Random sampling, commonly used in autonomous vehicle path planning, reduces computational load and enhances search speed, but faces challenges like high randomness in results and unstable search times. This paper proposes a heuristic periodic iterative RRT* algorithm to address these issues and applies it to path planning. The algorithm maps static obstacles to the Frenet coordinate system, constructs a sampling probability map, and provides search space and heuristic information. Based on RRT*, it adds pruning, reconstruction of the prior search tree, nearest neighbor search, and periodic iteration to reduce sampling workload and search time. The search results generate a drivable area for path planning, converting it into a quadratic programming problem. The experimental results show that this method can ensure the feasibility and smoothness of the autonomous vehicle's path in actual driving scenarios, and demonstrates high efficiency.