Two dimensional collision-free path planning using linear parametric curve

Abstract

An effective algorithm for planning a collision-free path based on linear parametric curve is developed. A collision-free path is viewed as a series of segmented polynomial curves in a space that does not interfere with any object in a given work space. It is assumed that the path connecting start and target points has no width. The algorithm presented here uses a linear parametric curve as a base curve and maps objects in Euclidean Space (ES) into objects in Control Point Space (CPS) through intersection checks between path and obstacles. A path having a single control point is investigated here. The Free Space (FS) of CPS identifies a collision-free path in ES, hence any point in the FS of CPS is a candidate for a collision-free path. A CPS completely occupied by obstacle images indicates no collision-free path is available with a single control point and a search based on a multiple control point is required. The shortest path with minimum search time is obtained by setting CPS in elliptic coordinate. Considerations are given to get a path with the smallest maximum curvature by selecting the control point toward the bisection line of ST and smoothing the path. ©1997 John Wiley & Sons, Inc.