Today, mobile robots have a wide range of real-world applications where they can replace or assist humans in many tasks, such as search and rescue, surveillance, patrolling, inspection, environmental monitoring, etc. These tasks usually require a robot to navigate through a dynamic environment with smooth, efficient, and safe motion. In this paper, we propose an online smooth-motion-planning method that generates a smooth, collision-free patrolling trajectory based on clothoid curves. Moreover, the proposed method combines global and local planning methods, which are suitable for changing large environments and enabling efficient path replanning with an arbitrary robot orientation. We propose a method for planning a smoothed path based on the golden ratio wherein a robot’s orientation is aligned with a new path that avoids unknown obstacles. The simulation results show that the proposed algorithm reduces the patrolling execution time, path length, and deviation of the tracked trajectory from the patrolling route compared to the original patrolling method without smoothing. Furthermore, the proposed algorithm is suitable for real-time operation due to its computational simplicity, and its performance was validated through the results of an experiment employing a differential-drive mobile robot.