Generating dynamically feasible trajectories for quadrotor cameras

When designing trajectories for quadrotor cameras, it is important that the trajectories respect the dynamics and physical limits of quadrotor hardware. We refer to such trajectories as being feasible. In this paper, we introduce a fast and user-friendly algorithm for generating feasible quadrotor camera trajectories. Our algorithm takes as input an infeasible trajectory designed by a user, and produces as output a feasible trajectory that is as similar as possible to the user's input. By design, our algorithm does not change the spatial layout or visual contents of the input trajectory. Instead, our algorithm guarantees the feasibility of the output trajectory by re-timing the input trajectory, perturbing its timing as little as possible while remaining within velocity and control force limits. Our choice to perturb the timing of a shot, while leaving the spatial layout and visual contents of the shot intact, leads to a well-behaved non-convex optimization problem that can be solved at interactive rates. We implement our algorithm in an open-source tool for designing quadrotor camera shots, where we achieve interactive performance across a wide range of camera trajectories. We demonstrate that our algorithm is between 25x and 45x faster than a spacetime constraints approach implemented using a commercially available solver. As we scale to more finely discretized trajectories, this performance gap widens, with our algorithm outperforming spacetime constraints by between 90x and 180x. Finally, we fly 5 feasible trajectories generated by our algorithm on a real quadrotor camera, producing video footage that is faithful to Google Earth shot previews, even when the trajectories are at the quadrotor's physical limits.