Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight

Abstract

With much research has been conducted into trajectory planning for quadrotors, planning with spatial and temporal optimal trajectories in real-time is still challenging. In this letter, we propose a framework for large-scale waypoint-based polynomial trajectory generation, with highlights on its superior computational efficiency and simultaneous spatial-temporal optimality. Exploiting the implicitly decoupled structure of the problem, we conduct alternating minimization between boundary conditions and time durations of trajectory pieces. Algebraic convenience of both sub-problems is leveraged to escape poor local minima and achieve the lowest time consumption. Theoretical analysis for the global/local convergence rate of our method is provided. Moreover, based on polynomial theory, an extremely fast feasibility checker is designed for various kinds of constraints. By incorporating it into our alternating structure, a constrained minimization algorithm is constructed to optimize trajectories on the premise of feasibility. Benchmark evaluation shows that our algorithm outperforms state-of-the-art waypoint-based methods regarding efficiency, optimality, and scalability. The algorithm can be incorporated in a high-level waypoint planner, which can rapidly search over a three-dimensional space for aggressive autonomous flights. The capability of our algorithm is experimentally demonstrated by quadrotor fast flights in a limited space with dense obstacles. We release our implementation as an open-source ros-package. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>