A shortest path algorithm for a nonrotating object among obstacles of arbitrary shapes

A shortest path algorithm for motion planning problem via mathematical morphology is proposed. The moving object and obstacles can be of arbitrary shapes of finite size. To speed up the computation of the free positions of a moving object, the idea of shape decomposition is developed. It is proven that the decomposition always reduces the number of iterations. In addition, a simple geometric algorithm is proposed to check the existence of safe paths between the given initial and final positions. Once the existence condition is verified, a modified grass fire algorithm via the grayscale morphology is then used to compute the shortest path. Finally, examples of various descriptions of moving objects among obstacles are demonstrated