Non-Uniform B-spline Trajectory Optimization using Control Point Representation Transformations

Online trajectory generation for unmanned aerial vehicles has attracted increased interest for a variety of autonomous applications. This paper explores the use of nonuniform B-splines to produce improved time-optimal trajectories in comparison to contemporary work that uses uniform B-splines. This paper introduces the non-uniform B-spline matrix form and the transformation of non-uniform B-spline control points to other parametric representations such as MINVO and Bézier control points. Conversion between control point representations allows the optimization to take advantage of the piecewise continuity of B-splines, as well as the tighter convex bounding properties of MINVO and Bézier curve representations. The results show that non-uniform B-spline trajectories significantly outperform uniform B-splines trajectories in time optimality and path length. However, computational performance is degraded when optimizing for non-uniform B-splines, thus requiring computational improvements for online use.