In the path tracking control of intelligent vehicles, the traditional linear control method is prone to high tracking errors for uncertain parameters of the steering transmission system and road conditions. Therefore, considering the mechanical friction in the dual-motor autonomous steering system and the nonlinearity of tires, this paper proposes a path tracking control strategy of intelligent vehicles for the dual-motor autonomous steering system that considers nonlinear characteristics. First, a dual-motor autonomous steering system considering mechanical friction and the variation of tire cornering stiffness under different tire–road friction coefficients was established based on the structure of an autonomous steering system. Second, a tire–road friction coefficient estimator was designed based on a PSO-LSTM neural network. The tire cornering stiffness under different tire–road friction coefficients was estimated through the recursive least-square algorithm. Then, the control strategy of the dual-motor autonomous steering system was designed by combining the LQR path tracking controller with the adaptive sliding mode control strategy based on field-oriented control. Here, mechanical friction and the variation of tire cornering stiffness were considered. Finally, simulation and HiL tests validated the method proposed in this paper. The results show that the proposed control strategy significantly improves the tracking accuracy and performance of the dual-motor autonomous steering system for intelligent vehicles.