Design of smooth path based on the conversion between η3 spline and Bezier curve

Abstract

Convex hull property is an important characteristic of designing control points of Bezier curves, which can be used for obstacle avoidance in path generating. η 3 -splines belong to a kind of 7 th degree G 3 polynomial curves that interpolate the boundary conditions of position, tangent, curvature and curvature derivative. In this research, the derivation of equivalence bijective transformation from simplified η 3 -splines to 7 th degree Bezier curves is presented to take advantage of these two kinds of curves. Therefore, the manipulation of simplified η 3 -splines becomes more intuitive, and the design of Bezier curves to satisfy boundary conditions on the curvature and curvature derivative is computationally simpler. In addition, the transformation allows a clear geometric interpretation of the η parameter in terms of the control points. We propose the usage of this transformation as a basis for a path design procedure with an illustration of vehicle entering into roundabout.