations are carried out to demonstrate the effectiveness of the proposed scheme.