High-Performance Path Tracking of a 4WD Autonomous Vehicle Using NMPC with Virtual 4WD Torque Distribution

This study proposes a reduced-complexity nonlinear model predictive control (NMPC) framework for high-performance path tracking of a four-wheel-drive (4WD) autonomous vehicle. A 4WD sports car equipped with four independent wheel motors is used as the test vehicle. Although the vehicle has four motors, the proposed NMPC directly optimizes the front-wheel steering command and the rear-left and rear-right wheel torque commands, while the front-wheel torques are generated using a gain-based virtual 4WD distribution law. Trajectory optimization (TRO) is performed offline to generate the reference racing line and velocity profile, while the online NMPC controller tracks the optimized reference trajectory using the front-wheel steering command and the rear-left and rear-right wheel torque commands as control inputs. This structure reduces the control complexity while maintaining the ability to improve traction utilization and yaw response. Under the investigated simulation conditions on the Shanghai International Circuit, the proposed reduced-dimensional NMPC with rear-dominant virtual 4WD torque distribution reduces the simulated lap time while maintaining bounded path-tracking errors and satisfying the track-boundary constraints. As the torque distribution gain Kr increases from 0 to 0.5, the lap time is reduced by approximately 10.3% (from 182.08 s to 163.30 s), while the maximum lateral tracking error remains below 0.33 m and the maximum heading-angle error remains below 2.95 deg for all stable cases. However, further increasing Kr beyond 0.5 leads to degraded tracking performance or loss of stable path following because excessive front-wheel longitudinal force reduces the available lateral tire force for steering. These results indicate that an appropriate torque distribution gain can improve corner-exit acceleration and overall lap-time performance, whereas excessive front torque assistance may degrade tracking accuracy and vehicle stability.