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This paper presents the finite-time attitude synchronization and tracking control method of undirected multi-spacecraft formation with external disturbances. First, a modified adaptive nonsingular fast terminal sliding mode surface (ANFTSMS) is designed by introducing a user-defined function, both of which avoid the singularity problem and continuous sliding surface, and, therefore, can freely adjust relative weighting between angular velocity error and attitude error adaptively, such that the controller can provide sufficient maneuvers and precision. This provides designers with a new technique to adjust and improve formation control performance. Second, by applying the ANFTSMS associated with adaptation, two proposed decentralized ANFTSM-controllers provide finite-time convergence, robustness to disturbance, and chattering free for continuous design. Finally, simulation results validate the proposed algorithms.

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Purpose -The purpose of this paper is to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft. Design/methodology/approach -Based on the concept of fractionated spacecraft, orbit design requirements for cluster flight in the case of fractionated spacecraft are proposed, and categorized into three requirements: stabilization requirement, passive safety requirement, and the maximum inter-satellite distance requirement. These design requirements are then reformulated in terms of relative eccentricity and inclination vectors (E/I vectors) using a relative motion model based on relative orbital elements (ROEs). By using ROEs theory, the cluster flight orbit design issue is modelled as the distribution of relative E/I vectors for each member satellite in the cluster, and solved by combining three different heuristic search methods and one nonlinear programming (NLP) method. Findings -The simulation results show that the NLP method is valid and efficient in solving the cluster flight orbit design problem and that for some cluster flight scenarios, the heuristic search methods can be adopted to give feasible solutions without the NLP method.Research limitations/implications -The cluster flight scenario in this paper is limited because the cluster should be in the near-circular low earth orbit (LEO), and the relative distance between the member satellites should be small enough to satisfy the relative motion linearization assumption. Practical implications -The cluster flight orbit design method proposed in this paper can be applied by fractionated spacecraft mission designers to propose potential cluster flight orbit solutions. Originality/value -In this paper, the relative E/I vectors method is adopted to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.