Euclidean and non-Euclidean Trajectory Optimization Approaches for Quadrotor Racing

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.