Fly Out the Window: Exploiting Discrete-Time Flatness for Fast Vision-Based Multirotor Flight

Recent work has demonstrated fast, agile flight using only vision as a position sensor and no GPS. Current feedback controllers for fast vision-based flight typically rely on a full-state estimate, including position, velocity and acceleration. An accurate full-state estimate is often challenging to obtain due to noisy IMU measurements, infrequent position updates from the vision system, and an imperfect motion model used to obtain high-rate state estimates required by the controller. In this letter, we present an alternative control design that bypasses the need for a full-state estimate by exploiting discrete-time flatness, a structural property of the underlying vehicle dynamics. First, we show that the Euler discretization of the multirotor dynamics is discrete-time flat. This allows us to design a predictive controller using only a window of inputs and outputs, the latter consisting of position and yaw estimates. We highlight in simulation that our approach outperforms controllers that rely on an incorrect full-state estimate. We perform extensive outdoor multirotor flight experiments and demonstrate reliable vision-based navigation. In these experiments, our discrete-time flatness-based controller achieves speeds up to 10 m/s and significantly outperforms similar controllers that hinge on full-state estimation, achieving up to 80% path error reduction.