To enhance the vehicle-following safety of connected and automated vehicles during curved-road maneuvers with large spacing errors and aggressive acceleration demands, an improved vehicle-following scheme considering lateral safety is proposed in this article. First, a backstepping-based longitudinal controller (BLC) is developed to maintain the desired inter-vehicle distance, with rigorous stability analysis. Then, a hierarchical assessment-decision strategy (HADS) is designed to evaluate the lateral instability risk induced by performance-oriented BLC. When lateral risk is detected, safety-assured reference motion states are reconstructed through convex optimization. A collaborative mechanism is further established to coordinate the performance-driven BLC and safety-critical HADS. In addition, a linear time-varying model predictive lateral controller is designed to track the desired path generated from the historical waypoints of the preceding vehicle. Co-simulation results demonstrate that the proposed method achieves more accurate longitudinal spacing regulation than the baseline controllers while maintaining precise lateral path tracking. In the lateral-risk scenario, the proposed HADS keeps the lateral acceleration below 0.4g, whereas the baseline controllers without HADS fails to complete the curve-following task. Field experiments further show that the maximum longitudinal spacing error, lateral spacing error, and lateral acceleration are 0.79 m, 0.15 m, and 0.25g, respectively. These results verify that the proposed scheme improves vehicle-following safety while maintaining accurate longitudinal and lateral tracking performance.
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