<p>In order to improve the motion performance of quadruped crawling robots in continuous convex terrains, a fixed-time non-singular fast terminal sliding mode control (FxNFTSMC) method based on sliding surface adjustment is proposed. Firstly, the dynamic model of the quadruped crawling robot is constructed using the Lagrange method for control purposes. Secondly, the sliding surface is designed based on the adjustment of the current state of the system to ensure the convergence performance of the control system at different stages. Thirdly, to achieve the fixed-time tracking independent of the initial state of the system, a non-singular terminal sliding mode control law is designed by using variable exponential power terms and a continuous sinusoidal function, and a hyperbolic tangent function is used to reduce chattering in the control signal. The fixed-time stability of the control system is proved by the Lyapunov theory. Finally, the effectiveness of the proposed control method is verified by the simulation results based on the prototype platform experiments.</p>