B-spline-to-Bezier conversion and applications on path planning

In this paper, we present a new approach to calculate the B-spline-to-Bézler conversion matrix which converts the control points of a uniform B-spline curve into the control points of an equivalent Bézier curve. It takes into account the order of the curve intervals and hence can provide the conversion of the whole curve at once. The algorithm is implemented so that the computation time only increases proportionally with the number of control points until a constant value before getting saturated. Applications include but are not limited to the efficient usage in different optimal path planning algorithms for navigation in 2D non-convex polytopic region as being presented.