Two finite-time control algorithms are developed for distributed cooperative attitude synchronisation of multiple spacecraft with a dynamic virtual leader. Each spacecraft is modelled as a rigid body incorporating with model uncertainty and unknown external disturbance. The virtual leader gives commands to some of the follower spacecraft, and the communication network between followers can be an undirected or a directed graph. By using two neighbourhood synchronisation error signals, a finite-time control algorithm is designed associated with adaptive mechanism such that all follower spacecraft synchronise to the virtual leader in finite time. Then a novel estimator-based finite-time distributed cooperative control algorithm is developed by using the followers' estimates of the virtual leader, and the convergence of the attitude and angular velocity errors can be guaranteed in finite time. Moreover, both of the control strategies are chattering-free for their continuous design. Simulation examples are illustrated to demonstrate the validity of the two algorithms.
IntroductionResearch on attitude control of spacecraft, especially attitude synchronisation among multiple spacecraft, has long been of interest in recent years because of the theoretical significance and broad applications [1][2][3][4][5][6][7][8][9][10][11][12]. For instance, in deep space exploration, a coordinated cluster of micro-satellites can replace the traditional large and expensive spacecraft to complete a common task, and such schemes can offer the superiorities of low cost, high flexibility, high impact and so on. Besides that, the requirement of keeping the precise relative attitude is essential in inter-spacecraft laser communication operation. This study can also be applied to formation manoeuvres in interferometry application, stereo imaging, passive radiometry, terrain mapping and so on [8,13]. Some solutions about attitude control problem for multiple spacecraft can be found in [7,[14][15][16][17][18]. However, they did not consider the model uncertainties or unknown disturbances. A virtual systems-based control algorithm was proposed for the attitude synchronisation problem in [7] without using the angular velocity measurements, it provided a new approach to address the timevarying communication delays and angular velocity unavailable together. A formation flying control problem of multiple spacecraft was studied in [16] by using a novel fast terminal sliding manifold (FTSM) and adaptive control, and a distributed attitude coordination control scheme was developed with a constraint about the initial condition to achieve finite time convergence. Similar to [16,17] also relied on a constraint about the initial condition and proposed a distributed output feedback attitude coordination control algorithm for spacecraft formation flying without using the angular velocities. A leader-following consensus problem was investigated in [18] for multiple rigid spacecraft, by applying a non-linear distributed observer, a distributed control scheme ...