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Halteres for the Micromechanical Flying Insect * W.C. Wu R.J. Wood R.S. Fearing Department of EECS, University of California, Berkeley, CA 94720 {wcwu, rjwood, ronf}@robotics.eecs.berkeley.edu Abstract The mechanism which real flying insects use to de- tect body rotation has been simulated. The results show that an angular rate sensor can be made based on such a biological mechanism. Two types of biomimetic gy- roscopes have been constructed using foils of stainless steel. The first device is connected directly to a com- pliant cantilever. The second device is placed on a mechanically amplifying fourbar structure. Both de- vices are driven by piezoelectric actuators and detect the Coriolis force using strain gages. The experimental results show successful measurements of angular veloc- ities and these devices have the benefits of low power and high sensitivity. 1 Introduction Micro aerial vehicles (MAVs) have drawn a great deal of attention in the past decade due to the quick advances in microtechnology. Commercial and mili- tary applications for micro-robotic devices have been identified including operations in hazardous environ- ments, search-and-rescue within collapsed buildings, reconnaissance and surveillance, etc.. Although sev- eral groups have worked on MAVs based on fixed and rotary wings [6], flapping flight provides superior maneuverability that would be beneficial in obstacle avoidance and for navigation in small spaces [11]. Inspired by the exceptional flight capabilities achieved by real insects, the UC Berkeley Microme- chanical Flying Insect (MFI) project uses biomimetic principles to develop a flapping wing MAV that will be capable of sustained autonomous flight. The over- all structure of the MFI has been designed and some components have been built and tested [3],[10],[11]. As with real insects, angular rotation detection by the sensory system of the MFI is important for stabilizing flight. Although precise MEMS gyroscopes are com- mercially available, their designs (package size, power requirements, etc.) are in general not suitable for the * This work was funded by NSF KDI ECS 9873474, ONR MURI N00014-98-1-0671, and DARPA. MFI. On the other hand, piezoelectric vibrating struc- tures have been developed and have proven to be able to detect Coriolis force with high accuracy [8]. There- fore, based on the gyroscopic sensing of real flies, a novel design using piezoelectric devices is being con- sidered. This paper describes the simulations and fab- rication of this type of biologically inspired angular rate sensor for use on the MFI. 2 Haltere Morphology Research on insect flight revealed that in order to maintain stable flight, insects use structures, called halteres, to detect body rotations via gyroscopic forces [5]. The halteres of a fly evolved from hindwings and are hidden in the space between thorax and abdomen so that air current has negligible effect on them (see figure 1). The halteres resemble small balls at the end of thin sticks. There are about 400 sensilla embedded in the flexible exoskeleton at the haltere base. These Figure 1: Schematic of enlarged halteres of a fly. mechanoreceptors function as strain gages to detect the Coriolis force exerted on the halteres [4]. During flight the halteres beat up and down in vertical planes through an average angle of nearly 180 o anti-phase to the wings at the wingbeat frequency. When a fly’s hal- teres are removed or immobilized, it quickly falls to the ground. In addition, the two halteres of a fly are non-
Transcript
Page 1: Halteres for the Micromechanical Flying Insectronf/PAPERS/ICRA02... · 2018. 3. 3. · haltere(againassumedtobegreaterthanthecan-tilevermass),E isthemodulusofthematerialused, andb,h,andl

Halteres for the Micromechanical Flying Insect ∗

W.C. Wu R.J. Wood R.S. Fearing

Department of EECS, University of California, Berkeley, CA 94720

{wcwu, rjwood, ronf}@robotics.eecs.berkeley.edu

Abstract

The mechanism which real flying insects use to de-

tect body rotation has been simulated. The results show

that an angular rate sensor can be made based on such

a biological mechanism. Two types of biomimetic gy-

roscopes have been constructed using foils of stainless

steel. The first device is connected directly to a com-

pliant cantilever. The second device is placed on a

mechanically amplifying fourbar structure. Both de-

vices are driven by piezoelectric actuators and detect

the Coriolis force using strain gages. The experimental

results show successful measurements of angular veloc-

ities and these devices have the benefits of low power

and high sensitivity.

1 Introduction

Micro aerial vehicles (MAVs) have drawn a greatdeal of attention in the past decade due to the quickadvances in microtechnology. Commercial and mili-tary applications for micro-robotic devices have beenidentified including operations in hazardous environ-ments, search-and-rescue within collapsed buildings,reconnaissance and surveillance, etc.. Although sev-eral groups have worked on MAVs based on fixedand rotary wings [6], flapping flight provides superiormaneuverability that would be beneficial in obstacleavoidance and for navigation in small spaces [11].Inspired by the exceptional flight capabilities

achieved by real insects, the UC Berkeley Microme-chanical Flying Insect (MFI) project uses biomimeticprinciples to develop a flapping wing MAV that willbe capable of sustained autonomous flight. The over-all structure of the MFI has been designed and somecomponents have been built and tested [3],[10],[11]. Aswith real insects, angular rotation detection by thesensory system of the MFI is important for stabilizingflight. Although precise MEMS gyroscopes are com-mercially available, their designs (package size, powerrequirements, etc.) are in general not suitable for the

∗This work was funded by NSF KDI ECS 9873474, ONR

MURI N00014-98-1-0671, and DARPA.

MFI. On the other hand, piezoelectric vibrating struc-tures have been developed and have proven to be ableto detect Coriolis force with high accuracy [8]. There-fore, based on the gyroscopic sensing of real flies, anovel design using piezoelectric devices is being con-sidered. This paper describes the simulations and fab-rication of this type of biologically inspired angularrate sensor for use on the MFI.

2 Haltere Morphology

Research on insect flight revealed that in order tomaintain stable flight, insects use structures, calledhalteres, to detect body rotations via gyroscopic forces[5]. The halteres of a fly evolved from hindwings andare hidden in the space between thorax and abdomenso that air current has negligible effect on them (seefigure 1). The halteres resemble small balls at the endof thin sticks. There are about 400 sensilla embeddedin the flexible exoskeleton at the haltere base. These ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Figure 1: Schematic of enlarged halteres of a fly.

mechanoreceptors function as strain gages to detectthe Coriolis force exerted on the halteres [4]. Duringflight the halteres beat up and down in vertical planesthrough an average angle of nearly 180o anti-phase tothe wings at the wingbeat frequency. When a fly’s hal-teres are removed or immobilized, it quickly falls to theground. In addition, the two halteres of a fly are non-

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��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Figure 2: Haltere force modulation.

coplanar (each is tilted backward from the transverseplane by about 30o) so that flies can detect rotationsabout all three turning axes.As detailed in [7], a complex force, as a result of

insect motion and haltere kinematics, acts on the hal-teres during flight (see figure 2). Assuming no transla-tional motion of the insect, this force can be expressedin vector notation by the following:

F = mg−ma−mω̇×r−mω×(ω×r)−2mω×v (1)

where m is the mass of the haltere, r, v, and a arethe position, velocity, and acceleration of the haltererelative to the insect body, ω and ω̇ are the angularvelocity and angular acceleration of the insect, and g isthe gravitational constant. Further, this force can bedecomposed into radial, tangential, and lateral compo-nents as depicted by the exploded view of the halterein figure 1. Insect’s body rotations produce centrifugal(−mω × (ω × r)) and Coriolis (−2mω × v) forces onthe halteres. The centrifugal force is generally smallerthan the Coriolis force and mostly in the radial andtangential directions. Moreover, since the centrifugalforce is proportional to the square of angular velocityof the insect, it provides no information on the signof rotations. The Coriolis force, on the other hand,is proportional to the product of the angular velocityof the insect and the instantaneous haltere velocity.The Coriolis force has components in all three direc-tions and contains information on the axis, sign, andmagnitude of the insect’s body rotation. The angularacceleration force (−mω̇ × r) is proportional to theproduct of the angular acceleration of the insect andthe instantaneous position of the haltere. The angularacceleration and the Coriolis force signals are separa-ble because of the 90o phase shift (they are orthogonalfunctions). The primary inertial force (−ma) dependson the haltere acceleration relative to the insect body.This force is orders of magnitude larger than the Cori-

olis force and has only radial and tangential compo-nents. The gravitational force (mg) is always constantand depending on the haltere position and the insect’sbody attitude in space, its distribution in the threedirections varies. However, the effect of this gravita-tional force on the angular velocity sensing is negligiblebecause it is a tonic lateral component which can beconsidered as DC offset on the Coriolis force and re-moved easily by the subsequent signal processing step.

3 Simulations

To detect angular rotations, the lateral forces on thehalteres are measured because the large primary iner-tial force has no contribution in the lateral directionand hence it is possible to measure the Coriolis sig-nal among all other interfering force signals appearingin this direction. Figure 3 shows the lateral compo-nents of the Coriolis force on both halteres for rota-tions about the roll, pitch, and yaw axes. Because ofthe dependence of the Coriolis force on the haltere ve-locity, these force signals are modulated in time withhaltere beat frequency. For a roll rotation, the sig-nal is modulated with the haltere beat frequency andthe left and right signals are 180o out-of-phase. For apitch rotation, the signal is also modulated with thehaltere beat frequency, but the left and right signalsare in-phase. For a yaw rotation, the signal is modu-lated with double the haltere beat frequency and theleft and right signals are 180o out-of-phase.

0 0.5 1−1

−0.5

0

0.5

1x 10

−4Left Haltere

forc

e (N

)

0 0.5 1−1

−0.5

0

0.5

1x 10

−4Right Haltere

0 0.5 1−2

−1

0

1

2x 10

−4

forc

e (N

)

0 0.5 1−2

−1

0

1

2x 10

−4

0 0.5 1−5

−2.5

0

2.5

5x 10

−5

forc

e (N

)

0 0.5 1−5

−2.5

0

2.5

5x 10

−5

Roll

Pitch

Yaw

Figure 3: Coriolis lateral forces for rotations aboutroll, pitch, and yaw axes. Signals during one halterecycle are shown.

Utilizing the characteristics (frequency, modula-tion, and phase) of these force signals on the left andright halteres, a demodulation scheme is proposed todistinguish roll, pitch, and yaw rotations. First, a

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pitch rotation can be separated from roll and yaw ro-tations by adding the left and right signals. Becausethe left and right signals are in-phase for pitch whileout-of-phase for roll and yaw, adding the left and rightsignals retains pitch component and eliminates roll andyaw components. Then, roll and yaw rotations can beseparated by multiplying demodulating signals of dif-ferent frequencies. A sinusoidal signal at the halterefrequency retrieves the roll signal while a sinusoidalsignal of double the haltere frequency retrieves the yawsignal. Figure 4 illustrates the proposed demodulationscheme. Ideally, the magnitudes of the amplifiers, Ar,Ay, and Ap, would be proportional to −1/2m, wherem is the mass of the haltere. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Figure 4: Demodulation scheme of haltere forces.

4 Haltere Design Issues

The results of the simulation show that abiomimetic mechanical haltere is feasible for the pa-rameters of a robotic flying insect. The next step is toshow with experimental results that it is feasible to usea mechanical haltere to measure angular velocity. Todo this, the simulation parameters are used as the de-sign parameters for the haltere. The key parametersfor the design are the haltere length, mass, velocity,and stroke amplitude. Little attention is paid to thehaltere orientation since it is assumed that it can bearbitrarily placed upon a robotic insect.

Unlike the force sensing methods used in [1],[2],[10],the haltere must have only one sensing degree of free-dom. The design of the haltere must allow for highstiffness in the tangential direction and compliance inthe lateral direction. Thus, the inertial forces will notbe sensed, and the smaller Coriolis forces can be de-tected. The best case mechanically for this is a flatbeam with the wide face in the plane of the halterebeating. The ratio of the stiffness in the two direc-

tions is given by the following:

kt

kl=

EIt

3l3

EIl

3l3

=It

Il=

bh3

12hb3

12

=b2

h2(2)

where It and Il are the tangential and lateral cross sec-tional moments of inertia, b is the width of the beam,and h is the thickness.One of the major concerns with the design of the

haltere is actuation. Since the Coriolis force is pro-portional to the haltere velocity, it is desired to havea high haltere beat frequency and a large stroke. Twomethods of actuation will be discussed here. The sim-pler of the two places the haltere on a vibrating struc-ture with a high Q compliant beam in between. Thevibrating structure, in this case a piezoelectric actua-tor, drives the haltere into resonance, while its high Qgives large stroke amplitudes. This method has thebenefits of not only being simple to construct, butalso this structure has the ability to be driven par-asitically from the body vibrations of the MFI. Thesecond method places the haltere on the output linkof a fourbar mechanism driven by a piezoelectric ac-tuator, similar to the method used to drive the MFIwing as described in [3],[9],[11].The first design to be discussed is the piezo-actuated

vibrating structure. The mechanical haltere measuresthe Coriolis force using strain gages at its base whichmeasure moments applied in the direction orthogonalto its beating plane. The first step in the haltere de-sign is to determine from the simulation parameterswhat the minimum Coriolis force acting on the halterewill be. Using the simulation parameters of 400Hzbeat frequency at an amplitude of α = 0.5rad, and alength l of 5.5mm, the peak velocity of the mass isfound to be 2.27m/s. Now, as a low-end estimate of asmall angular velocity that a flying robotic insect willencounter, ωmin was set to 1rad/s. Finally, the masswas set to 10mg, so that the minimum Coriolis forceacting on the mass is 22.7µN .The haltere can be thought of as a cantilever, with

one end fixed at the point of rotation. Thus, the Cori-olis force acting on the mass produces a strain in thebeam defined by the following:

Fc =M

l − x=

EIε

z(l − x)(3)

where Fc is the Coriolis force, M is the generated mo-ment, x is the distance from the base of the cantileverto the strain gage, E is the Young’s modulus of thehaltere material, I is the cross sectional moment ofinertia, z is the distance from the neutral axis to thestrain gage, and ε is the strain in the haltere. From

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equation 3, it is clear that the maximum moment, andthus the maximum sensitivity will occur by placingthe gage as close to the point of rotation as possible.The haltere is constructed in such a way that there isa high Q compliant section to allow for rotation, andthen the beam is twisted to allow compliance in the de-sired direction. Thus, the minimum dimension x wasconstrained to be 2mm. The modulus E is given tobe 193 GPa since the material used was stainless steel.The cross sectional moment of inertia is defined to be I= bh3/12, thus the final parameters to be determinedfor the haltere were b and h. Using a thickness of 50µmand a width of 0.5mm, along with the minimum Cori-olis force gives the minimum strain εmin = 2×10

−6

which is above the noise floor for typical strain gagesignal conditioners. Also, from equation 2, the ratioof tangential to lateral stiffness is 100. For actuation,the haltere was connected directly to the free end of acantilevered PZT unimorph. This was done in such away that the Q of the haltere was sufficiently high toallow for greater motion than that of the PZT alone.

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Figure 5: Haltere description and design parameters.

The last design issue was how to orient the straingages and deal with their wires. Since the gages areextremely sensitive to thermal drifts, a fullWheatstone

Bridge is the most desirable configuration for the sen-sors. However, because of the limited surface area ofthe haltere, only a half bridge was possible. This wasdone by placing one gage on either side so that onewould always be in compression while the other was intension. The sensors used were 1mm long × 100µmwide semiconductor strain gages made by Entran, Inc.The main concern with the gage placement is success-fully using the delicate gold leads to bring the signaloff the haltere while not damaging them or adding ad-ditional parallel stiffness to the structure. This wasdone by placing bond pads on the compliant end ofthe haltere as shown in figure 5. The lead wires werefixed to these pads and more sturdy wire was coiled

and connected to the pads. Figure 6 shows the com-pleted haltere.

��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������

Figure 6: Completed haltere with half bridge strainsensor.

The design of the second haltere is similar to the de-sign of the MFI thorax structure as is described in [3].Instead of driving the haltere from a vibrating struc-ture, it is placed on the output link of a mechanicallyamplifying fourbar structure. The fourbar takes thesmall linear displacement of the actuator and trans-forms this into large angles at the output [3],[11]. Thistechnique gives better control over the motion of thehaltere, allowing for large stroke amplitudes at highresonant frequencies. Since the Coriolis force actingon the haltere mass is proportional to the haltere ve-locity, this method of actuation should give greatersensitivity for detection of body angular velocity.Assuming similar kinematic and dynamic con-

straints as the MFI thorax, 120o stroke amplitudeat 150Hz, and resolution constraints for sensing theforces, there are again four parameters to determine.Three geometric parameters and the mass of the hal-tere are constrained by four defining equations. First,it is desired that the stiffness in the lateral directionof the haltere is significantly higher than the drive fre-quency so that the lateral resonant mode is not ex-cited during actuation. Setting the lateral resonantfrequency at 500Hz gives the following:

2π · 500 =

kl

m=

Ebh3

4l3m(4)

where kl is the lateral stiffness, m is the mass of thehaltere (again assumed to be greater than the can-tilever mass), E is the modulus of the material used,and b, h, and l are the width, thickness, and lengthof the cantilever, respectively. Next, the minimumCoriolis force is given as a function of the minimumdetectable strain.

Fcmin =Ebh3

6lεmin (5)

For the given kinematic parameters and the desireddrive frequency, the haltere velocity is 200π · l. Now

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from equation 1, the minimum Coriolis force can berelated to the minimum detectable angular velocity(again assumed to be 1rad/s) by the following:

Fcmin = 2mωmin × v = 400π ·m · l (6)

Equating equations 5 and 6 gives the following:

Ebh3εmin = 2400π ·m · l2 (7)

where the minimum detectable strain is a known pa-rameter. The last constraint is from the dynamics ofthe MFI thorax and is based upon the desired MFIwing inertia. Equating the haltere inertia with thewing inertia gives the following:

J = m · l2 (8)

The inertia of the haltere, J = 40mg-mm2, is onlytwice the MFI wing inertia [11]. Choosing b = 1mmbecause of geometric constraints of the fourbar givesthree unknown parameters to be solved from equa-tions 5, 7, and 8. Choosing m = 4mg, l = 5mm, andh = 50µm gives a close fit to the three constraints,while still considering construction difficulties.

5 Experimental Setting

5.1 Test Setup

To test the first haltere, it was setup on a servo mo-tor, oriented such that at rest the haltere was along theω-axis. This experiment would be equivalent to sens-ing the pitch angular velocity. The servo motor had anangular velocity range of approximately 0.1−10rad/s.Ideally, the motor would be allowed to freely rotate tosense a pure angular velocity. However, for wiring con-cerns, the range of motion was restricted. One concernin the actuation of the haltere was to orient the haltereon the actuator such that when there was an appliedangular velocity, the inertial force of the haltere wouldnot interfere with the sensed signal. However, as-suming perfect alignment, the inertial force sensed bythe haltere at ω = 1rad/s is mω2sin(α/2) = 2.59µN ,roughly an order of magnitude lower than the Coriolisforce. Much care was taken to ensure that the halterewas aligned directly along the ω-axis. The fourbardriven haltere was tested in a similar manner to thefirst haltere. However, to obtain a smother angularvelocity, the structure was placed on a harmonic oscil-lator. The position of the structure on the oscillatorwas determined by using high-speed video footage andsome simple image processing. After construction, thehaltere resonant frequency was found to be 70Hz, ata stroke amplitude of 90o. This haltere structure canbe seen in figure 7.

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Figure 7: Fourbar actuated haltere at rest.

5.2 Results

The experimental results for the first haltere setupshowed that the haltere detects both the Coriolis forceand the inertial force of the mass. Figure 8 shows themeasured angular velocity and the angular velocity ofthe motor. The measured signal was demodulated asdescribed in Section 3. First, the signal was multi-plied with a unity magnitude sine wave of preciselythe haltere frequency and phase. Note that the halterephase was not measured because position sensors forthe haltere are difficult to implement on such a smallscale. Instead, the actuator phase was measured, andsince the haltere is at resonance, it is assumed thatits phase lags 90o behind that of the actuator. Then,this demodulated signal was filtered with a 3rd orderButterworth lowpass filter with a cutoff frequency of4Hz to eliminate remaining high frequency noise.

0.2 0.4 0.6 0.8 1 1.2−4

−3

−2

−1

0

1

2

3

4

Time (s)

Ang

ular

Vel

ocity

(ra

d/s)

ωmeasured ω

Figure 8: Pitch detection by the first haltere.

The results for the second structure are seen in fig-ure 9. One key difference between the two is that withthe fourbar driven structure, the position of the haltere

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can be sensed using actuator-mounted strain sensors asdescribed in [10]. After testing, this position was nor-malized to yield a unity magnitude sine wave whichrepresented the haltere phase. This was then used todemodulate the signal using the same demodulationscheme as the first structure.

1 2 3 4 5 6 7 8 9

−15

−10

−5

0

5

10

15

Time (s)

Ang

ular

Vel

ocity

(ra

d/s)

ActualHaltere Meas.

3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6

−6

−4

−2

0

2

4

6

Time (s)

Ang

ular

Vel

ocity

(ra

d/s)

ActualHaltere Meas.

Figure 9: (a) Result for the fourbar actuated haltere;(b) Zoomed in to show accuracy.

6 Conclusions and Future Work

There are several advantages for the MFI in usinghalteres instead of MEMS gyroscopes as angular ratesensors. First, the haltere needs very little power sinceit does not use active actuation. It can be driven para-sitically from the body vibrations when it is placed onthe MFI body. Second, the haltere has a large dynam-ical range. It can detect angular velocities from as lowas tens of degrees per second to as high as hundredsof thousands of degrees per second, which is often en-countered during sharp turns of flying insects. Finally,when the wings of the MFI are flapping, the wing in-ertia will cause the MFI body to oscillate about theaxis perpendicular to the stroke plane. The halterecan reduce the error caused by these oscillations byphase-locking to the wing. Table 1 shows a compar-ison of the halteres to a MEMS gyroscope made byIrvine Sensors Corp. In future revisions, the wiring ofthe haltere will be passed through slip rings such thatthe entire structure is free to rotate during testing. Inaddition, two halteres will be used together and ori-ented differently along the ω-axis to sense each of thethree angular velocities and further test the demodu-lation techniques.

Haltere I1,2 Haltere II1,2 MEMS Gyro3

Mass (mg) 12 30 1Res. (o/s) 50 50 6

Max Rate (o/s) ±100, 000 ±300, 000 ±60B.W. (Hz) 5 15 10

Power (mW ) 1 1 45

1 Assuming parasitic drive.2 Assuming 1% duty cycle strain gage sampling.3 Using thinned Si micromachined device.

Table 1: Comparison of different angular rate sensors.

Acknowledgments

The authors thank M. Dickinson for insight intothe haltere physiology and dynamics, S. Avadhanulaand L. Schenato for helpful discussions on the halteredesign and simulations.

References

[1] K. Abe, T. Miwa, and M. Uchiyama. Developmentof a 3-axis planar force/torque sensor for very smallforce/torque measurement. Trans Jpn Soc Mech Eng,42(2):376–382, 1999.

[2] A. Bicchi, A. Caiti, and D. Prattichizzo. Optimal de-sign of a multi-axis force/torque sensor. In Proc of

the IEEE International Conference on Decision and

Control, pages 2981–2986, Phoenix, AZ, Dec 1999.

[3] R.S. Fearing, K.H. Chiang, M.H. Dickinson, D.L.Pick, M. Sitti, and J. Yan. Wing transmission for amicromechanical flying insect. In Proc of the IEEE In-

ternational Conference on Robotics and Automation,pages 1509–1516, San Francisco, CA, April 2000.

[4] G. Fraenkel and J.W.S. Pringle. Halteres of flies asgyroscopic organs of equilibrium. Nature, 141:919–921, 1938.

[5] R. Hengstenberg. Mechanosensory control of compen-satory head roll during flight in the blowfly Calliphoraerythrocephala Meig. Journal of Comparative Physi-

ology A, 163:151–165, 1988.

[6] B. Motazed, D. Vos, and M. Drela. Aerodymaticsand flight control design for hovering MAVs. In Proc

of Amer Control Conference, Philadelphia, PA, June1998.

[7] G. Nalbach. The halteres of the blowfly Calliphora:I. kinematics and dynamics. Journal of Comparative

Physiology A, 173:293–300, 1993.

[8] H. Sato, T. Fukuda, F. Arai, H. Iwata, andK. Itoigawa. Analysis of parallel beam gyroscope.In Proc of the IEEE International Conference on

Robotics and Automation, pages 1632–1637, Detroit,MI, May 1999.

[9] M. Sitti, D. Campolo, J. Yan, R.S. Fearing, T. Su,and D. Taylor. Development of PZT and PZN-PTbased unimorph actuators for micromechanical flap-ping structures. In Proc of the IEEE International

Conference on Robotics and Automation, pages 3839–3846, Seoul, South Korea, May 2001.

[10] R.J. Wood and R.S. Fearing. Flight force measure-ment for a micromechanical flying insect. In Intel-

ligent Robots and Systems, Maui, HI, Oct 29-Nov 32001.

[11] J. Yan, R.J. Wood, S. Avadhanula, R.S. Fearing, andM. Sitti. Towards flapping wing control for a microme-chanical flying insect. In Proc of the IEEE Interna-

tional Conference on Robotics and Automation, pages3901–3908, Seoul, South Korea, May 2001.


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