This paper studies the following path planning problem for a robot. There is a given path avoiding obstacles. If existing obstacles change their location or new obstacles appear, the preplanned path must be appropriately deformed for all obstacles avoidance. We develop a solution approach based on the component-wise method of smoothing the path curvature and the method of potentials. The proposed approach enables to avoid obstacles and smooth the path and its curvature (in the 2D and 3D cases).