Optimal Time Allocation for Quadrotor Trajectory Generation

In this paper, we present a framework to do optimal time allocation for quadrotor trajectory generation. Using this method, we can generate minimum-time piecewise polynomial trajectories for quadrotor flights. We decouple the quadrotor trajectory generation problem into two folds. Firstly we generate a smooth and safe curve which is parameterized by a virtual variable. This curve named spatial trajectory is independent of time and has fixed spatial properties. Then a mapping function which decides how the quadrotor moves along the spatial trajectory respecting kinodynamic limits is found by minimizing total trajectory time. The mapping function maps the virtual variable to time is named temporal trajectory. We formulate the minimum-time temporal trajectory generation problem as a convex program which can be efficiently solved. We show that the proposed method can corporate with various types of previous trajectory generation method to obtain the optimal time allocation. The proposed method is integrated into a customized light-weight quadrotor platform and is validated by presenting autonomous flights in indoor and outdoor environments. We release our code for time optimization as an open-source ros-package.