Adaptive control for bioinspired flapping wing robots

This paper derives the governing equations of motion for a flapping wing robot that is used to study and synthesize bio-inspired closed loop control laws. Lagrange's equations are employed to derive the geometrically nonlinear equations of motion. The Denavit-Hartenberg convention is used to model the wing flapping kinematics and the aerodynamic loads are represented using quasi-steady models of aerodynamics over each of the wing sections. The governing system is then cast in terms of a standard first order system with matched uncertainties that are due to the aerodynamic contributions. The closed loop control drives the system states such that they asymptotically track trajectories obtained from experimental observations of flapping wings of birds. Convergence and asymptotic stability of the tracking error closed loop dynamics is discussed. Finally, sufficient conditions are discussed under which the Lyapunov analysis guarantees identification of the aerodynamic loads, a topic of great interest to the research community investigating the aerodynamics of flapping flight.