An improved rapidly-exploring random tree algorithm is introduced to address the limitations of the traditional method in mobile robot path planning. In the initial stage of the algorithm, the sampling unit decomposition method is used to divide the map into workable and obstacle regions. Then, path planning is carried out according to the relationship between the regions. Finally, the path is optimized to improve the curvature of the path. Simulation results indicate that, compared to the conventional rapidly-exploring random tree algorithm, the enhanced version cuts the search time and sample count by over 50%. Compared with other algorithms, it reduces more than 30% of the search time. The improved algorithm reduces the blindness and randomness of node search, and the optimized path has fewer turning points, which meets the actual application of mobile robots.