The RRT algorithm based on random sampling is widely used in planning problems with non-holonomic constraints. In indoor environments, narrow passages exist in the map, and the RRT method suffers from slow convergence speed and poor path quality. Additionally, the typical feature of large indoor room spaces with small exits creates traps where RRT can easily become stuck, making it difficult to find a path quickly. To solve the above problems, this paper proposes an improved RRT algorithm. This method first uses the simplified Bridge Test and point cloud clustering algorithm to locate the narrow passages on the map and place the root nodes in the narrow passage. Then grow multiple random trees from the root nodes, starting and endpoints. As the number of samples increases, the random trees gradually expand and connect to each other. The trees are connected to each other to build a complete path. Finally, the initial path is optimized and the final planning result is obtained. The simulation of the improved RRT, RRT*, RRT, and Bi-RRT is carried out. The simulation results show that the improved RRT algorithm proposed in this paper outperforms in terms of path length, number of exploring nodes, and processing time. We also tested 4 algorithms on a real robot, and the results prove the practical value of the improved algorithm.