A minimal longitudinal dynamic model of a tailless flapping wing robot for control design

Abstract

Recently, several insect-and hummingbird-inspired tailless flapping wing robots have been introduced. However, their flight dynamics, which are likely to be similar to that of their biological counterparts, remain yet to be fully understood. We propose a minimal dynamic model that is not only validated with experimental data, but also able to predict the consequences of various important design changes. Specifically, the model captures the flapping-cycle-averaged longitudinal dynamics, considering the main aerodynamic effects. We validated the model with flight data captured with a tailless flapping wing robot, the DelFly Nimble, for air speeds from nearhover flight up to 3.5 m/s. Moreover, the model succeeds in predicting the effects of changes to the center of mass location, and to the control system gains. Hence, the model is suitable even for the initial control design phase. To demonstrate this, we have used the simulation model to tune the robot's control system for higher speeds. Using the new control parameters on the real robot improved its maximal stable speed from 4 m/s to 7 m/s.

Longitudinal Grey-Box Model Identification of a Tailless Flapping-Wing MAV Based on Free-Flight Data

“…This coordinate frame is used Figure 3: Controller architecture. The setpoint is denoted by subscript sp, reference by ref and measurement by m. Source: [24] in order to prevent singularity issues when manoeuvres for system identification in hover and forward flight are performed. Note that the X body axis in Figure 4 coincides with the X-axis in Figure 2.…”

“…Since the feedback gains mute the natural dynamic response of the vehicle we weakened the original feedback gains of the Nimble. Based on previous studies on the DelFly Nimble [24] we were able to gain insight into the dynamic response of the Nimble with changing feedback gains and adjusted the gain settings accordingly ( Table 2).…”

“…This higher resolution is only important when accurate analysis is required at a sub flap-cycle time scale. For the case of the DelFly Nimble, on-board data, such as the motor speed, could be recorded on a sd-card with a rate of approximately 100 Hz [24] and IMU data at a rate of 500 Hz. However, for the purpose of modelling the flight dynamics of the DelFly Nimble, the refresh rate of 360 Hz of the OptiTrack system is more than adequate for accurate analysis on a flight dynamics time scale [19].…”

“…Still some work has been done on tailless FWMAVs, such as the work by A Roshanbin et al which used a simple linear model that captures the longitudinal pitch dynamics, and the parameters in the model are estimated using pendulum experiments [10]. In addition, a minimal longitudinal dynamic model of a tailless FWMAV, the DelFly Nimble, has recently been developed [24]. The DelFly Nimble is a bio-inspired tailless FW-MAV developed at Delft University of Technology (Figure 1).…”

“…In this paper it is shown that simple, accurate and computational efficient models are able to capture the complex flight dynamics of the DelFly Nimble in the longitudinal plane. Although models of the Nimble have been developed in a previous study [24], this study focusses on identifying linear models using a more structured aircraft system identification approach, where the estimated parameters are longitudinal-directional derivatives (stability-and control derivatives). These derivatives effectively provide information regarding how much change occurs in the aerodynamic-forces and moments acting on the DelFly Nimble when there is a small change in states and control surfaces deflection.…”