Generalized Sigmoid Path Generation and Fractional-Order Accumulation Preview Control for Autonomous Vehicles

Conventional Sigmoid-based path generation for autonomous vehicles suffers from inherent central symmetry and limited curvature tunability, which restricts its adaptability to asymmetric driving scenarios and complex boundary matching requirements. On the control side, traditional preview control architectures, predominantly relying on single-point or fixed integer-order weighting strategies, fail to fully capture the continuous trend of the path ahead, and face an inherent trade-off among tracking accuracy, response speed, and ride comfort. To address these limitations, this paper proposes a systematic fractional-order framework covering both reference path generation and lateral trajectory tracking. First, a generalized Sigmoid path function is constructed by replacing the exponential term in the standard Sigmoid form with the two-parameter Mittag–Leffler function. Two independent parameters α and β are introduced to realize continuous tuning of path smoothness, morphological asymmetry, heading angle distribution, and curvature profile. Second, an fractional-order accumulation preview tracking controller (FOA-PTC) is designed for vehicle lateral dynamics. By weighting lateral errors at multiple preview positions with fractional-order coefficients, the controller achieves nonlocal spatial fusion of preview information without introducing additional temporal states, and the fractional order ν enables continuous balancing between far-field trend anticipation and near-field tracking precision. Simulations are carried out based on a nonlinear two-degree-of-freedom vehicle model with the Pacejka Magic Formula tire model, covering both gentle urban lane-change scenarios and sharp low-speed obstacle-avoidance scenarios. Comparative evaluations against five representative baseline control schemes—single-point preview, equal-weight multipoint, linear weighting, exponential weighting, and Gaussian weighting—demonstrate that the proposed FOA-PTC consistently achieves the optimal comprehensive performance in both scenarios. For the sharp-curvature generalized Sigmoid path, it reduces the maximum lateral tracking error by 42.1% (from 0.337 m to 0.195 m) and the root-mean-square error (RMSE) by 54.0% (from 0.176 m to 0.081 m) compared with the single-point preview baseline. For the gentle-curvature lane-change scenario, the corresponding reduction rates are 59.0% and 46.7%, respectively. Further simulation-based validation indicates that the proposed method achieves better robustness performance than baseline controllers within the tested parameter range, and shows acceptable computational overhead for potential embedded deployment. The proposed framework improves the geometric flexibility of path planning and the tracking performance of lateral control, providing a tunable framework with potential for autonomous navigation in complex driving scenarios.