Optimal Constrained Trajectory Generation for Quadrotors Through Smoothing Splines

Abstract

In this paper, we present a trajectory generation method for quadrotors based on the optimal smoothing B-spline. Compared to existing methods which rely on polynomial splines or time optimal control techniques, our method systematically addresses the issue of axes-coupled and interval-wise constraints. These constraints can be used to construct safe flying zones and satisfy vehicle's physical limits. The proposed approach has also been extended to generate trajectories from the nominal plan which consists of not only points but also lines and planes, opening a door for new improvements and applications. Moreover, a closed-form solution can be obtained for cases without inequality constraints. Such a solution is numerically stable for the large-scale fitting problem, which allows us to directly fit the human sketching input from the touch device and capture all subtle details. Our approach is verified by various real flight experiments..