Using a MEMS gyroscope to stabilize the attitude of a

fly-sized hovering robotSawyer B. Fuller†, E. Farrell Helbling†, Pakpong Chirarattananon, and Robert J. Wood∗

ABSTRACT

Creating an autonomous flying vehicle the sizeof a honeybee presents a number of technicalchallenges because of its small scale. As vehiclewingspan diminishes, angular acceleration ratesincrease, necessitating sensing and control sys-tems with high bandwidth. Hovering demonstra-tions have so far required feedback from high-speed motion capture cameras to estimate the an-gular velocity, attitude, and position of the ve-hicle to provide the continuous corrective feed-back necessary to avoid tumbling. To achieveautonomous flight, it will be necessary to incor-porate a suite of sensors carried onboard. Herewe present a step in this direction by integrating aMEMS gyroscope onto an 80 mg flapping-wingmicro air vehicle to provide attitude feedback inflight. This enables 2–5 s hovering flights inwhich the motion capture system provides onlyposition feedback. Our vehicle, and likely oth-ers in the future of similar scale, is propelledby flapping wings that generate vibration. Ourresults indicate that the resulting accelerations,measured as high as 5 g by the sensor’s ac-celerometer, significantly distort readings fromthe accelerometer but not the gyroscope.

1 INTRODUCTION

Significant challenges accompany the reduction of a fly-ing robot to the size of a fly or bee. As vehicle size dimin-ishes, conventional propulsion approaches (e.g. as in rotor-craft) become impractical because of physical scaling laws.For example, energy losses per unit mass of an electromag-netic motor increase as l−2 [1], where l is some character-istic length of the vehicle such as the chord length. Biolog-ical organisms at this scale instead use flapping wings [2].Most small flying animals, from hummingbirds to flies,have evolved a convergent solution of hovering by flappingwings to overcome the low glide ratio of fixed wings at lowReynold’s numbers [3]. The resulting unsteady aerodynamicsaugment lift [2, 4].

∗†Authors contributed equally. All authors are with the School ofEngineering and Applied Sciences and the Wyss Institute for Biologi-cally Inspired Engineering, Harvard University, Cambridge MA 02138USA (E-mail: minster@seas.harvard.edu, ehelbling@seas.harvard.edu,pakpongc@seas.harvard.edu, and rjwood@eecs.harvard.edu)

Figure 1: A robotic fly (81 mg) carries an onboard inertialmeasurement unit (40 mg) attached to the anterior to measureangular velocity. This feedback was used by the controllerto apply corrective torques through the wings to stabilize itsflight and hover.

The challenges at small scale extend to sensing and con-trol. As the vehicle becomes smaller, the rate of rotationalacceleration increases, scaling as l−1 [5]. This challenge isexacerbated by dynamic instability for designs that have thesame basic body plan as hovering insects such as flies andbees, whose body hangs below the wings. Aeromechanicssimulations suggest that typical baseline hovering wing kine-matics lead to a dynamically unstable system [6, 7, 8]. There-fore, not only must a flight controller for such vehicles per-form continuous corrective maneuvers as is required in fighterjets [9], it must do so with a time delay that is orders of mag-nitude shorter because of the smaller length scale. This isbecause fundamental control limits place an upper bound onthe time delay that can be tolerated in a control loop thatmust stabilize a dynamically unstable system [10]. A vehi-cle the size of a fly or bee is nevertheless large enough that itis foreseeable that currently-available sensing and computa-tion technologies could be miniaturized to fit within its massand power constraints. An initial step toward flight autonomyis to equip a sensor that can stabilize its attitude dynamics.

The first fly-sized robot to carry its own weight over-came the propulsion challenge by driving flapping wingsusing piezoelectric actuators [4, 11]. Piezoelectric actua-tors have no moving components, allowing them to scaledownward more favorably compared to motors that require

1

bearings and gears [1]. A complementary laser-based mi-crofabrication process was developed to quickly and pre-cisely create flexure-based articulated mechanisms out ofhigh-performance materials such as carbon fiber and poly-imide [12].

Here we consider the attitude control problem of sucha vehicle. Advances in fabrication and design led to an81 mg prototype with the actuation capability to control itsflight motions [13], shown in Figure 1. Using an array ofexternal motion capture cameras and reflective markers at-tached to the vehicle to provide attitude and position feed-back, a controller was developed that enabled it to performcontrolled flight maneuvers [14]. To fly this vehicle au-tonomously outside of laboratory conditions, however, scale-appropriate sensing and control must be developed. Stabil-ity has previously been achieved with airfoils such as airdampers [7] or a tail [15, 16], but this makes the vehiclesusceptible to wind disturbances and sacrifices maneuverabil-ity. An alternate approach, inspired by the ocelli of flyinginsects, achieved upright stability using four light-sensitivephototransistors and a light source above the vehicle [17]. Inthis work we use an inertial measurement unit (IMU) builtfrom micro-electromechanical systems (MEMS) to provideinformation about the attitude of the vehicle so that it can sta-bilize its flight motions. Feedback from onboard gyroscopeshas previously been used on flapping-wing vehicles, such asa 20 g hummingbird vehicle [18] and a 13 g four-winged or-nithopter [15], but these vehicles are more than two orders ofmagnitude more massive.

Key questions to be addressed in the current study arewhether the vehicle can be tuned to stably carry the weightof the sensor, which adds approximately 50% to the totalvehicle weight, whether data can be returned through thetether with high fidelity, and whether the sensor’s operationis disrupted by the high-frequency vibratory environment offlapping flight. In [18], it was found that certain MEMSgyroscopes produce nonsensical output when mounted on aflapping-wing vehicle. Gyroscope output was numericallyintegrated successfully to estimate absolute attitude for shortperiods on Baek’s ornithopter [15]. Both of these platforms,however, flap at only ~20 Hz. It is therefore unknown whethersensor output will be disrupted at the much higher 120 Hzflapping frequency of our vehicle.

Our results show that by carefully calibrating the vehi-cle, it can carry the extra payload of the sensor. We find thatneither communication nor gyroscopic fidelity is significantlydisrupted by deployment on the tiny flapping-wing vehicle.In Sections 2 and 3, we describe the MEMS IMU and theflapping-wing micro air vehicle used in our test flights. InSection 4 we give an analysis of how rate feedback can giveupright stability and demonstrate this principle using flighttests, reproducing earlier results using ocelli [17]. In Sec-tion 5 we show how this sensor was used to achieve shortduration hovering, by demonstrating a series of flight tests

Table 1: Characteristics of the MPU9150 Inertial Measure-ment Unit

Characteristic Typical Value

Mass 36 mgArea 4 × 4 mm2

Height 1 mmPower 2.4 V, 9.4 mWMax. Output Data Rate

Gyroscope 8 kHzAccelerometer 1 kHzMagnetometer 8 HzMax. RangeGyroscope ±2000◦/sAccelerometer ±16gMagnetometer ±1200µTMax. Sensitivity

Gyroscope 16.4 LSB/(◦/s)Accelerometer 2048 LSB/gMagnetometer 0.3 LSB/µT

Figure 2: IMU connected to the custom flex circuit. A) Un-populated circuit board. B) Sensor and three capacitors (two01-005 and one 04-02 size) after attachment to the circuitboard, showing four-wire connection at the top. The outerborder of the flex circuit has been modified from A to B toaccommodate placement on the top of the robot. C) Popu-lated circuit board shown from the back.

in which successively fewer components of external motioncapture measurements are used for feedback control.

2 MEMS INERTIAL MEASUREMENT UNIT

2.1 Selection and Fabrication

The MPU9150 (Invensense, San Jose, CA, U.S.A.) wasthe first MEMS device to include a 3-axis accelerometer, a3-axis gyroscope, and a 3-axis magnetometer in a packagesmall enough for our robotic fly to carry (see Table 1 for spec-ifications). It communicates using the I2C protocol, provid-ing feedback rates as high as 1 kHz. This is a higher ratethan the 500 Hz motion capture system which has previouslybeen used to stabilize the robot [14]. The sensor requires aminimum of three capacitors—one bypass capacitor, a filtercapacitor and a charge pump capacitor. In addition, the pinsfor external clock input, frame synchronization input, and the

1.4 1.5 1.6 1.7 1.8 1.9−10

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ω (r

ad/s

)

time (s)

1.35 1.4 1.45 1.5−15

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−5

0

5

10

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ad/s

)

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Figure 3: (top) Data from the flight in Figure 6 comparingfiltered estimates of angular velocity ω from the gyroscope(thick lines) to that of the motion capture system (thin lines).The wings ramp-up flapping starting at t=1.35 s; red, green,and blue correspond to ωx, ωy, and ωz , respectively. Spikesin the motion tracking estimates from the period t=1.5 to 1.7 sare due to imperfect tracking. (bottom) A close-up of read-ings from the gyroscope before filtering (thin lines, 1 kHzsampling frequency can be observed) and after filtering bya 3rd order low-pass Butterworth filter with a 40 Hz cutofffrequency. A prominent oscillation at the 120 Hz flappingfrequency of the wings can be observed in the unfiltered mea-surements.

slave address least significant bit need to be pulled low. Thelogic voltage and supply voltage were connected to reduce thenumber of wires and weight. To satisfy these requirementswe designed a custom printed circuit board (flex circuit) tomount on the robot.

The sensor itself has a mass 36 mg (Table 1). The addi-tional components of the capacitors, board, and solder addedan additional 4 mg. In [13], measured lift forces indicatedthat the robotic fly could carry an additional 60-70 mg whileflapping with a maximum wingbeat amplitude. But operatingthe wings at full amplitude leaves no capability to modulatewing kinematics to apply torques around the pitch and rollaxes (Section 3). The lower the payload, the greater the con-trol torques that can be applied. Accordingly, to minimizemass the board was made from thin copper-clad flex circuitmaterial (18 µm copper, 12.7 µm polyimide). The circuit wasfabricated using a direct-write photolithography and etchingprocess and components were then hand-soldered (Figure 2).To minimize torque due to an off-axis placement, the sensorwas attached at the anterior of the vehicle, as shown in Fig-ure 1.

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Figure 4: Accelerometer measurements in flight. (top) In ahovering test, the vehicle begins flapping its wings at t=2 sand flies to the setpoint altitude. (middle) A plot of ac-celerometer readings over a shorter time window shows the120 Hz oscillations induced by the flapping wings and fil-tered version (approximately horizontal lines). Red, green,and blue are body x-, y-, and z-axis measurements, respec-tively. Accelerations up to ±5 g are measured along theforward-backward direction of the flapping wings. (bottom)Motion capture estimate of acceleration (filtered, light line)compared to accelerometer measurements along the z-axis(filtered, dark line, data rotated to world frame).

2.2 Communication interface and control

Sensor data was communicated over I2C at 400 kbpsthrough four 51-gauge copper wires measuring approxi-mately 30 cm. Control computations were performed by adesktop computer running an xPC Target realtime operatingsystem (Mathworks, Natick, MA, USA). The data rate is suf-ficient to communicate gyroscope and accelerometer readingsat a rate of 1 kHz. The control loop on this computer oper-ated at 10 kHz to provide smooth analog signals to externalhigh-voltage amplifiers. Because the I2C protocol requiresdigital communication at rates much higher than the con-trol loop frequency, a field-programmable-gate-array (FPGA)add-in card (Speedgoat GmbH, Liebefeld, Switzerland) wasprogrammed to implement the I2C protocol. A voltage levelshifter (Phillips GTL2002) allowed digital electrical commu-nication between the MPU9150 (max 3.3 V) and the FPGAboard (5V TTL). Embedded Matlab software translated the16-bit signed integer sensor readouts into floating point quan-tities for use in the controller.

2.3 Initial Characterization

To characterize the sensor, we compared the outputs ofthe gyroscope and the accelerometer to motion capture mea-surements during open and closed-loop flight experiments

(see Figure 3 (top) for comparison). The filtered gyroscopedata reproduces the motion capture measurement faithfully,with approximately 10 ms less latency.

As can be seen in Figure 4, the measured accelerationalong the z-axis of the robot can generally track the motioncapture estimate; however, when the wings begin flapping atapproximately t=2.1 s, the accelerometer estimate becomesnegative (Figure 4). Given the altitude trajectory, we ex-pect a positive acceleration at the start that approaches zeroas the robot reaches the desired altitude. This is reflected inthe motion capture measurement. The raw signal from theaccelerometer, however, shows high frequency noise with amaximum amplitude of (±5 g) along the y-axis. This is in thesame direction as the forward-backward motion induced bythe flapping wings. It is possible this large oscillation cross-couples to other degrees of freedom or moves the sensor intoa nonlinear regime in which it is slightly less precise. Thedistortion is nearly −2 m/s2, is larger than the accelerationsof interest, which are on the order of 1 m/s2 (Figure 4). In-tegrating this sensor’s output twice to estimate position givesan error on the order of one meter within a second in all di-rections, suggesting it cannot be used for motion estimationexcept at very short timescales.

3 ROBOTIC FLY

As described in more detail in [13, 14], the robotic fly pro-totype considered here (Figure 1) has a pair of independently-actuated wings that can produce sufficient lift to take off andinduce torques independently about orthogonal axes to con-trol the vehicle’s motion. We define a right-handed coordi-nate system for the body in which the right wing points alongthe positive x-axis, the y-axis points forward, and the z-axispoints upward (Figure 5). In this definition, the long axis ofthe body hangs downward in the negative-z direction. Rolltorque is induced by varying the relative stroke amplitudes ofthe left vs. right wing. Pitch torque is induced by moving the“mean stroke angle”–the time-averaged angle of the forward-backward motion of the wings–in front (+y) or behind (−y)the center of mass [13].

The robot is given power and controlled through alightweight compliant tether wire that has little effect on ve-hicle dynamics [14, 17]. Power and control commands aretransmitted over four 51-gauge (0.022 mm diameter) copperwires and feedback from the IMU is returned through a sec-ond bundle of four. Limitations in the current manufacturingprocess limit vehicle lifetime of each laboriously-fabricatedvehicle [11] to just a few minutes of flight, after which flex-ure joints fail and the vehicle must be replaced. Accordingly,only a few flights were possible in this study.

4 UPRIGHT STABILITY IN FLIGHT

The simplest way to utilize a gyroscope to stabilize flightmotions is to take advantage of the natural dynamics of thevehicle. In previous work [17] it was shown analytically and

mg

θ

fl

} rwτc

v

z

y

fd

xX

Z

Y

Figure 5: Model and axis convention for the robotic fly. Thevehicle state is given by three quantities, the rotation angleθ, the rotation velocity ω, and the lateral velocity in bodycoordinates v. A lift force fl generated by the flapping wingsacts at a distance rw away from the center of mass and alongthe body-z direction, an aerodynamic drag force fd acts at adistance rw from the CM, and the gravitational force mg actsat the center of mass. The right-handed axis convention forworld coordinates is shown, with y pointing into the paper.A feedback controller applies a control torque τc by alteringbaseline wing kinematics.

experimentally on the flapping-wing robot testbed that sta-bility of the vehicle can be achieved by applying a torqueproportional to the angular velocity in the pitch and roll di-rections. This is because the body of the robotic fly hangsbelow the wings, exhibiting pendulum-like dynamics that areunstable without feedback, but can be stabilized through avelocity-proportional feedback that induces a “damping” ef-fect. In that work, an ocelli-inspired light sensor was usedto estimate angular velocity. Here, we first aimed to verifywhether angular velocity feedback measured from the gyro-scope could be used as a substitute.

4.1 Stability Analysis

A diagram of the planar dynamics is shown in Figure 5. Atest of this vehicle flapping in a wind tunnel indicated that thestroke-averaged drag force on the wings is nearly linear withthe incident airspeed for typical wing kinematics. This is thecase for wind in both the x- and y-directions. Accordingly,the model for aerodynamic drag in both cases is:

fd = −bwvw,

where vw is the lateral velocity of the point on the airframeat the midpoint between the two wings and bw is a drag con-stant. If the vehicle is rotating at angular velocity ω, thenthe velocity of the wings, when linearized around θ = 0,is vw = rwω + v, where rw is the distance from the mid-point of the wings to the CM. Similarly, the force arisingfrom aerodynamic drag is fd = −bw(v + rwω) and thetorque about the center of mass due to this force is τd =−rwfd = bwrwv − bwr2wω. With lift force due to the flap-ping wings (fl) approximately balancing out weight (mg),the lateral force due to the tilted thrust vector is equal to−fl sin θ = −mg sin θ ≈ −mgθ for small θ.

With a control law that applies a torque proportional tothe rate of rotation,

τc = −kdω, (1)

and assuming planar motion, we can neglect second-ordercross-product terms and equate forces and torques to veloc-ities according to f = mvx and τ = J ω. The linearizedequations of motion about zero pitch angle θ can be writtenas a state-space dynamical system q = Aq with the state vec-tor q = [θ, ω, v]T expressed in body coordinates, where

A =

⎡

⎣

0 1 00 − 1

J(bwr2w + kd) 1

Jbwrw

−g bwrwm

− bwm

⎤

⎦ . (2)

Using the Routh-Hurwitz stability criterion gives a lowerbound on the velocity feedback gain in the controller givenin Equation (1) necessary to achieve asymptotic stability at[θ, ω, v] = 0 for the robotic fly. Using previously-publishedparameters and the addition of the 40 mg mass of sensor theon the anterior of the robot, 1.5 mm above the leading edgeof the wing, we found that a gain of kd = 2 × 10−7 wassufficient to achieve stability for both xz- and yz- dynamics.

4.2 Flight Tests

Tuning in preparation for closed-loop flights was initiatedas follows. If the vehicle is sufficiently well-fabricated thatit can take off without a torque bias, then the direction ofpitch or roll velocity after take-off is observed. Trim valuesfor pitch and roll torque are altered to the maximum extremeto oppose its initial torque. If in the subsequent take-off thevehicle is observed to apply a net torque in the opposite direc-tion, the vehicle is deemed worthy of further testing. A searchis then performed to find trim parameters for which takeoff isnearly vertical.

The vehicle’s flight trajectory with feedback from the gy-roscope alone is shown in Figure 6. In this flight, feedbackfrom the gyroscope was applied according to the control lawin Equation (1). The vehicle remains stably upright duringthis flight, indicating that gyroscopic feedback is able to sta-bilize its upright orientation as desired. Without feedback, inall trials yet observed, the vehicle quickly tumbles.

5 HOVERING

In this section we build on the demonstration of achiev-ing upright stability using gyroscope feedback to demonstratehovering using a combination of gyroscope feedback and mo-tion capture.

The hovering controller used here incorporates improve-ments over that reported in [14] that includes an adaptivecomponent that continuously estimates vehicle parameterssuch as torque offsets [19]. We provide an overview here.The flight controller requires three inputs: angular velocityω (body coordinates), attitude [x, y, z] = RT (the unit vec-tors of the axes of the vehicle in world coordinates, equiv-alent to the transpose of the rotation matrix R), and position

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x (m)y (m)

z (m

)

Figure 6: Plot of flight trajectory in which angular velocityfeedback from the gyroscope was used to maintain an up-right orientation. In this flight, position was not under feed-back control. Vehicle attitude is rendered at 20 ms intervals.Dots represent the location of the CM of the vehicle and theblack line denotes the long axis of the body; projections ofthe trajectory are shown in grey in the background. In the z-projection below the vehicle, the “forward” +y direction ofthe vehicle is projected rather than its long axis to indicate thevehicle’s heading.

[X,Y, Z]T (world coordinates). An independent altitude con-troller modulates the thrust force to maintain the desired al-titude given position feedback. An outer position loop com-putes a desired direction of the z vector, zd, based on theposition error. By inclining the axis of the vehicle, lateralthrusts can be generated. The attitude error is defined ase = [y · zd, −x · zd, 0]T . Based on this error, the attitudecontroller calculates torques as a function of the attitude errore and angular velocity ω according to:

τc = f(e,ω) + τo

= −Ka(ω + Λe)− (Λe× Jω)− JΛe+ τo (3)

where Ka and Λ are positive diagonal gain matrices that areexperimentally tuned, τo is the trimmed offset torque neces-sary to compensate for manufacturing irregularity, and J isthe estimate of the inertia matrix.

To use gyroscope feedback in this controller, note that theoutput of the three-axis gyroscope is an estimate of ω. Ad-ditionally, from Equation (3), an estimate of attitude error eis needed. We parameterize the vehicle attitude using a zyx-convention for Euler Angles to avoid representation singular-ities at hover. In this convention, attitude is defined by firstrotating the frame by an angle θ3 ∈ (−π,π] (yaw) aroundthe body z-axis, then θ2 ∈

(

−π2, π2

)

(roll) around the new

body y-axis, and then θ1 ∈(

−π2, π2

)

(pitch) around that bodyx-axis. Performing the same rotations about world axes butin the opposite order, that is, XY Z , gives the same attitude.With this convention, the rates of change of these angles asa function of the angular velocity vector ω are given by the

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Figure 7: Plot of flight trajectory, rendered at 20 ms intervals.This flight used feedback entirely from motion capture, pro-viding a baseline performance measure. The desired hoveringposition is indicated by a red circle. Other figure conventionsare the same as in Figure 6.

product

⎡

⎣

θ1θ2θ3

⎤

⎦ =

⎡

⎣

cos θ3/ cos θ2 − sin θ3/ cos θ2 0sin θ3 cos θ3 0

− cos θ3 tan θ2 sin θ3 tan θ2 1

⎤

⎦

⎡

⎣

ω1

ω2

ω3

⎤

⎦ .

(4)By integrating Equation (4) over time, an estimate of the atti-tude can be computed from the rotation matrix derived fromthese Euler Angles [19], from which e and its derivative canbe computed.

Because of the limited lifetime of the robot, we performedthe experiments incrementally. First, we verified that hover-ing was operational using only feedback from motion cap-ture, insuring that the necessary amount of control authoritywas available after incorporating the additional payload, andto quantify a baseline flight performance. Next, we incorpo-rated the angular velocity estimate ω from the gyroscope intothe feedback loop. Finally we additionally incorporated theattitude estimate z derived from integrating gyroscope output(Equation (4)) so that motion capture feedback was entirelyeliminated from attitude control of the robot.

5.1 Motion Capture Feedback

Figure 7 shows that, with appropriate tuning of controllergains and trim values, the robot was able to carry the extrapayload and take off and hover near the desired setpoint po-sition [X, Y, Z]T = [0.1 , 0, 0.06]T m using motion capturefeedback. Its mean position for the 2 s period after reachingthe desired altitude was [0.109, 0.0077, 0.056]T m.

5.2 Angular Velocity Feedback

Having demonstrated in Section 2 that the angular veloc-ity estimate of ω from the gyroscope accurately tracks theground truth measurement from motion capture, with lower

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Figure 8: Plot of hovering flight trajectory in which gyro-scope provided an estimate of the angular velocity ω. Otherdetails are the same as in Figure (7).

latency, we incorporated this estimate into the hovering atti-tude controller. Figure 8 shows that the robot achieves hover-ing flight, flying near the set point, maintaining a mean posi-tion of [0.093, 0.0058, 0.056]T m and comparable error.

5.3 Attitude Feedback

In this experiment, we performed a zero-order hold nu-merical integration of Equation (4), initialized using the mo-tion capture estimate of attitude at t=0 s. Figure 9 shows thetrajectory of the robot during a flight in which both angularvelocity and attitude were estimated by feedback from theonboard gyroscope. In this experiment the robot remainednear the setpoint position for approximately 2 s, after whichit began to exhibit significant position error. This may beattributable to drift in the attitude estimate causing a lateralthrust error. During the initial 2 s period of tracking, the robotmaintained a mean position of [0.075, 0.029, 0.057]T m.

5.4 Analysis

The flight using only motion capture estimates produceda mean Euclidean distance error of less than 0.01 m from thesetpoint. When the ω estimate from the gyroscope was in-corporated, the mean error was a comparable 0.01 m. For theflight in which gyroscope feedback additionally estimated theattitude z, the error increased to 0.03 m. A possible explana-tion for the error is that, as can be observed in Figure 10, avisible drift is noticeable along the pitch (red) axis, reachingan error of 6◦ (0.1 rad). This drift, perhaps arising becausethe largest oscillations occur about this axis because of theforward-backward motions of the wings (Figure 3), wouldcause a force error in the y-direction as the vehicle tilted inresponse.

In addition to plotting the 3D trajectory of each flight andcomparing the mean position of each flight experiment, wecalculated the root mean square error (RMSE, see Figure 11).We expect comparable levels of RMSE in altitude because

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Figure 9: Plot of flight trajectory in which the gyroscope pro-vided all attitude feedback in the flight controller, includingboth angular velocity ω and attitude z. In this flight, the po-sition error was somewhat larger than in Figure (8), possiblybecause of drift in the attitude estimate. Other details are thesame as in Figure (7).

the altitude controller runs independently of the attitude con-troller and receives the same measurements in all tests, ascan be observed in Figure 11. RMSE is comparable betweenthe motion capture-only experiment and experiment in whichthe gyroscope estimated ω for both x-position, where the er-rors are 1.17 cm and 1.39 cm, respectively, as well as forthe y-position, where the errors are 1.26 cm and 1.05 cm,respectively. The RMSE of the lateral position of the flightwith attitude estimation from the gyroscope is significantlylarger at 2.72 cm in x−position and 2.95 cm in y-position.Given that the robot had difficulty correcting its pitch angleand drifted away from the set point during flight, these val-ues are not unexpected. These results indicate that estimatesfrom the gyroscope can be substituted for those from the mo-tion capture system and still maintain stability and control ofthe vehicle despite its fast and unstable dynamics.

6 CONCLUSIONS

In this work we demonstrated a MEMS IMU integratedwith a fly-sized robotic vehicle. Feedback from this sensorwas shown to be sufficient to stabilize this vehicle’s uprightorientation and estimate the vehicle’s attitude for short peri-ods for use in an inner attitude control loop. This constitutesthe first demonstration of controlled flight in fly-sized robotin which only position feedback was derived from externalsensors.

Our results indicate that gyroscope sensor readings aresomewhat, though not significantly impaired by vibrationsinduced by the wings. Because the flapping frequency isknown, a future improvement could refine the filter designto better eliminate it, either by a notch filter or by adaptivecancellation, and thus reduce feedback latency even further.

2 2.5 3 3.5 4−2

−1.5

−1

−0.5

0

0.5

thet

a (ra

d)

time (s)

Figure 10: Comparison of measured Euler Angles – pitch(red), roll (green), and yaw (blue) – from motion capture (thinline) to the estimate derived by integrating gyroscope feed-back (thick line) from the flight shown in Figure (9). Theflight starts at t=2.0 s. Drifting over time can be observed,particularly about the x-axis (pitch).

0

0.005

0.01

0.015

0.02

0.025

0.03

X Y Z

RM

SE

(m

)

Figure 11: Root Mean Square Error (RMSE) position er-ror for x-, y-, and z-coordinates for three flight experiments:motion capture feedback (blue), ω estimate from gyroscope(green), and full attitude measurements (ω, z) from gyro-scope (red).

Our results indicate that the accelerometer component ex-hibited significant noise and distortion in the presence of theflapping wings. This suggests alternative sensing modes maybe necessary to quickly sense translational motions for high-bandwidth control, such as infrared proximity sensors, vision,or a pressure sensor (for altitude). We cannot rule out thatsonar or laser rangefinders could be sufficiently miniaturized.

As the fabrication process matures, more flights will bepossible, which will permit a more comprehensive charac-terization of the system dynamics presented here. To permitlonger flight times, drift in the attitude estimate could be re-duced by incorporating accelerometer or magnetometer feed-back using a Kalman Filter.

The results reported here provide a baseline sensor suitefor stable flight that will enable future flight control studies.They motivate further development in lightweight sensing,

computation, power source, and control technologies appro-priate for bee- or fly-sized flying vehicles.

7 ACKNOWLEDGEMENTS

This work was partially supported by the National Sci-ence Foundation (award numbers CMMI-0746638 and CCF-0926148) and the Wyss Institute for Biologically Inspired Re-search. Any opinions, findings, conclusions, or recommenda-tions expressed in this material are those of the authors anddo not necessarily reflect the views of the National ScienceFoundation.

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