New numerically stable solutions for minimum-snap quadcopter aggressive maneuvers

This paper addresses quadcopter minimum-snap trajectory generation for performing precise aggressive maneuvers. The solution that has been most widely used in recent works relies on using a set of truncated basis functions to generate a trajectory that satisfies waypoint specifications. This is typically performed through solving a quadratic programming problem minimizing translational snap of the vehicle. However, this previous solution is potentially subject to ill-conditioning issues that are strongly impacted by the problem's dimension. The present work introduces a new approach for finding the minimum snap trajectory for a quadcopter by using kinematics for trajectory generation, instead of truncated basis functions. We show that the new method provides better numerical stability, finding solutions in situations where the previous method fails. An example is shown for aggressive trajectory planning for flying through a vertical window.