As the application of mobile robots becomes increasingly widespread, many navigation applications now require more than just obstacle avoidance capabilities. There is a growing demand for robots to follow predetermined global paths. Inspired by stamping technology in the metalworking field, this paper proposes a two-stage local path planning algorithm based on sampling and optimization, termed the path stamping forming algorithm. In the exploration stage, the path stamping forming algorithm finds a preliminary path that avoids obstacles and runs parallel to the global path. The subsequent optimization stage determines the optimal local path that meets specific constraints. Finally, we compared the proposed algorithm with existing advanced navigation algorithms through simulations and experiments, demonstrating its superior performance. The results indicate that the proposed algorithm enables mobile robots to avoid obstacles and follow the global path without the need to re-plan the global path. Compared with the traditional local path planning algorithm, the performance of the proposed algorithm in following the global path is improved by up to 52.71%.