Based on the spectral representation method of random function and combined with memoryless nonlinear translation theory, this paper analyzes the transformation relationship between potential Gaussian random process and non-Gaussian random process, and successfully generates a stationary non-Gaussian random process that conforms to the target non-Gaussian random process. For the non-stationary non-Gaussian random process simulation, on the basis of the stationary Gaussian random process, the intensity non-stationary uniform modulation model is used to modulate it, and combined with the nonlinear translation theory, the non-stationary non-Gaussian random process conforming to the target non-Gaussian random process is obtained. Aiming at the single-leg bouncing model based on the flexible rotary hip joint, the stability of its bouncing motion under passive motion is studied, and the influence of the flexible hip rotary joint on the motion stability is analyzed by comparing the single-leg bouncing motion characteristics of the free rotary hip joint. Based on the inverse dynamic control of the air phase, the fixed point distribution of the single-leg bounce of the flexible rotary hip joint was improved, and the function of the flexible rotary hip joint in the energy conversion of the bouncing motion was studied by establishing the energy consumption evaluation function. The kinematic performance verification, dynamic performance verification, dynamic parameter identification verification, and modal experiment simulation analysis were carried out for the built experimental platform, and the comparison and analysis with its theoretical model were carried out. The results show that the theoretical motion trajectory of the test mobile platform is basically consistent with the actual motion trajectory in the X and Y directions, and there is a small error in the Z-axis direction, and the error is within an acceptable range, indicating that the experimental platform system can be used to simulate the human hip joint. There is a large error between the theoretical value of the driving torque calculated by the theoretical value of the dynamic parameters and the measured value, and the dynamic theoretical model cannot accurately predict the driving torque. The predicted value of the driving torque calculated by using the identification value of the dynamic parameters is in good agreement with the measured torque, and its confidence is increased by 10–16%, indicating that the dynamic parameter identification method in this paper has a high degree of confidence.