Computing a Collision-Free Path using the monogenic scale space

Mobile robots have been used for various purposes with different functionalities which require them to freely move in environments containing both static and dynamic obstacles to accomplish given tasks. One of the most relevant capabilities in terms of navigating a mobile robot in such an environment is to find a safe path to a goal position. This paper shows that there exists an accurate solution to the Laplace equation which allows finding a collision-free path and that it can be efficiently calculated for a rectangular bounded domain such as a map which is represented as an image. This is accomplished by the use of the monogenic scale space resulting in a vector field which describes the attracting and repelling forces from the obstacles and the goal. The method is shown to work in reasonably convex domains and by the use of tessellation of the environment map for non-convex environments.