Flexible Quadrotor Unmanned Aerial Vehicles: Spatially Distributed Modeling and Delay-Resistant Control

This paper introduces an analytical framework for the derivation of distributed-parameter equations of motion of a flexible quadrotor. This approach helps obtain rigid and elastic equations of motion simultaneously, in a decoupled form, to facilitate the controller design. A delay-resistant low-frequency adaptive controller is employed, which prevents excessive oscillations due to flexible dynamics, compensates uncertainties, and addresses the inherent time delay. In addition to this, a delay-dependent stability condition for the overall system dynamics is obtained including the human operator with reaction time delay, the adaptive controller, and the flexible quadrotor dynamics with input delay. With comparative simulation studies, it is demonstrated that the flexible arm tip oscillations are significantly reduced when the low-frequency delay-resistant closed-loop reference model adaptive controller is used, compared to a closed-loop reference model adaptive controller and a conventional model reference adaptive controller.