A frequency domain iterative learning algorithm for high-performance, periodic quadrocopter maneuvers

Quadrocopters offer an attractive platform for aerial robotic applications due to, amongst others, their hovering capability and large dynamic potential. Their high-speed flight dynamics are complex, however, and the modeling thereof has proven difficult. Control algorithms typically rely on simplified models, with feedback corrections compensating for unmodeled effects. This can lead to significant tracking errors during high-performance flight, and repeated execution typically leads to a large part of the tracking errors being repeated. This paper introduces an iterative learning scheme that non-causally compensates repeatable trajectory tracking errors during the repeated execution of periodic flight maneuvers. An underlying feedback control loop is leveraged by using its set point as a learning input, increasing repeatability and simplifying the dynamics considered in the learning algorithm. The learning is carried out in the frequency domain, and is based on a Fourier series decomposition of the input and output signals. The resulting algorithm requires little computational power and memory, and its convergence properties under process and measurement noise are shown. Furthermore, a time scaling method allows the transfer of learnt maneuvers to different execution speeds through a prediction of the disturbance change. This allows the initial learning to occur at reduced speeds, and thereby extends the applicability of the algorithm for high-performance maneuvers. The presented methods are validated in experiments, with a quadrocopter flying a figure-eight maneuver at high speed. The experimental results highlight the effectiveness of the approach, with the tracking errors after learning being similar in magnitude to the repeatability of the system.