Navigation algorithms for autonomous vehicles have become the subject of increasing interest, but most of them heavily rely on expensive high-precision positioning equipment, which hinders autonomous vehicles’ development. In this article, we propose a path planning and control framework for autonomous vehicles with low-cost positioning. For the path planning layer, a potential field is constructed by the potential functions of road boundaries, obstacles, and reference waypoints. According to the potential field, a reinforcement learning agent is developed to generate a collision-free path for path tracking. For the control layer, a model predictive control based on vehicle dynamics is designed and a linear terminal constraint is considered. Simulation results show that the proposed algorithm can effectively avoid static and dynamic obstacles. Moreover, compared with traditional methods, the proposed algorithm performs better when the positioning devices are imprecise. Furthermore, the real-time performance can meet the requirements of navigation.