Abstract: Considering the issue of rapidly tracking and long-term staring between two feature points attached to a chaser spacecraft and a tumbling target respectively, a new model for relative kinematically-coupled motion of two feature points is derived in feature point directing (FPD) frame originated in the target’s feature point, and the nonsingular terminal sliding mode (NTSM) technique is applied both for the relative orbit and the attitude control. Firstly, compared with the traditional point-mass models derived in target’s LVLH frame, the new proposed model not only reduces the computational complexity when determining the relative reference trajectories, but also simplifies the conditions of the terminal constraint. Next, based on the NTSM method, a finite-time controller for coupled translational-rotational dynamics is established. Through theoretical analysis, results show that the proposed controller could satisfy the Lyapunov stability condition and guarantee the tracking errors  to reach zero in finite time. Finally, numerical simulations are given to demonstrate that both orbital and attitude relative motion track the reference trajectories well under the proposed control law. The article also provides a certain reference for future space on-orbit maintenance, manipulation and asteroid hovering and landing in deep space.

Key words: spacecraft feature point, feature point directing (FPD) frame, translation-rotation coupling, finite-time control, nonsingular terminal sliding mode (NTSM), staring and tracking