Extended incremental nonlinear dynamic inversion for optical flow control of micro air vehicles

Optical flow-based control strategies have always inspired robotic scientists, especially those in the field of Micro Air Vehicles (MAVs), thanks to their computational efficiency and relative simplicity. A major problem is that the success of optical flow control is governed by the availability of distance estimates, while optical flow provides only the ratio of velocity to distance. Therefore, with only monocular visual information, the inherent nonlinearity of optical flow observables has imposed several challenges in the controller design. In this paper, we propose a newly formulated controller, Extended Incremental Nonlinear Dynamic Inversion (EINDI), to deal with nonlinearities in the system output, such as optical flow control problems. The proposed method unlocks the potential of its predecessor (INDI) in output feedback control by removing the common assumption of time-scale separation, allowing internal dynamics to exist, and requiring only the input and output measurements. Furthermore, the EINDI method has been implemented on an MAV and tested successfully for optical flow landing in a simulation and a real-world outdoor environment. Both simulation and flight test results show 1) good tracking performance of the EINDI control compared to the conventional feedback control, 2) smooth landing trajectories without any oscillation, and 3) fast adaptation of the EINDI control even for landings at different heights and desired setpoints.