Modeling and adaptive control for tracking wing trajectories

Studies of Micro Air Vehicles (MAVs) have gained increased attention over the past decade, while a significant range of open problems in this emerging field remain unaddressed. This paper highlights the investigations entailing flapping wing vehicles, designed based on inspiration from observations of avian flight. The nonlinear equations of motion of a ground fixed flapping wing robot are derived that incorporates a quasi-steady model of aerodynamics. The equations of motion are developed using Lagrange's equations and the aerodynamic contributions are formulated using virtual work principles. The aerodynamics are constructed with a quasi-steady state formulation where the functions representing lift and drag coefficients as a function of angle of attack are treated as unknowns. An adaptive controller is introduced that seeks to learn the aerodynamic effects. A Lyapunov analysis of the controller guarantees boundedness of all error terms and asymptotic stability in both the joint position and derivative error. The controllers are simulated using two dynamic models based on flapping wing prototypes designed at Virginia Tech. The numerical experiments validate the Lyapunov analysis and verify that unknown parameters are learned if persistently excited.