Direct Thrust and Velocity Measurement for a Micro UAV Rotor

Edwin Davis, Paul EI Pounds∗

University of Queensland, Australia{�rstname.lastname}@uq.edu.au

Abstract

Thrust and velocity sensing is very importantfor the control of micro UAVs. Contemporaryhigh-performance quadrotor motion control re-lies on accurate high-speed trajectory sensing.However, position and velocity sensing is chal-lenging outside of an indoor Vicon arena: GPSis slow and noisy, optical �ow sensors do notwork far from ground, and pitot tubes performpoorly at low speeds.

Our approach is to use a compact force-torquesensor to directly measure rotor forces andpitch-roll torques. The sensor is constructedfrom MEMS barometers encapsulated in anelastic compound, attached to a load plate.The sensor can provide sub-mN thrust forcesensing at 1 kHz, with torque sensitivity bet-ter than 0.1 mN·m. Using a lumped parame-ter model of rotor induced drag and �appingtorque-velocity coupling, we can accurately es-timate translational velocity of a rotor. Thevelocity output is linear for translational veloc-ities from below 0.25 to over 0.8 ms−1.

1 Introduction

Precision �ight control of miniature robot aircraft re-quires an accurate model of vehicle dynamics and theforces acting upon it [Mellinger et al, 2012]. However, theprinciple source of force applied to a multirotor aircraft� its rotor � provides a variable amount of force de-pending upon the local aerodynamic conditions, proxim-ity of objects and the manoeuvres of the aircraft [Davis etal, 2015]. As a consequence, typical control approachesrely on very accurate and high-speed sensing of trajec-tory, using onboard MEMS intertial measurement units(IMUs) and systems such as Vicon, to detect and cor-rect for deviation induced by disturbances or by errors in

∗Corresponding author. This work is supported by Aus-tralian Research Council grant DE130100885.

Figure 1: Force sensor mounted under motor.

the rotor actuation model. Unfortunately, low-cost ac-celerometers are not accurate enough for precision dead-reckoning and precision IR tracking tools are not e�ec-tive outdoors due to insolation.

Other sensors are not able to �ll the gap: GPS isslow and noisy, optical �ow sensors do not function farfrom ground, and pitot tubes do not function well at lowspeeds. While barometers are generally e�ective for al-titude measurement within ±100 mm, there is currentlyno e�ective lateral velocity sensor.

An alternative approach is to focus on improving thedynamic model of the aircraft and estimate the internalstates of the rotor, so as to improve trajectory track-ing in the framework of less capable sensors. Banguraand Mahony use a sophisticated rotor model, combinedwith a motor power sensor and estimator to estimatethe rotor force and lateral velocity [Bangura and Ma-hony, 2012] [Bangura and Mahony, 2014] [Bangura et al,2015]. However, this requires access to the electronicspeed controller internals, and high-speed processing.

Our approach is to instead directly sense the force andtransverse torques generated at the rotor, to feed intothe dynamic model of the aircraft. In this way, irrespec-tive of the local aerodynamic conditions of the rotor, thecorrect desired thrust may always be applied through atight feedback control loop. Furthermore, by exploitingthe known coupled mechanics between rotorcraft trans-lation and pitch velocity through induced drag and �ap-ping, we can construct a direct measurement of the speedof the aircraft.In this paper we present a novel rotor thrust and trans-

verse torque sensor that can measure the axial and o�-axis thrust of the rotor. In Section 2 we describe theconstruction and function of the sensor. In Section 3 wederive a simple lumped parameter model for translatingtransverse thrust components into an estimate of trans-lational velocity. In Section 4 we present experimentsverifying the sensitivity and linearity of the sensor whenmounted on a rotating velocity test-rig. In Section 5we discuss the features, performance and applications ofthe sensor, based on the measured results, and a briefconclusion completes the paper.

2 Force Sensor

We developed a lightweight and low cost motor force sen-sor capable of measuring one lift force and two transverserotor torques of a small BLDC (Brushless DC) rotor sys-tem. The design leverages the technique developed atHarvard for using low-cost MEMS barometers as tactileforce sensors by encasing them in polyurethane rubber[Tenzer et al, 2014]. The Harvard, and later Right HandRobotics �Takktile�, sensors use Freescale MPL115A2MEMS barometers which feature a large opening in thecase directly above the silicon sensing element. Thesesensor arrays can measure tactile contact forces with asensitivity of 1 g. We build upon this technique by us-ing a small array of potted sensors as the elements of aminiature load cell.

2.1 Construction

The force sensor is comprised of four sensors, a microcon-troller and USB connection mounted to a PCB (PrintedCircuit Board). Four threaded stand-o�s are soldered tothe PCB for securing the sensor the the quadrotor. Anacrylic load plate is glued to the top of the polyurethaneencased pressure sensors and retains four captive screwsfor attaching the motor. The complete sensor is shownin Figures 2 and 3. The completed sensor mass is 3 g.It was found that the MPL115A2 sensors sensors did

not o�er su�cient resolution for accurately measuringsmall motor forces. Instead we use the MeasurementSpecialties MS5611, which o�ers two orders of magni-tude improvement in resolution and nearly triple themaximum sampling frequency at up to 1.8 kHz.

During operation the sensors heat up, causing the rub-ber to expand against the sensing element and rapidlysaturate device. This was due to the incompressible na-ture of the polyurethane rubber and the lack of a largeopening in the stainless steel cap above the sensor forthe rubber to expand out of. To improve sensitivity wede-capped the MS5611 sensor by forcibly removing thestainless steel case to directly expose the MEMS sensordie. It was found that the rotor pulling on the rub-ber sensor mounts gave better reading than compressingthem.An e�ective method for moulding the Smooth-on

Vyta�ex 20 polyurethane over the sensors is to use amould that was laser cut out of acrylic and screwed toPCB through the threaded stand-o�s. A second pieceof acrylic was used as a lid to cover the top of thesensor moulds and pressed down to displace the ex-cess polyurethane and produce moulded parts of uniformthickness with a smooth glass like top surface. A thinsmear of petroleum jelly was applied to the acrylic mouldparts to act as a release agent.The total bill of materials cost per sensor is approxi-

mately $50 in quantities of 10.

2.2 Force Model

An arrangement of four pressure sensors in a square al-lows for independent measurement of the torques alongeach diagonal by taking the di�erence of two oppositesensor readings. The thrust produced by the motor canbe computed by taking the sum of all four scaled sensorreadings.The force Fn on each sensor element approximated as

a simple spring is given by:

Fn = kpn (1)

where k is the sensor coe�cient and pn is the tared sensorreading under gauge load given by pn = pn − pn0.The total vertical force Fz measured by the die sensor

array is given by:

Fz =∑

Fn (2)

Fz = k(p1 + p2 + p3 + p4) (3)

The torques τx and τy measured by the motor forcesensor are given by:

τx = kd(p1 − p3) (4)

τy = kd(p2 − p4) (5)

where d is the horizontal distance of the sensing elementsfrom the central of the motor force sensor.The sensor coe�cient was determined by loading the

sensor with a series of known masses and found to bek = 3058 units/N.

Figure 2: Assembled force sensor front.

Figure 3: Assembled force sensor back.

𝑧

𝑦

𝑥 𝜏𝑥 𝐹𝑧

𝜏𝑦

Figure 4: Mounted sensor with reference frame and vectors.

2.3 Sensor Comparison

To test the performance of the motor force sensor it wasattached to a test rig as shown in Figure 5 along with a$5000 JR3 force torque sensor for comparison. The JR36-DOF force torque sensor is attached the the bench.Because the JR3 sensor is designed to measure muchlarger forces and has a lower resolution a force multiply-ing arm was used to improve sensitivity. The motor andsensor were attached to the end of this arm. In placeof a rotor a pulley and suspended cup were attachedto the motor shaft. A single point calibration of boththe JR3 and motor force sensor were performed using aknown mass and measuring the o�sets from sensor cen-tres. After taring the sensor readings a water bottle wasused to gradually �ll the cup while time stamped sensormeasurements were recorded at 190 Hz for the JR3 and1000 Hz for the force sensor. For comparison purposesthe JR3 readings were scaled by the ratio of the leverarms, 1.01 m/0.022 m = 49.5. The JR3 force torquesensor was �ltered using a built in 125 Hz low-pass �l-ter. No �ltering was applied to the motor force sensor.The comparison results are shown in Figure 6.The result show that the motor force sensor accurately

tracks the torque as measured by the substantially moreexpensive JR3. There are some oscillations in the JR3readings which are likely due to the experimental setup.As the cup is �lled it begins to bounce around on the endof the lever arm which bends and transmits the motioninto the JR3 sensor at the base, the motor force sensormoves with the cup.

3 Velocity Torque Model

When a horizontal rotor is translating sideways withsome velocity, induced drag and blade �apping cause therotor to apply a component of force against the directionof travel [Martin and Salaün, 2010] [Pounds et al, 2010].The horizontal force subtends a torque about the verti-cal o�set between the rotor plane and load plate whichcan be measured by the load cell.The free body diagram of a simpli�ed planar model

comprised of two sensing elements is considered as shownin Figure 7. The force sensors are compressible and allowsmall de�ections under load.We treat the action of blade �apping and induced drag

as an e�ective force vector de�ection given by:

Tx = T (q1x− q2θ) (6)

where q1 and q2 are the lumped translational and pitchvelocity coe�cients, x is the longitudinal velocity of therotor and θ is the pitch velocity.In dynamic maneuvers, this value may be measured

by a precision gyro and cancelled; in quasi static hov-ering �ight, θ ≈ 0. The component of thrust directed

Figure 5: Static force sensor and JR3 load cell apparatus fortorque comparison test.

0 5 10 15 20

time /s

-1

0

1

2

3

4

5

6

7

8

torq

ue

/N

m10−

3

Sensor

JR3

Figure 6: Force sensor comparison with JR3 load cell.

𝑇𝑥

𝑇𝑧

ℎ

𝑑

𝐹2𝐹1

𝑥

Oncoming wind

Figure 7: System free body diagram.

into the horizontal by induced drag and blade �appingis therefore given by:

Tx = (F1 + F2)q1x (7)

Under load the motor rotor system will tilt to somestatic equilibrium in which the torques around the centreof rotation will be equal:

Tq1xh = d∆F (8)

x =d

q1h

∆F

T(9)

x =d

q1h

F1 − F2

F1 + F2(10)

where h is the height of the rotor aerodynamic centreabove the centre of rotation, d is the horizontal distanceof the sensor element from the centre of rotation, ∆F isthe di�erence between the sensor element forces, F1 andF2 are the individual sensor element forces.Using this relation, the sensor measurements may be

used to compute an estimate of x. Parameters for themotor, rotor and prototype sensor are given in Table 1.

4 Lateral Velocity Experiments

A series of experiments were carried out to characterisethe rotor-motor-sensor system and determine the e�ec-tiveness of the force sensor in measuring the lateral veloc-ity of a rotor. Basic testing to demonstrate the functionof the force measurement elements was trivial, and is notincluded here.The validation of the lateral sensing function required

accurate replication of steady, constant-velocity motion.

Table 1: Sensor, Motor and Rotor Parameters.

d sensor o�set 0.0045 mh rotor height o�set 0.02 mk sensor coe�cient 3058 units/Nq1 rotor coe�cient 0.138 s/m

Figure 8: Swing-arm apparatus.

0 10 20 30 40 50 60 70 80 90

time /s

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

sen

sor

read

ing

τx/Nm10−3

τy/Nm10−3

Fz/N

Figure 9: Exemplar sensor measurement, x = −0.53 ms−1.

We constructed a long swing-arm mechanism to move arotor through a circular arc, approximating linear mo-tion. The arm is a 1 m long, 6 mm diameter woven car-bon �bre tube, attached to a Dynamixel MX64 motormounted to a tripod. The motor is a Dragon�y MC13063100 KV motor, with a T-Motor 6.5x3.5� rotor, drivenby a Dys XM10A ESC powered by a 8.4 V bench sup-ply. The motor is secured to the tube with a 3D printedmount.The force sensor, ESC and Dynamixel were connected

to a computer via USB for control and data capture. Thecomplete experimental apparatus is shown in �gure 8.During each experiment, the sensor force and torque

data was recorded at 1000 Hz starting with 10 s whenthe rotor and platform were stationary. The applied mo-tor voltage was then gradually increased to 30 per cent,approximately hover thrust for a 200 g quadrotor. After10 s of settling time, the platform started to rotate atthe speci�ed rate until it completed three revolutions,whereupon it halted. A further 10 s of data was cap-tured with the platform stationary and the rotor stillspinning before the rotor was brought to a stop. A �nal10 s of sensor data was recorded before the experimentwas concluded.An exemplar test of the sensor moving with a tangen-

tial velocity of -0.53 ms−1 is shown in �gure 9.Four translation sensing experiments were undertaken:

a control test with the rotor stationary, rotation of theswing-arm clockwise and counter-clockwise, operation ofthe sensor with and without air conditioning active, anda set of tests to establish the linearity of the sensor.

4.1 Sensing with Clockwise andCounter-Clockwise Arm Rotation

To determine the e�ect of platform rotation directionon the sensor measurements, two tests were conductedwith the swing-arm rotating �rst counter-clockwise andthen clockwise � see �gures 10a and 10b. When rotat-ing counter-clockwise, the torque τy was positive; whenrotating clockwise at the same speed it was of similarmagnitude and negative, as expected. The tangential ve-

locity of the rotor during each test was -0.66 ms−1 and0.66 ms−1 for counter-clockwise and clockwise swings,respectively.

Contrary to expectations, Fz was observed to in-crease slightly during counter-clockwise swing-arm rota-tion, but decrease in clockwise rotation � a total changeof less than 5 per cent. A 10 Hz �lter was applied to thesensor data to make this o�set more apparent. It is notclear if this e�ect re�ects an actual change in the mea-sured thrust value, or an artifact of the sensor or testingapparatus. A mutual increase could be explained bytranslational lift of the rotor, but a change in opposingdirection must have a di�erent explanation.

The source of this di�erence could be narrowed downby conducting additional experiments with the rotorspinning in the opposite direction and again observingthe thrust change for clockwise and counter-clockwiseswing-arm rotation.

4.2 Sensor with Rotor Stationary

To determine the in�uence of the platform motion onthe force sensor readings, an experiment was conductedwithout the rotor spinning. This removes the in�uenceof aerodynamic e�ects, leaving only forces induced bythe apparatus, as shown in Figure 11. The tangentialvelocity of the rotor was -0.66 ms−1.

This shows the coupling of the platform arm move-ment into the sensor readings � in particular the high-frequency transients at the beginning and end of motion.This is believed to be due to torsional oscillation of thehigh-mounted motor weight about the axis of the tube,excited by the step change in Dynamixel velocity.

4.3 E�ect of Air Conditioning on Sensor

During initial function testing of the sensor, it was no-ticed that the measured rotor forces were substantiallymore variable and noisy than expected. We realised thatthe sensor is su�ciently sensitive to detect the transientaerodynamic disturbance patterns in the room inducedby the laboratory air conditioning.

0 10 20 30 40 50 60 70 80 90

time /s

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5se

nso

rre

adin

gτx/Nm10−3

τy/Nm10−3

Fz/N

(a) CCW rotation of the platform

0 10 20 30 40 50 60 70 80 90

time /s

−1.5

−1.0

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1.0

1.5

senso

rre

adin

g

τx/Nm10−3

τy/Nm10−3

Fz/N

(b) CW rotation of the platform

Figure 10: Thrust and moment forces for motion in both directions, x = ±0.66 ms−1 with a 10 Hz low pass �lter applied.

Experiments were conducted with and without airconditioning on (see Fig. 12). The tangential velocity ofthe rotor during each arm swing was -0.53 ms−1. It wasfound that air conditioning increased the cyclic measure-ment deviation in tests by a factor of ∼5 � the threeoscillations in the torque measurements roughly corre-spond to the three revolutions of the swing-arm, andindicate that the observed variation is linked to a globalambient �ow �eld.To reduce the e�ect of these disturbances during char-

acterisation experiments, the air conditioning was turnedo� for all other tests.

0 10 20 30 40 50 60 70 80 90

time /s

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

senso

rre

adin

g

τx/Nm10−3

τy/Nm10−3

Fz/N

Figure 11: Sensor measurements during an experimentwithout the rotor spinning, x = −0.66 ms−1.

4.4 Velocity Sensor Linearity

To determine the linearity of the sensor for velocity esti-mation, an array of trials were conducted with the swing-arm set with incrementally increasing speed. This wasachieved by varying the Dynamixel �moving speed� pa-rameter from 20 to 60 units in increments of 5 units. Therotor was spinning at a constant speed near hover thrustfor a 200 g micro quadrotor, providing 50 g of force.The torque measured around the radius of the platformarm, τy, was averaged during the middle revolution ofplatform and plotted against the tangential velocity ofthe platform in Figure 13. The plot shows a strong lin-ear trend for the range of velocities tested (R = 0.995),and demonstrates the e�ectiveness of the force sensor inmeasuring the lateral velocity of a rotor.

5 Discussion

The sensor performed well during testing, demonstratingsu�cient sensitivity to capture unintended phenomena,such as the swing-arm resonance and ambient AC �ow�elds. Compensating for these e�ects will form some ofthe future work of the project.

The mechanical coupling of the motor and �exibleswing-arm tubes is not expected to pose a problem forapplications on a micro UAV. The arms of a typicalquadrotor are substantially shorter and sti�er than theshaft used. Furthermore, these types of coupled motions,and those due to pitch and roll motions in particular, canbe compensated for when the sensor is combined withangular velocity measurements from the IMU.

Low speed measurements have not yet been capturedfor the sensor, due to the limitations of the testing ap-

0 10 20 30 40 50 60 70 80 90

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(a)

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τx/Nm10−3

τy/Nm10−3

Fz/N

(b)

Figure 12: Thrust and moment forces with (a) and without (b) the AC turned on, both with x = −0.53 ms−1.

0.0 0.2 0.4 0.6 0.8 1.0

lateral velocity /ms−1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

torq

ue

senso

rre

adin

g/N

m10−

3

Figure 13: Torque sensor reading for varying lateral velocityof the rotor.

paratus. The current apparatus is insu�cient for testingat lower velocities as the Dynamixel would oscillate in-stead of maintaining a constant rotation speed. A mod-i�ed experimental apparatus will be developed to allowfor measuring sensor performance at slower speeds.

However, it is observed that the projected intercept ofthe graph is not precisely zero. This is thought to bedue to small o�sets in the torque values that arise oncethe rotor is spinning. This is likely due to the sensorconstruction and slight rotor-sensor axial misalignment.A second calibration phase with a spinning rotor shouldbe able to compensate for this.

The results of this paper only begin to touch the sur-face of the potential utility of the motor force sensors.In particular, the sensors have obvious uses for dynamicfeedback control for precision manoeuvering of microquadrotors, thrust control in ground e�ect and reject-ing transient winds, and sensing of obstacles throughtheir disturbance to the rotor wake �eld. In the nearfuture work we will characterise the motor force sensorsat lower speeds and attach them to a micro quadrotor toimplement closed loop velocity control on the quadrotorusing the sensors for feedback.

6 Conclusions and Future Work

We have developed a light weight motor force sensor ca-pable of measuring thrust and lateral torques for use ona micro quadrotor UAV. Using the cross-coupling be-tween transverse rotor torque, we were able to derivea linear mapping between sensor moment and velocity.Experimental results demonstrated that the sensor canmeasure the torque due to lateral velocity of a spinning

rotor producing a constant thrust of ∼50 g, at speeds be-tween 0.25 and 0.8 ms−1, and can measure rotor thrustsin excess of 100 g. This system has very strong promisefor application in the precision dynamic control of microUAVs.

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