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There has been a growing interest in nonlinear model predictive control (NMPC) for the motion control of autonomous driving. However, it is odd that integration stability has not been considered enough when developing these applications for autonomous driving, which results in inefficient performance of NMPC-based motion controllers. The stabilized explicit Runge–Kutta (RK) integration method is adopted in this paper to solve the integration stability problem in motion control of autonomous vehicles (AVs). In comparison with other explicit integration methods, this method provides a wider stable region and is more efficient than implicit integration methods. This integration method is integrated into the framework of offset free nonlinear model predictive control (OF-NMPC) solver based on gradient-based MPC (GRAMPC) by us. As a result, the problem of computational stability at low speeds of motion control can …