This paper proposes an improvement to the RRT algorithm for path planning. The new bi-directional RRT utilizes comparison optimization and fuzzy inference to address the limitations of the base algorithm, such as instability and potential deviation from the optimal path. Firstly, two random trees are established separately using the starting position and target position as the root nodes. Two trees are extended to the nodes of their opposite trees, according to the introduced effort function simultaneously. Secondly, a more reasonable measure function and a comparison optimization strategy are introduced to greatly increase the planning stability. Finally, exploring probability and the extension step length are adjusted by fuzzy control theory dynamically combined with environment information of current node, so that the efficiency and ability to search unknown areas of the algorithm are improved effectively. Simulations confirm the algorithm's enhanced stability in complex environments, allowing for robust path planning. Furthermore, the achieved paths demonstrate a high degree of optimality, minimizing unnecessary movement.