A global collision-free path planning using parametric parabola through Geometry Mapping of obstacles in robot work space

Abstract

In this paper, a new algorithm for palnning collision-free path connecting from start to target point is developed using Bezier curve of order two. The control point, i. e. the mid-point of quadratic Bezier curve, determines the shape of parabola and constitutes the Control Point Space, and this process is difined a Geometry Mapping. After Geometry Mapping of all obstacles, the clear area of CPS, an area not occupied by obstacle images, identifies collision-free path. The path planning algorithm, heance, transform path planning problem in Euclidian Space to point selection problem in CPS. The calculations involved in the algorithm do not require iterative procedures and all the formulas of the solution are derived in closed form. A CPS completely filled with obstacle images indicates that path planning based on parabola is not possible and requires higher order curve with more than one control point.