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Stabilization of a Quadrotor in Wind with Flow Sensing: Linear Modeling andControl for Attitude and Position Hold
William CraigGraduate Research Assistant
University of MarylandCollege Park, MD, USA
J.T. LewisUndergraduate Research
AssistantUniversity of MarylandCollege Park, MD, USA
Derek A. PaleyWillis H. Young Jr. Professor
of Aerospace EngineeringEducation
University of MarylandCollege Park, MD, USA
ABSTRACTAs quadrotor missions increase in complexity, we must also seek to increase their capability. This work addressesthe ongoing challenge of flight in windy conditions through the use of a custom flow-sensing and feedback-controlarchitecture utilizing two separate probes to measure lateral and longitudinal flow. A linear model is developed byperforming system identification using CIFER R© software on a 210mm quadrotor that runs customized Cleanflightfirmware. A linear controller is then optimized for disturbance rejection using CONDUIT R© software to meet desiredhandling qualities specifications. Experiments performed in an indoor gust-generation facility show improvement inboth short and long time-scale gusts through the use of flow feedback.
NOTATION
eθ Pitch error, rad
eq Pitch rate error, rad/s
eu Longitudinal velocity error, m/s
ex Longitudinal position error, m
Kθ Pitch attitude gain
Kq Pitch rate gain
Ku Longitudinal velocity gain
Kx Longitudinal position gain
Ksat Saturation function slope gain
M∆u Angular-acceleration response to wind
q Pitch rate, rad/s
u Longitudinal speed, m/s
V∞ Wind velocity, m/s
X∆u Linear-acceleration response to wind
∆u Longitudinal wind speed, m/s
∆′u Measured longitudinal wind speed, m/s
Presented at the Vertical Flight Society Autonomous VTOL Techni-cal Meeting and eVTOL Symposium 2019, Mesa, Arizona, Jan. 28–Feb. 1, 2019. Copyright c© 2019 by AHS - The Vertical Flight Soci-ety. All rights reserved.
θ Pitch angle, rad
θ1s Longitudinal control input, %
θd1 Outer-loop contribution to desired pitch angle, rad
θd2 Inner-loop contribution to desired pitch angle, rad
τ1s Longitudinal time delay, s
ωi Angular velocity of propeller i, rad/s
INTRODUCTION
In recent years, quadrotors have become highly capable toolswith both commercial and military viability. The ability totake off and land vertically makes them attractive comparedto fixed-wing Unmanned Aerial Systems (UAS) and their me-chanical simplicity is an advantage compared to single-main-rotor helicopters. Current and foreseen missions, includingagricultural monitoring, package delivery, and aiding in nat-ural disasters, require stable and reliable flight in a variety ofconditions.
Traditionally, stable and reliable flight for quadrotors isachieved with a trial-and-error methodology, where nominalgains are chosen based on experience, then tested in flight andadjusted as necessary. Trial and error may yield an initiallyunstable platform, but is often successful due to the mechani-cal simplicity, structural integrity, and low cost of replacementparts for quadrotors. A more rigorous approach may also betaken, using, for example, eigenvalue analysis (Ref. 1), ro-bust control techniques (Ref. 2), or Lyapunov stability crite-ria (Refs. 3, 4) to provide flight stability based on system dy-namics.
1
More recently, an approach typically used to evaluate full-scale helicopter stability and performance based on handlingqualities metrics has also been pursued (Ref. 5), which in-volves first identifying a linear model of the vehicle, then de-signing a controller such that the vehicle meets the desiredhandling qualities specifications. A systematic approach thatuses CIFER R© software (Ref. 6) for frequency-domain sys-tem identification and CONDUIT R© software (Ref. 7) for con-troller gain optimization has been used in Refs. 8, 9. We alsorely on CIFER R© and CONDUIT R© software for model iden-tification and controller optimization, using handling qualityspecifications informed by Refs. 5, 8, 9.
As quadrotors become increasingly reliable, a variety of workis being performed to extend their mission capability, in-cluding aerobatic flight (Ref. 10), sensing and perceptionof unknown environments (Refs. 2, 11, 12), flying with sus-pended loads (Refs. 13, 14), and in-flight hardware failures(Ref. 15). This work addresses flight stability of quadro-tors in windy conditions, which has also been investigatedby Refs. 2, 9, 11, 16–18. Gremillion et al. use distributed ac-celerometers to directly estimate the forces and moments act-ing on the vehicle (Ref. 2), which are then directly cancelledin control feedback. Berrios et al. use the Control-Equivalent-Turbulence-Input (CETI) model from Ref. 19 to design acontroller that is inherently robust to disturbances with fre-quency content typical of turbulent wind by optimizing gainsin CONDUIT R© using handling qualities criteria (Ref. 9). Yeoet al. use flow probes to measure downwash from anotherquadrotor to estimate its position and avoid the resulting dis-turbance (Ref. 11).
The feedback control approach described here relies on on-board flow measurements in the lateral and longitudinal di-rections from multi-hole probes to estimate the aerodynamicforces and moments acting on the quadrotor. By combin-ing flow measurements with inertial sensing, the controlleris able to react to wind before the aerodynamic forces andmoments have propagated to the rigid-body dynamics, yield-ing improved performance compared to using inertial sens-ing alone. Work validating the application of flow feedbackfor gust rejection using nonlinear feedback-linearization con-trollers was performed for a one degree-of-freedom (DOF)pitch stand in Yeo et al. (Ref. 16), a three DOF attitudestand in Craig et al. (Ref. 17), and for a six DOF free flightquadrotor in Craig et al. (Ref. 18). Here we use a linear con-trol framework optimized for gust disturbance rejection withCONDUIT R© software. The linear control uses flow feedbackto cancel the effect of wind on the quadrotor dynamics. Theflow sensor package consists of lateral and longitudinal facingprobe pairs connected to a microcontroller with flexible tub-ing (Ref. 11), which measures differential pressure and trans-mits a digital signal to the onboard flight controller.
The contributions of this paper are (1) the addition of flowfeedback to a linear controller optimized for gust rejectionusing handling qualities criteria and (2) the experimentaldemonstration of the benefit of adding flow feedback to a lin-ear controller that has been designed for gust rejection. This
work parallels the work in Craig et al., in which a nonlin-ear controller was designed with flow feedback for gust dis-turbance rejection, but the use of an optimized linear frame-work is beneficial because it highlights the effect of flow feed-back in an optimized, linear controller specifically designedfor gust disturbance rejection.
The outline of the paper is as follows. The first section de-scribes the software and hardware used for system identi-fication and experimental testing. The second section de-scribes the system identification process using CIFER R© soft-ware. The third section uses the identified model to designan optimal controller based on handling qualities criterion inCONDUIT R©. The fourth section shows experimental resultsof the six DOF quadrotor subjected to a series of gusts, andthe final section summarizes the paper and discusses ongoingwork.
SYSTEM DESCRIPTION
Figure 1 shows the 540g custom-built quadrotor used in thiswork. The vehicle has a 210mm carbon fiber ShendronesKrieger frame and a Matek F405-STD flight controller pairedwith a Matek FCHUB-6S power distribution board. The flightcontroller includes a three-axis accelerometer and three-axisgyroscope for inertial sensing. EMAX Lightning 20A ESCscontrol EMAX RS-2205 motors, which are paired with Gem-fan 5030 five inch diameter propellers. Figure 1 also showsthe differential-pressure lateral and longitudinal flow probeshighlighted in red.
Fig. 1. Quadrotor used for experimental testing with flowprobes highlighted in red
The overall experimental testbed is shown in Figure 2. Outer-loop sensing is performed using an 18 camera, 15’ x 10’ x 12’motion capture facility that records position and attitude dataat 100Hz. The data recorded in motion capture is streamedlocally to Matlab, which runs the outer loop position andheading controller. Desired attitude is transmitted using a 2.4
2
Fig. 2. Inner- and outer-loop experimental control structure for longitudinal direction
GHz Spektrum DX8 radio transmitter to the quadrotor’s on-board flight controller, which solves for desired inputs. Theonboard flight controller runs open-source Cleanflight soft-ware for inner-loop attitude stabilization, which has been cus-tomized to run the optimized linear controller and incorporateserial flow-sensor data. Onboard data collection is completedusing the built in Blackbox feature that records states and flowdata at 250Hz.
Fig. 3. Gust generation system consists of a set of eightDyson fans behind remotely operated blinds
Gust rejection testing was completed in an indoor gust facility,shown in Figure 3, which consists of eight Dyson fans behinda set of remotely operated blinds, controlled by an Arduinothrough LabVIEW, that open and close to produce gusts. Twosquare-wave pattern gusts of different periods were tested toinvestigate the effects of longer and shorter frequency scales.First, the blinds were opened for five seconds at a time, givingthe vehicle a chance to reach steady-state type behavior. Sec-ond, the blinds were opened for two seconds at a time, thereby
not allowing the quadrotor to to reach steady state during thegust or recover fully after a gust. The quadrotor experienceda wind speed of ten knots in the five-second gust testing, andeight knots in the two-second gust testing.
MODEL IDENTIFICATION
Modeling results are presented for the longitudinal degree offreedom (the process is the same for each of the other degreesof freedom). Define inertial frame I , (O,e1,e2,e3) in anorth, west, up orientation with O at a known point on theground, and body frame B , (O′,b1,b2,b3) in a forward, left,up orientation with O′ at the center of mass of the quadrotor,as shown in Figure 4. In the longitudinal degree-of-freedom,u is the velocity along b1, q is the pitch rate along b2, θ isthe pitch angle along b2, and ∆u is the wind velocity in theb1 direction. Let Xu and Mu be the linear acceleration andangular acceleration response to velocity u, respectively. Wealso define X∆u and M∆u as the linear and angular accelerationresponse to wind ∆u, respectively. The state-space descriptionof the system is
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Fig. 4. Quadrotor reference frames and wind velocity
3
uqθ
=
Xu 0 gMu 0 00 1 0
uqθ
+ 0
Mθ1s0
θ1s(t−τ1s)+
X∆u
M∆u
0
∆u,
(1)
y =
1 0 00 1 00 0 10 0 0
u
qθ
+
0001
∆u. (2)
System identification is performed with CIFER R©, which usesfrequency sweeps over each channel to develop a linear modelfit. Sweep profiles are performed automatically by insertinga frequency chirp into the flight-controller software. Chirpssweep from 0.62 rad/s to over 100 rad/s; an example is shownin Figure 5. Large spikes in the data are user inputs to limittranslational drift.
0 10 20 30 40 50 60
-50
0
50
0 10 20 30 40 50 60
-5
0
5
0 10 20 30 40 50 60
-0.5
0
0.5
0 10 20 30 40 50 60
-2
0
2
Fig. 5. Chirp data for longitudinal degree of freedom usedas input to CIFER R©
The resulting model fit to the flight data is shown in Fig-ure 6. Stability derivatives are presented in Table 1, as wellas Cramer-Rao bounds and insensitivities showing the levelof confidence of the identification (Ref. 6). The value for Xuhas been fixed based on insensitivity analysis. The model hasalso been validated in the time domain against independentdata from separate flight tests, showing good agreement inFigure 7.
Table 1. Model parameters (see Eq. 1)Parameter Value C-R % Insensitivity %
Xu -0.05 - -Mu -10.26 4.54 1.59
Mθ1s 5.79 3.16 1.09τ1s 0.0196 5.49 2.74
We initially predicted that the effect of wind moving over thequadrotor is equivalent to the effect of the quadrotor movingforward in air, such that X∆u = −Xu and M∆u = −Mu. How-ever, after experimental results showed only a small effectof adding flow feedback, the gust stability derivative was ad-justed based on prior force-torque measurement experimentalresults (Ref. 16) to be approximately twice the magnitude ofthe velocity derivatives. Work is ongoing to identify the guststability derivative X∆u using frequency domain system iden-tification techniques.
CONTROLLER DEVELOPMENT
The quadrotor flight controller structure shown in Figure 8uses a fast inner-loop running at 2kHz to control the attitudedynamics, and a slower outer-loop running at 100Hz to con-trol the position and heading dynamics. The outer loop ap-plies gains to velocity and position in proportional-integral(PI) control, and also uses a saturation function to limit themaximum desired velocity produced by the position error.The gain-adjusted velocity error is transmitted to the innerloop, where the onboard wind measurements are incorporatedto produce the desired attitude. Gains are applied to attitudeand rate in a proportional-derivative (PD) controller and com-bined with flow feedback to produce the final inputs to themotors.
To implement the PID controller, we feed back position andspeed to the outer loop; and attitude, attitude rate, and windspeed to the inner loop. This example shows the developmentin the longitudinal direction (the process for each other degreeof freedom is similar). To limit the maximum reference speed,we pass the desired position through a saturation function, i.e.,
ud = sat(Ksat(x− xd)), (3)
where Ksat sets the slope of the saturation function. We thenset the position and velocity errors
eu = u−ud ,
ex = x− xd ,(4)
and apply a PI controller to yield our desired dynamics, i.e.;
ud =−Kueu−Kxex. (5)
Inserting Equation (5) into the dynamics (1) yields
u = Xuu+gθ +X∆u∆u =−Kueu−Kxex. (6)
Taking θ as our control input to the outer loop system andsolving for the desired pitch angle we find
θd =1g(−Kueu−Kxex−Xuu−X∆u∆u). (7)
The nature of onboard versus offboard sensing necessitatessplitting the desired pitch angle into separate outer- and inner-loop components, where the outer loop component θd1 usesthe position and velocity data only available through motion
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Fig. 7. Model validation against time-series datacapture, and the inner loop component θd2 uses the wind dataonly available from the onboard flow sensors. Note, the flowprobes measure the combination of wind speed and flightspeed, such that the actual measurement ∆′u = ∆u−u. We thencalculate the stabilizing portion of the feedback, 1/g(−Kueu−Kxex), in the outer loop, and the dynamic cancellation portion,1/g(−Xuu−X∆u∆u), in the inner loop. Based on the initial as-sumption that X∆u ≈−Xu, we multiplied by the measured flowspeed such that X∆u∆′u = X∆u∆u−X∆uu≈ X∆u∆u+Xuu to yieldthe desired value. Thus, the outer-loop component is
θd1 =1g(−Kueu−Kxex), (8)
and the inner-loop component is
θd2 =1g(−X∆u∆
′u). (9)
Once θd = θd1 +θd2 is identified in the inner loop, we find
eθ = θ −θd (10)
andeq = q− d
dtθd . (11)
We then establish our desired dynamics:
q =−Kqeq−Kθ eθ , (12)
and substitute into the system dynamics (1),
q = Muu+Mθ1s θ1s +M∆u∆u =−Kqeq−Kθ eθ . (13)
Rearranging, with θ1s as the input, the value sent to the mixeris
θ1s =1
Mθ1s
(−Kqeq−Kθ eθ −Muu−M∆u∆u), (14)
where we again account for both wind velocity and rigid bodyvelocity using the measurement from the flow sensor to yield
θ1s =1
Mθ1s
(−Kqeq−Kθ eθ −M∆u∆′u). (15)
A Simulink model of the controller in combination withthe identified linear model yields optimal gains using theCONDUIT R© environment. CONDUIT R© requires users tochoose a number of specifications relating to handling qual-ities stability and performance, then uses a multiobjective op-timization engine to adjust gains such that each of the pre-scribed handling qualities specifications is achieved. Moredetails on the CONDUIT R© software are available in Ref. 7.Handling qualities are characterized as level one, two, orthree, with one as the best and three as the worst. TheCONDUIT R© software is designed to achieve level one han-dling qualities for all specifications, while also minimizing
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Fig. 8. Quadrotor control architecture
actuator usage. Hard specifications (H) address stability andare required to be met by the optimization, soft specifications(S) address performance based metrics and are desirable butnot mandatory, and summed objective (J) specifications aredesigned to reduce actuator usage and are correspondinglyminimized.
Nominal handling qualities specifications in CONDUIT R© aredesigned for full-scale manned aircraft. The small size andunmanned nature of quadrotor UAS lead to different han-dling qualities requirements, so the CONDUIT R© specifi-cations have been adjusted based on previous work usingCONDUIT R© for small quadrotor UAS (Refs. 5,8). Additionaladjustments were also made based on pilot feedback and flightperformance. The specifications to which the gains were op-timized for the longitudinal outer loop for position control areshown in Table 3, with comments addressing adjustments tohandling qualities boundaries. The resulting handling quali-ties window is shown in Figure 9, and shows that each of thespecifications meets level 1 requirements. The correspondingcharacteristics of the control law design are shown in Table 3.
EXPERIMENTAL RESULTS
Experimental testing was performed by subjecting the quadro-tor to a series of square-wave gusts at different periods in anindoor gust generation facility. Figures 10 and 11 show dis-placement in the e1 direction as well as the flow speed experi-enced by the quadrotor. Figures 12 and 13 show the e1-e2 dis-placement on the left plot and the e1-e3 displacement on the
right plot over the course of each test.
From Figures 10 and 11 we see improvement in station hold-ing through the use of flow sensing for both tests. The longertime-scale gusts in Figure 10 show a more significant im-provement, where both controllers are able to settle beforeand after the gusts. Without flow feedback, the quadrotor isblown back by the wind where it keeps a very consistent posi-tion until the gust ceases, and with flow feedback the quadro-tor quickly compensates for the wind, and experiences onlya slight movement in the direction of the wind. The shortertime scale results in Figure 11 still show an improvementthrough the addition of flow feedback, but highlight the ben-efits of designing the controller for disturbance rejection inCONDUIT R© for the controller without flow feedback, and thesusceptibility to noise when using flow feedback.
The linear controller produced by CONDUIT R© is designedto address higher frequency turbulent wind using the distur-bance rejection bandwidth specification (Ref. 20) without theuse of flow sensing, and thus shows comparatively better re-sults in the two second gusts versus testing with five secondgusts. Adding flow feedback does reduce the e1 error in thesystem, however the movement appears slightly more erraticthan in the longer time-scale case. The error at the beginningand end of each gust remains consistent between the longerand shorter gusts, however the shorter gusts limit the system’stime to stabilize and so we see the quadrotor repeatedly over-shooting the desired position as wind conditions change.
The differences in performance for the two time scales arehighlighted in Figures 12 and 13, where we see that in the
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Fig. 9. CONDUIT R© handling qualities window. Level one in blue, level two in pink, level three in red. Triangles andflags indicate the value of the handling quality, green arrows indicate an off-screen value, and the line in Nichols robuststability indicates the value across simultaneous changes in gain and phase.
longer time-scale gusts the systems generally maintain a tightposition with or without flow sensing apart from the dynamicportion of the gust. Figure 13 shows the quadrotor unable tomaintain the tight position in the presence of more rapid gustsfor both cases and we also see significant motion in the e2 di-rection when flow feedback is utilized, resulting from noiseand measurements in the flow signal in the lateral direction.In the longer-time-scale gusts, the e2 flow error reduces asthe vehicle settles. However, the more dynamic wind in theshorter time-scale leads to consistent fluctuation in the e2 di-rection in addition to the response to the primary flow in thee1 direction. Efforts to better address noise in the flow sensorsto improve performance is ongoing.
CONCLUSION
This paper describes a linear controller that has been opti-mized for gust rejection using CONDUIT R©, based on sys-tem identification performed with CIFER R©. Additionally, acustom flow probe package was used to investigate the ben-efits of flow feedback for gust rejection. Experiments wereperformed with a 210mm quadrotor system running Clean-
flight software, where flow feedback yielded improvementsfor both short and long time-scale gusts, particularly for thelonger time-scale five second gusts when the vehicle had timeto settle in the wind. In ongoing work, we are investigatingsensor noise to specifically reduce off-axis response and alsoplanning outdoor flight testing.
ACKNOWLEDGMENTS
This work was supported by the University of Maryland Ver-tical Lift Rotorcraft Center of Excellence Army Grant No.W911W6-17-2-0004.
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Table 2. Design SpecificationsParameter Description Type Std. Bounds? Comments
EigLcG1 Eigenvalues Hard YStbMgG1 Stability Margins Hard N L1/L2 at 4dB, 20 degNicMgG1 Nichols Margins Hard N L1/L2 at 160 degDrbRoX1 Disturbance Rejection Bandwidth Soft N L1/L2 at 1.33 rad/sDrpAvH1 Disturbance Rejection Peak Soft N L1/L2 at 3.33 rad/sCrsMnG2 Minimum Crossover Frequency Soft N L1/L2 at 4.33 rad/sCrsLnG1 Crossover Frequency Sum. Obj. N L1/L2 at 10 rad/s
RmsAcG1 Actuator RMS Sum. Obj. Y
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-0.4
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-0.6 -0.4 -0.2 0 0.2 0.40
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Fig. 12. Experimental quadrotor position response to 5 s duration 10 kt gusts in the −e1 direction.
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-0.4
-0.2
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Fig. 13. Experimental quadrotor position response to 2 s duration 8 kt gusts in the −e1 direction.
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