Progressive Barrier Tightened Fast Nonlinear Model Predictive Control for High-Performance Path Tracking

In this article, we propose a novel, fast, and accurate numerical algorithm for nonlinear model predictive control (NMPC) with application to path-tracking of autonomous vehicles (AVs). First, a reformulation method for the input-constrained optimal control problem (OCP) is introduced, replacing inequality constraints with commonly used barrier terms and squashing functions. In the context of the real-time iteration (RTI) scheme, an improved progressive barrier-tightened RTI (btRTI) is then proposed for the reformulated problem to further improve solution accuracy. Compared to existing methods, this approach is more refined, involving the enhancement of the warm-start point by solving an advanced problem and progressively adjusting barrier parameters logarithmically throughout both the problem evolution and the prediction horizon. In addition, the btRTI retains and effectively leverages the specific structure of the underlying problem, such as the convex-over-nonlinear properties to obtain a positive semi-definite Hessian approximation, allowing it to be efficiently solved with a linear computational cost. Eventually, the high-fidelity co-simulation and hardware-in-the-loop (HiL) test are carried out to fully validate the effectiveness of the proposed control strategy. The comparative results indicate its high performance in terms of tracking error and computational efficiency.