In the process of obstacle avoidance, intelligent vehicles encounter issues such as slow response and poor safety during trajectory tracking. To address these problems, this paper presents a novel obstacle avoidance control strategy that does not require local trajectory replanning. By utilizing the trajectory tracking task and the geometric relationship between the obstacle and the vehicle, equality and inequality constraints are formulated. Through a potential function transformation, the obstacle avoidance inequality constraint is converted into an equality constraint. Consequently, the trajectory tracking task, which takes obstacle avoidance into account, is transformed into a constraint-following problem. Based on the Udwadia-Kalaba (U-K) approach, a control strategy in an analytic form is proposed. Simulations were conducted using the CarSim and MATLAB/Simulink platforms. The results demonstrate that the proposed control strategy ensures the vehicle’s trajectory tracking performance and collision-free property.