Minimizing the maximum curvature of quadratic Bézier curves with a tetragonal concave polygonal boundary constraint

In curve design such as highway design and motion planning of autonomous vehicles, it may be important to minimize the maximum curvature. In this paper we address the problem of minimizing the maximum curvature of a quadratic Bézier curve within a boundary constraint determined by a tetragonal concave polygon. The curve is parameterized by lengths between its control points, called the “control lengths”. Finally, numerical results demonstrate applicability of the method to smooth a piecewise linear path resulting from a path search technique. The results apply whenever it is desired to have a smooth transition between intersecting straight lines.

► We formulize the control lengths that minimize the maximum curvature of a quadratic Bezier curve. ► The formula is extended to satisfy a boundary (obstacle) constraint imposed on the curve. ► The formula is efficiently used to smooth a piecewise linear path under obstacle avoidance constraint.