Efficient nonlinear model predictive motion controller for autonomous vehicles from standstill to extreme conditions based on split integration method

Abstract

Autonomous driving motion control based on nonlinear model predictive control (NMPC) faces integration stability issues when driving at low speeds. However, this issue has not received sufficient attention or been adequately addressed. Ensuring integration stability requires the adoption of an implicit method, which incurs a high computational burden, making this phenomenon crucial to the performance of NMPC. In this paper, a split integration method is proposed to utilize the gradient-based augmented Lagrangian approach (GRAMPC) to solve the integration stability problem and significantly improve the efficiency of NMPC. The proposed split integration method integrates the explicit second-order Runge–Kutta (RK) method and the second-order L-stable Rosenbrock (ROS2) method. To enhance integration stability for the stiff part of the state equation, the ROS2 method is used. For the non-stiff part of the system, the RK method is used to improve its efficiency. This approach results in an efficient nonlinear NMPC system that can be adapted to full range speeds. Simulations and real-world experiments demonstrate that the low-speed integration stability problem of NMPC is entirely resolved without compromising its efficiency.