To solve the problems of uncertain parameters and unknown disturbances in robotic systems, a composite control strategy based on dual sliding mode observers and non-singular fast terminal sliding mode control is proposed in this paper. First, to estimate and compensate the unknown dynamics caused by uncertain parameters and external disturbances in the model, a sliding mode observer is constructed based on the Euler-Lagrange model to optimize the trajectory tracking control performance of the robotic systems. Meanwhile, an auxiliary sliding mode observer is designed to solve the chattering problem in the observer. By compensating the observation error, the chattering phenomenon of the observer is suppressed and the observation accuracy is further improved. Then, to realize system immunity and trajectory tracking, a finite-time sliding mode controller is proposed. By adjusting the switching gain in sliding mode control, the convergence time can be shortened effectively and the robustness of the system can be improved. Finally, the stability of the closed-loop system is proved by the Lyapunov stability theory, and the effectiveness of the proposed method is verified by simulation results.