  We present two quadrotor raceline optimization approaches which differ in
using Euclidean or non-Euclidean geometry to describe vehicle position. Both
approaches use high-fidelity quadrotor dynamics and avoid the need to
approximate gates using waypoints. We demonstrate both approaches on simulated
racetracks with realistic vehicle parameters where we demonstrate 100x faster
compute time than comparable published methods and improved solver convergence.
We then extend the non-Euclidean approach to compute racelines in the presence
of numerous static obstacles.
