We present two approaches to compute raceline trajectories for quadrotors by solving an optimal control problem. The approaches involve expressing quadrotor pose in either a Euclidean or non-Euclidean frame of reference and are both based on collocation. The compute times of both approaches are over 100x faster than published methods. Additionally, both approaches compute trajectories with faster lap time and show improved numerical convergence. In the last part of the paper we devise a novel method to compute racelines in dense obstacle fields using the non-Euclidean approach.

翻译：本文提出两种通过求解最优控制问题计算四旋翼竞赛航迹的方法。这两种方法分别采用欧氏与非欧氏参考系描述四旋翼位姿，且均基于配点法。两种方法的计算时间均比已公开方法快100倍以上，同时能计算出更短圈时轨迹并展现出更优的数值收敛性。在论文最后部分，我们提出一种基于非欧氏方法的新型计算方案，可在密集障碍场中生成竞赛航迹。