Saturation-based actuation for flapping MAVs in hovering and forward flight
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O R I G I N A L PA P E R
Saturation-based actuation for flapping MAVs in hovering and forward flight Haithem E. Taha · Ali H. Nayfeh · Muhammad R. Hajj
Received: 10 October 2012 / Accepted: 4 March 2013 © Springer Science+Business Media Dordrecht 2013
Abstract Stringent weight and size constraints on flapping-wing microair-vehicles dictate minimal actuation. Unfortunately, hovering and forward flight require different wing motions and, as such, independent actuators. Therefore, either a hovering or a forwardflight requirement should be included in the mission and design statements of a flapping-wing microairvehicle. This work proposes a design for an actuation mechanism that would provide the required kinematics in each flight condition using only one actuator. The idea is to exploit the nonlinear dynamics of the flapping wing to induce the saturation phenomenon. One physical spring in the plunging direction is needed along with a feedback of the plunging angle into the control torque of the actuator in the back and forth flapping direction. By detuning the feedback gains away from the saturation requirement, we obtain the flapping kinematics required for hovering. In contrast, tuning the feedback gains to induce the saturation phenomenon transfers the motion into the plunging direction. Moreover, the actuating torque (in the back and forth flapping direction) would then provide H.E. Taha · A.H. Nayfeh · M.R. Hajj () Virginia Tech, Blacksburg, VA, USA e-mail: [email protected] H.E. Taha e-mail: [email protected] A.H. Nayfeh e-mail: [email protected]
a direct control over the amplitude of the plunging motion, while the amplitude of the actuated flapping motion saturates and does not change as the amplitude of the actuating torque increases. Keywords Saturation phenomenon · Micro-air vehicles · Actuation · Nonlinear dynamics Nomenclature c¯ Mean chord length g Gravitational acceleration Masses of the vehicle and wing mv , mw respectively r Radial coordinate along the wing R Wing radius (length) S Area of one wing t Time variable T, f Flapping period and frequency xI , yI , and zI Inertial fixed frame xw , yw , and zw Wing fixed frame η Pitching angle ϕ Back and forth flapping angle ϑ Plunging angle
1 Introduction Recently, flapping wing microair-vehicles (FWMAVs) have received considerable attention. This is because of the numerous motivating applications and the technical challenges encountered in the analysis and de-
H.E. Taha et al. Fig. 1 Favorable kinematics for both of hovering and forward flight. The dot represents the leading edge
sign of such vehicles. A FWMAV represents a complex multidisciplinary system whose analysis invokes frontiers of the aerospace engineering disciplines. From the aerodynamic point of view, a nonlinear, unsteady flow is created by the flapping motion. In addition, nonconventional contributors, such as the leading edge vortex, to the aerodynamic loads become dominant in flight. On the other hand, the flight dynamics of a FWMAV constitutes a nonlinear, nonautonomous dynamical system. Furth
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