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The flexible space manipulator is a highly nonlinear and coupled dynamic system. This paper proposes a novel composite sliding mode control to deal with the vibration suppression and trajectory tracking of a free‐floating space rigid‐flexible coupling manipulator with a rigid payload. First, the dynamic equations of this system are established by using Lagrange and assumed mode methods and in the meantime this dynamic modelling allows consideration of the modelling errors, the external disturbance and the vibration damping of a flexible link. Then, in modal space, the problems of the manipulator system’s trajectory tracking and the vibration suppression are discussed by using the composite control approach, which combines a non‐ singular terminal sliding mode control (NTSMC) with an active vibration suppression control (AVSC). The NTSMC uses a fuzzy logic outputinstead ofthe symbol item, which smoothes the control signal, thereby inhibiting the chattering of the sliding mode control. Compared with common sliding mode control (SMC), the approach not only can reduce the chattering of the sliding mode control, but also can eliminate the singular phenomenon of the system’s control input. In addition, it can assure the trajectory tracking and the vibration suppression. Many space missions can benefit from this modelling system, such as autonomous docking of satellites, rescuing and satellite servicing. Finally, the numerical simulations were carried out, which confirmed the effectiveness of these methods

Composite Sliding Mode Control for a Free-Floating Space Rigid-Flexible Coupling Manipulator System