Polynomial Trajectory Planning for Quadrotor Flight

We explore the challenges of planning trajectories through complex environments for quadrotors. We use the RRT* algorithm to generate an initial route through a 3D environment and then construct a trajectory consisting of a sequence of polynomial spline segments to follow that route. We present a method of jointly optimizing polynomial path segments that is numerically stable for high-order polynomials and large numbers of segments, and is easily formulated for efficient sparse computation. Using a differentially flat representation of the quadrotor, these polynomial trajectories encode the complete dynamics of the vehicle and allow calculation of feed-forward control commands in closed form, eliminating the need to sample in a high-dimensional state space or carry out expensive dynamics simulations during planning. Our approach generates high-quality trajectories much faster than purely sampling-based kinodynamic planning methods, but sacrifices convergence to the global optimum. We demonstrate the performance of our algorithm by efficiently generating a trajectories through challenging indoor spaces and successfully traversing them at speeds up to 8m/s.