On dynamic motion planning problems

A novel method for solving the motion planning problem in the presence of moving obstacles is presented. Compared to previous approaches, the proposed method is more general in that obstacles are allowed to move with translation and rotation at nonlinear velocity. Using path/velocity decomposition, the method emphasizes the development of an efficient algorithm for collision detection between the robot and moving polygons. This algorithm is devised using transversability vector theory to determine the geometric relationships between any two convex polygons or convex components of concave polygons. The interference between the robot and the moving obstacles is detected and registered on the constraint map to represent time constraints on the robot´s motion along the path. The constraint map is then used for velocity planning using a simple algorithm. The problem of a robot crossing the street is used as an example for computational analysis