Unmanned pavement construction is of great significance in China, and one of the most important issues is how to follow the designed path near the boundary of the pavement construction area to avoid curbs or railings. In this paper, we raise a simple yet effective controller, named the proportional-integral-radius and improved particle swarm optimization (PIR-IPSO) controller, for fast non-overshooting path-following control of an unmanned articulated vehicle (UAV). Firstly, UAV kinematics model is introduced and segmented UAV steering dynamics model is built through field experiments; then, the raw data collected by differential global positioning system (DGPS) is used to build the measurement error distribution model that simulates positioning errors. Next, line of sight (LOS) guidance law is introduced and the LOS initial parameter is assigned based on human driving behavior. Besides, the initial control parameters tuned by the Ziegler-Nichols (ZN) method are used as the initial iterative parameters of the PSO controller. An improved PSO fitness function is also designed to achieve fast non-overshoot control performance. Experiments show that compared with the PSO, ZN and ZN-PSO controller, the PIR-PSO-based controller has significantly less settling time and almost no overshoot in various UAV initial states. Furthermore, compared with other controllers, the proposed PIR-IPSO-based controller achieves precise non-overshoot control, relatively less settling time and centimeter-level positioning error in various initial deviations.