Parameter estimation for the pitching dynamics of a flapping-wing flying robot

In this paper we consider the problem of plant parameter estimation for a flapping wing flying robot. These parameters are the coefficients of polynomials appearing in transfer functions that govern some robot dynamics e.g pitching, and their values are completely unknown and even susceptible to variation over time. First, we analyse the pitching dynamics of the SlowHawk2 flapping wing flying robot under study and derive the linearized state-space model. Our analysis shows that in addition to the elevator deflection inducing pitching motion on the flying robot, extraneous pitching is also caused by the flapping wings. Thus, our derivations yield a multiple-input single-output (MISO) system consisting of two uncoupled transfer functions where both the elevator deflection and the wing-flapping action are the inputs that determine the pitching. Subsequently, an online parameter estimator is designed for the MISO system in order to estimate values of coefficients in the transfer functions. We use the recursive least squares method with the so-called forgetting factor. How the parameter estimator is designed using only the known input signals and measured output signals is described in detail. Using real sensor data obtained from real test flights, the designed estimator shows that the values of the unknown parameters can be accurately and robustly determined.