Modelling and Simulation -MS 20065/24/2006 - 5/26/2006 Montreal, QC, Canada Editor(s): R. Wamkeue 630 pages
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Bahram Tarvirdizadeh University of Tehran Mechanical Engineering School of Mechanical Engineering, University of Tehran, Amir abad Av., Tehran, Iran Tehran Tehran Iran 11365/4563 Dear Mr. Tarvirdizadeh, Re: 530-137 A Mathematical Model for a Flapping-Wing Micro Aerial Vehicle. Congratulations, your paper has been accepted for presentation and publication at the lASTED International Conference on Modelling and Simulation (MS 2006), to be held from May 24, 2006 to May 26, 2006, in Montreal, Canada. We cordially invite you to attend and present your paper at the conference. We also encourage you to register and book your flight as soon as possible, if you have not already done so. Please complete the following by the registration deadline of Apr 01, 2006. 1. Registration Form and Payment (mandatory) 2. Author Information Form (mandatory) 3. Hotel Reservation Form (if you need assistance in reserving a hotel room) The above materials are available for viewing on our website at http://www.iasted.org/conferences/2006/Montreal/ms-reg.htm. Please let me know if you have any questions regarding registration. Once again, congratulations on your MS 2006 acceptance. We are very excited to be able to include your research and ideas in the conference, and we look forward to seeing you in Montreal, Canada. Sincerely,
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Proceedings of the 17th IAS'T'ED jnternational MODELLING AJ~D SIMULATION May 24-26, 2006, Montreal. QC Canada
Conference
A MATHE1\IATICAL l\10DEL FOR A FLAPPING-WING MICRO AERIAL VEHICLE Bahram Tarvirdizadeh Graduate Student, University of Tehran School of Mechanical Engineering, University of Tehran. Bahram 79kntu(Wvahoo.com Hesam Maleki Aghil Yousefi-Koma, Esmaeel Khanmirza, Assistant Professor, University of Tehran. Graduate Srudent, University of Tehran. Graduate Student, Civil org yousefi koma(aiVahoo.com e khanmirza(c1lvahoo.com of aviation. pes maJeki . ahoo
ABSTRACT
The goal of this paper is to unveil some of the', important features of insect flight from a control poiri; view, placing particular emphasis on' electromechanical constraints. Similar to aerial vehj: based on rotary wings, such as helicopter, flying' .' control their flight by controlling their attirude and' magnitude of the vertical thrust. This is accomplished' the controlling the aerodynamic forces and toni generated by the wings during flapping. However, unl' helicopters, aerodynamic forces on insect wings' highly nonlinear and timevarying along a wingbeat, the periodic motion of the wings cannot be ignored. As~ result, the system dynamics cannot be approximated by. linear time-invariant model, widely adopted in helicopt' theory based on quasistatic assumption on the TO blades. The motion of the insect is a nonlinear sys with forced periodic inputs. On the other hand,. wingbeat frequency is much higher than the dynamics. the insect itself, since flying insects requires sev.' wingbeat periods to complete a complex maneuvers s' as a saccade. Moreover. the wing pattern motion in real insect does change dramatically from one wingbeat to an~ wingbeat, even during fast maneuvers. These two facts lie at the core of the control approach flapping MA Vs proposed in [2], which is based averaging the system with respect to the wingbeat pe and on parameterizing the wing motion accordin biomimetically inspired parameters that can be c on a wingbeat-by-wingbeat basis [2]. However, our approach based on wing m parametrization, which mimics real insect wing mob. leads naturally to a time invaIiant system where artifi virtual control inputs appear naturally as a simple fund of the wing parameters. thus facilitating the synthe :. feedback control design. Here we focus on a model.: very limited wing kinematics [2].
In this paper a dynamic model of a flapping micro aerial vehicles (MA Vs) is developed. We focus on a MA V with very limited wing kinematics and simple input control schemes. In particular, we parameterize wing trajectory based on biomimetic principles. i.e. principles that are directly inspired by observation of real insect flight. Flapping flight IS analyzed from' three different perspectives: biological, technological and control perspectives. Three specific aerodynamic effects are shown as the cause of u lift gain at low Re (Re)llold's number): the circulation generated by the rotation of the wing at the end of a stroke. the delayed stall due to the instationnarity of the movement, and finally the wake capture. as the wing re-enters the flow it has previously disrurbed.
KEYWORDS Kay wards: Flapping FiightModelling - MA V.
Micro Aerial Vehicles -
INTRODL'CTlON The Micro Aerial Vehicles (MA Vs) represent nowadays a large field of investigation. due to their interests in both civil and military domains. Such small and autonomous devices could be used for inspecting high monuments. monitoring risks of forest fires, or more generally for interventions in narrow and able to be both fully auronomous and carriable by a single infantryman, with foreseen applications such as rescuing or reconnaissance ("behind the hill" missions) [1]. However. the latest advances m insect flight aerodynamics and m microtechnologyhazardous environments, where it would be dangerous to send a human agent. Concerning the military domain, MA Vs prove their interest in being. seem to provide the sufficient tools to fabricate flying microrobots mimicking real flying insects. Despite flying microrobots have limited payload capacity and require still air, their unmatched maneuverability, low fabrication cost and small size make them very attractive for costcritical miSSions m environments which are unpinetrable for larger size Unmanned Aerial Vehicles (UA V'S) [3].
530-137
Flapping Flight in Biological Insects ':. In this section the some aspects of biological insect fl!, is reviewed, such that aerodynamic mechanis-ms andi sensory system.
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Aerodynamic
Mechanisms
proportional to the product of the angular velocity and translational velocity. However, there is a major difference between a rotating wing and a rotating ball. In fact, while the rotational lift is perpendicular to the velocity in a rotating ball, the rotational lift is perpendicular to the surface of a rotating wing. Rotational lift is present in flapping flight at the end of each halfstroke when the wing is about to invert the direction of its motion [6]. The last mechanism present in flapping flight is the wake capture. It is present at the beginning of each half-stroke after the wing has inverted its motion and started to move. The wake capture appears when the wing interacts with the effects of past strokes on the ambient fluid environment. The fluid behind the wing is dragged along with the motion of the wing. As the wing slows down and inverts the direction of motion, it hits the fluid which is still moving because of its momentum. Therefore, the velocity of the wing relative to the fluid is larger than the velocity of the wing alone, and therefore results in the generation of a larger force. This is a simplified explanation of the principle behind the phenomenon of wake capture [6].
The aerodynamics of flapping flight is quite different from fixed or rotary winged flight for two main reasons: the first is that they act in t\vo different aerodynamic regimes. and the second is that the velocity of the wing or blade relative to the fluid is time-varying [4]. In insect flight, the Reynold's number, a dimensionless parameter that is related to fluid viscosity and wing velocity. ranges from few hundred to few thousand in insects and from few tens of thousands to hundred thousands in manmade vehicles. In addition, the velocity of the wing or blade relative to the fluid in flapping flight is time-varying, while it remains constant in fixed or rotary winged flight. Therefore, steady state hydrodynamics developed for manmade vehicles is not suitable to describe flapping flight [4]' Although numerical solutions of hydrodynamical equations are available today, a clear understanding of flapping flight aerodynamics have been obtained by dynamically scaled models of insect wings that can reproduce the same aerodynamics mechanis~s present in insect flight. These experiments have unveiled three main aerodynamic mechanisms involved with flapping flight: the delayed stall, the rotational lift. and the wake capture [6]. The delayed slall appears at the onset of motion of the wing. As the wing starts moving a small vortex appears behind the leading edge, and an asymmetric, opposite swirl appears in the fluid close to the original resting position of the wing [6]. The presence of two vortices moving in opposite directions but with identical strength is the equivalent principle of conservation of momentum for fluids. The vortex above the wing creates a lower pressure on its back surface, thus producing a net aerodynamic force perpendicular to the wing surface [6].
The Senso!")' System Flying insects possess a diverse set of sensors, ranging from mechanoreceptive to optical, and from inertial to chemical. Each of these sensors is dedicated to a specific task that ranges from flight stabilization to navigation [5]. Mechanoreceptors Insects wings and other parts of the body such as the antennae, neck and legs are innervated by campaniform sensilla. These nerves can sense and encode pressure forces when they are stretched or strained. A large number of sensilla are located at the base of the wing. They are thought to be able to measure aerodynamic forces acting on the wings during motion and to elicit a compensatory mechanism to stabilize flight as observed by Hengstenberg [5]. In principle, these sensors could also be used by insect to compensate for external disturbances, although this has not been confirmed experimentally [5]. Ocelli Ocelli are a sensory system present in many flying insects. This system comprises of three wide angle photoreceptors placed on the head of the insect. They are oriented in such a way that they have poor image resolution, but arc able to collect light from large regions of the sky. They play a fundamental role in insect attitude stabilization, particularly horizon stabilization. Halteres Research on insect flight revealed that in order to maintain stability insects use structures called halteres which detect body rotational velocities by measuring gyroscopic forces [5]. It is possible to identify five main units. each of which is responsible for a distinct task: the locomotory unit. the sensory system unit. the power supply unit. the communication unit and the control unit [5]. The locomotory unit. eomposed of the electromechanical thorax-wings system. is responsible for controlling the
~s the wing moves, the vortex behind the leading edge Increases along with the aerodynamic force. However, after a certain distance a new vortex starts appearing behind the trailing edge to keep the total fluid momentum constant. This vortex has a rotation direction opposite to that of the leading edge vortex and in turn decreases the force production. Moreover, the vortex on the leading edge keeps on increasing till it reaches a critical size at which point it detaches from the wing and is shed into the fluid. thus decreasing even further the force production. As soon as the leading edge vortex detaches. a new vortex starts appearing behind the leading edge and this process of the vortex building and detaching repeats itself endlessly [6]. The roealional lift mechanism is the result of a combination of the translation and rotation of the wing. ThiS mechanism is analogous to the one that allows a ball to Curve when it is thrown with some spin. as eommonlv seen in baseball or tennis. In fact. an aerodYnamic fore;
]
~erpendicular to the translational velocity ~ppears if the all has a back-spill. The mal!nitude of the aerodvnamic force generated by the rotati~nal lift is approxi~ately
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