Development of a miniature low cost UAV helicopter autopilot platform and formation flight control of UAV teams 2

4.3.1 Modeling of BabyLion UAV Helicopter A model which could accurately capture BabyLion’s aerodynamics is of great importancesince it will directly affect the designed flight control l

Dynamic Modeling and Control of the Miniature UAV Helicopter

In this chapter, we present the work on the dynamic modeling and control law design for ourminiature size UAV helicopter The helicopter has inherently unstable, complicated, andnonlinear dynamic, under the significant influence of exogenous disturbances and parameterperturbations The system has to be stabilized using a feedback controller To design areliable automatic control law, an accurate model which could accurately capture the input-output dynamics is necessary

Due to the complexity of the helicopter dynamics, there have been efforts to apply model-based approaches such as PID (proportional-integral-derivative) tuning, fuzzy-logiccontrol, neural network control, or a combination of these, etc [53] While these approachesare attractive because no identification is required, they do not guarantee closed-loop sta-bility while they are being tuned or learnt

non-The stabilizing controller may also be designed by the model-based mathematical proach The mathematical model-based approach assumes the availability of a linear ornonlinear system model for the controller design In this case, the system identificationprocess takes up a significant amount out of the whole research effort of building a UAVhelicopter

ap-73

Fortunately during the construction of HeLion UAV helicopters, we have obtained a lot

of experience, which enables us to conquer various problems in modeling nd control of theminiature UAV helicopter, BabyLion In order to increase the fidelity and application scope

of the developed model, we have sequentially implemented a variety of model derivationmethods, including: time-domain system identification and frequency-domain system iden-tification [11] These two methods are for linear model identification By conducting andcomparing the different methods, we have successfully obtained a high-fidelity linear modelbased on the helicopter dynamics for the purpose of control law design and implementation.The remaining content of this chapter is organized as follows Section 4.1 presents thedata collection and preprocessing for the modeling and Section 4.2 introduces the modelstructure for the helicopter Section 4.3 focus on first principle modeling technique based

on the MIMO model Section 4.4 presents the complete procedure for deriving an mentable model which is suitable for small UAV helicopters and with minimum complexitybased on classical modeling method The implementation results and necessary comparisonsbetween the two methods are also addressed in Section 4.5.3 In Section 4.5, we draw someconcluding remarks

Data collection is a state-of-the-art process and with great importance Without high-qualitydata, it could be never possible to identify the dynamic models accurately and reliably Toensure the quality of collected flight test data, we sequentially carry out the following threesub-steps, including, (1) select the input signals, (2) collect flight test data via suitablyconducted experiments, and (3) preprocess the raw data

4.1.1 Select the Input Signals

Frequency sweep and symmetric doublets are selected as the input signals for the purposes

of model identification and model validation, respectively

Frequency sweep is a class of control inputs that has a quasi-sinusoidal shape of creasing frequency [56] One typical frequency-sweep input signal is described by (4.1) andvisually shown in Fig 4.1 To persistently excite the linear dynamics which is dominantwithin the desired frequency range for the small-scale UAV helicopter, the issued frequency-sweep signal needs to meet a series of requirements.

in-1 Initial frequency: The initial frequency is required to be as low as possible Consideringthe pilot’s maneuverability, we choose an initial frequency as 0.2 Hz (e.g., 5s longperiod);

2 Highest frequency: The highest frequency for the frequency sweep input is also limited

to avoid introducing unnecessary nonlinearities and structural vibrations For theminiature scale UAV helicopter, the upper limitation is set as 2 Hz;

3 Frequency-increasing progression: To ensure the low frequency range (0.2 ∼ 0.5 Hz)

is fully excited, the pilot will issue two concatenated long-period ( 5 ∼ 6 sec) input

at the beginning of each perturbation After that, the input frequency is required toincrease smoothly to the highest threshold value (2 Hz);

4 Amplitude: It is not necessary to keep the amplitude constant during the whole quency sweep perturbation period Typically the adjusting range is ±10 − 20% How-ever, the aerodynamics should be guaranteed linear

where t is the time, u(t) is the generated frequency sweep signal with respect to time t, a isthe adjustable amplitude, f0 and f (t) is the initial and time-increasing frequencies in Hz.Symmetric doublet, which is illustrated in Fig 4.2, is an easy-to-issue input signalwhich could provide a clear visualization of key dynamic characteristics and model perfor-

Figure 4.1: Typical frequency sweep input signal.

mance [56] Such signal is commonly used for model validation on both full- and small-scalehelicopters [55, 43, 17]

4.1.2 Collect Flight Test Data

The overall data collection procedure involves two tasks, namely data collection for modelidentification, and data collection for model validation

The collection of flight data has been conducted under human control of the helicopter.Special flight maneuvers were carried out while the avionics system was running and loggingthe flight data which consists of all the helicopter outputs and the measured RC inputs Re-garding the input signal, we choose the frequency sweep signal, which has a quasi-sinusoidalshape of increasing frequency in the interested range, for the model identification and a dou-blet signal for model validation since they have been commonly used in numerous full-scaleand small-scale UAV helicopter system identification [10]

Figure 4.2: Typical doublet input signal.

The procedure of data collection is as follows Firstly the helicopter is brought to a hoverand input trim values are set for each of the control input to keep it at a desired operatingpoint When such a flight condition is achieved, the pilot is required to issue the frequencysweep for each of the four input channels which include aileron, elevator, collective pitch andrudder, while keeping the basic hovering flight condition The resultant input and outputdata are then recorded for the purpose of identification This experiment was also iteratedseveral times until enough high quality flight data was obtained for the model validation Avisual illustration of one set of inputs and outputs collected in a rudder channel perturbationexperiment is shown in Figures 4.3 to 4.7

Data collection for model validation is conducted at the end of each flight test Afterachieving certain trimmed flight status, the symmetric doublet input signal is injected toeach of the four input channels Since the doublet signal is much easier to issue comparedwith frequency sweeps, only two to three set of experiment results are recorded per flighttest

555 560 565 570 575

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9 9.5 10 10.5

18 19 20 21

555 560 565 570 575

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555 560 565 570 575

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Figure 4.7: Euler angles in the yaw channel perturbation experiment

4.1.3 Preprocessing of the Raw Dataset

The raw dataset is required to be preprocessed such that the side effects caused by the zero trimming values, the piloted feedback input, and noises or disturbances are minimized.For the time-domain dataset, we can only conduct the basic preprocessing, which includes:

non-1 Data range selection:

From the continuously recorded raw dataset, we need to pick out the meaningful slotsrelated to frequency sweep and doublet perturbation This is easy to realize sinceinput shapes of frequency sweep and doublet are characteristic

Table 4.1: Trim values for the tested flight conditions

States Hovering Forward 1 m/s Backward 1 m/s Heave 1m/s Side slip 1m/s

3 Data filtering:

The high frequency vibrations caused by the engine, main rotor and tail rotor maycorrupt the data quality and thus should be further attenuated For BabyLion, weapply a first order low-pass filter with the cut-off frequency with -3 dB at 10 Hz toboth input and output channels Note that using the identical filters for both inputsand outputs is compulsory to avoid extra time-delay caused by the filtering procedure

The model structure specifies the order and form of the differential equations which describethe dynamics The model used in this project is adapted directly from the UAV group in

the National University of Singapore Control and Simulation Laboratory [9] This modelstructure was established through the analysis of physical effects using the first principles.Specifically the model structure consists of three parts, namely, the 6-DOF rigid-body dy-namics, coupled rotor flapping dynamics, and yaw rate gyro dynamics

4.2.1 6 Degree of Freedom (DOF) Rigid-body Dynamics

The 6-DOF rigid-body dynamics is described using Newton-Euler equation 4.2 Note thatthe tip-path-plane (TPP) flapping angles as and bsare involved due to the strong couplingbetween the main rotor and the fuselage of the small-scale UAV helicopters Therefore,

4.2.2 Coupled Rotor Flapping Dynamics

Recalling the “hybrid model” structure developed in [7, 30] for the full-scale helicopters, themain rotor dynamics is described by two coupled first-order equations which represent thelateral and longitudinal flapping motions of the assumed tip-path-plane Physically, the tip-path-plane is the top of the corn-shaped rotor, defined by the first-harmonic representation

of the main blade flapping motion [43] An illustration of the TPP, which can also be found

Figure 4.8: An illustration for tip-path-plane.

in [43], is given in Fig 4.8 for easy understanding β represents the blade flapping anglerelative to hub plane, and β0 is the coning angle of the rotating rotor

Compared with the full-scale counterpart, the main difference residing in the scale helicopters is that the main rotor is commonly augmented by a stabilizer bar, whichacts as a secondary rotor with much smaller aerodynamic surface and 90o phase difference

small-to effectively dampen the inputs of aileron and elevasmall-tor servos (δlat and δlon) Based on[19, 43, 44], the stabilizer bar dynamics can be lumped into the bare main rotor dynamics.The final first-order coupled rotor flapping dynamics is represented in 4.3

deriva-4.2.3 Yaw Rate Gyro Dynamics

The recently developed RC helicopters are commonly equipped with a yaw rate gyro tofacilitate pilot to control the yaw rate and heading angle In the selected model struc-ture [43], an arbitrary yaw rate gyro dynamics with poor physical meaning is adopted and

proved applicable Without considering the off-axis coupling terms related to variable set{v, p, w, δcol}, the yaw channel dynamics is represented in 4.4.

 ˙r = Nrr + Nrf brf b+ Npedδped

˙

rf b = Krr + Krf brf b

(4.4)where ()r, ()rf b and ()ped are unknown derivatives

In the last section, a classic helicopter aerodynamic model is given In this section, weidentify the MIMO model using advanced system identification techniques

4.3.1 Modeling of BabyLion UAV Helicopter

A model which could accurately capture BabyLion’s aerodynamics is of great importancesince it will directly affect the designed flight control law’s performance Currently the mostcommon modeling method for small-scale UAV helicopters is system identification technique,which is based on the practical flight test data In [43] and [9], system identification hasbeen successfully implemented on HeLion and R50 to obtain high fidelity linearized model.However in the following content of this section, we will show that for BabyLion UAVhelicopter, such a method is only partially applicable which is mainly due to its rapiddynamics and noisy sensor To maintain the reliability of the derived model, we implement

a comprehensive modeling approach which combines both system identification and firstprinciple modeling Specifically such approach is composed of the following four steps,namely, model structure determination, system identification, first principle modeling, andmodel validation

MIMO Model Structure Determination

Based on the helicopter aerodynamic model given in 4.2, 4.3 and 4.4, an eleventh orderlinearized model can be obtained There is an extended dynamic model of seventeenthorder linearized model, which is proposed in [45] and expressed in 4.5 In this structure,two main unique features of RC helicopters, stabilizer bar and yaw rate gyro have beenincluded, which is developed in [43] The detailed information of the inner model structurecan be found in [43] However, in order to minimize the model complexity, we do notadopt the extended seventeenth order linearized model Another reason is that with thesuccessful implementation for HeLion, reported in [9], it has been proven that the eleventhorder model is accurate enough to cover the small-scale UAV helicopter’s dynamics Thephysical meanings of the state and input variables are listed in Table 4.2

MIMO System Identification

Based on the selected model structure, we carry out the system identification to obtain theunknown parameters Similar to the identification procedure of HeLion/SheLion, we firstconduct one set of special flight tests to collect necessary input/output data Specifically thepilot manually executes the chirp signal, which is a sinusoidal signal with smooth increasingfrequency over the interested frequency range, in each of the four helicopter input channels

to perturb the helicopter in roll, pitch, heave and yaw directions sequentially During theseperturbations, the pilot needs to ensure the hover or near hover condition and the least

Table 4.2: State and input variables with the physical meanings

States and Inputs Physical Meaning

u (m/s) Body frame X-axis velocity

v (m/s) Body frame Y-axis velocity

p (rad/s) Roll angular rate (rad/s)

q (rad/s) Pitch angular rate

φ (rad) Roll angle

θ (rad) Pitch angle

as (rad) Lateral tip-path plane flapping angle

bs (rad) Longitudinal tip-path plane flapping angle

w (m/s) Body frame Z-axis velocity

r (rad/s) Yaw angular rate

rf b(rad/s) Yaw rate feedback

δlat (-1∼1) Aileron servo input

δlon (-1∼1) Ellevator servo input

δcol (-1∼1) Collective pitch servo input

δped (-1∼1) Rudder servo input

off-axis or correlated inputs The input and output data are then recorded for further dataanalysis, system identification, and model validation The overall experiment set has beeninitiated for four to five times to ensure that enough high quality data has been collected

In our initial plan, the parameter identification process is further categorized into threesub-steps Firstly, the angular rate dynamics is identified Then, the translational dynamics

is identified based on the results in previous step Lastly, all of the identified parametersare reiterated and the overall linearized model is obtained One advanced frequency-domainsystem identification toolkit, call CIFR (Comprehensive Identification from Frequency Re-sponse software package) [56], is implemented As there is high frequency noise in theangular velocity output from the low-cost small-size IMU, we need further pre-process theavailable data in su-step 1 The angular velocity data is taken as measurement information

We introduce a low-pass filter to pre-process these measurement data Meanwhile the servoinput data-taken as control input, also pass the same low-pass filter to reduce the delay ef-

Table 4.3: Estimated parameters through system identification, MIMO modeling method.

Parameters Identified Value CR bound (%) Insens bound(%)

* Fixed derivative tied to a free derivative.

fect We notice that in sub-step 2, the reliable identification results for partial translationaldynamics could not be achieved This is mainly caused by the over sensitive aerodynamics

in hover and near hover conditions due to BabyLion’s ultra small size Since collectingthe effective translational identification data is extremely difficult for BabyLion, we decide

to keep the reliable identified parameters which are obtained in sub-step 1/2 and listed inTable 4.3 along with the accuracy indices (Cramer-Rao bound and Insensitivity bound).The first principle modeling approach is then used to estimate the remaining undeterminedparameters

First Principle Modeling

The first principle modeling approach has been widely used in full-scale manned of unmannedhelicopters Such a method is mainly based on the various helicopter physical parameters

Table 4.4: Estimated parameters through first principle modeling approach

Parameters Identified Value

† Fixed value in the model.

to derive nonlinear/linear models for different flight conditions For our BabyLion UAVwhose physical parameters are easy to measure, such method is well suited to identify theremaining parameters One famous first principle modeling toolkit, named FLIGHTLAB[26], is adopted The complete physical parameter set for, fuselage, main rotor, stabilizerbar, tail rotor, and brushless motor is injected to FLIGHTLAB for model generation Thefinal identified parameters are listed in Table 4.4 Combining the identified parametersshown in Table 4.3, we could fully determine the model for BabyLion UAV in hover andnear hover conditions

Model Validation

The model validation procedure is performed in time-domain One comparison result for allnecessary BabyLion’s outputs has been shown in Figure 4.9 The close agreement betweenthe simulation response and real flight data indicates the identified model is accurate enough

to reflect the BabyLion’s dynamics, and suitable for the flight control law design which willpresented in the next section

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δ el

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0.46

δ co

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0.2

Figure 4.10: General flight control scheme for UAVs.

4.3.2 Control Law Design for BabyLion UAV Helicopter

Based on the identified mathematic model, we proceed to design the flight control law.The general scheme for a flight control system is depicted in Figure 4.10, which consists ofthree hierarchical control loops, i.e., an inner-loop control block for internal stabilization

of the BabyLion, and an outer-loop control block to control the position; and lastly, 3) aflight scheduling block which is to navigate BabyLion to follow flight paths generated by theground station Since our aim for current stage is to realize the initial automatic control inhover and near hover conditions, we hereby only focus on the design of inner and outer-loopcontrol blocks

Inner-loop Control Law Design

The inner-loop control law is designed using the Linear Quadratic Gaussian (LQG) nique First, we rewrite the identified model as follows,

where x, u, h and y are the state variable, control variable, controlled output and measuredoutput respectively C1 and C2 are as defined by

Then we carry out the following two steps,

Step 1: Design a linear quadratic regulator as

where rref = [u, v, w, r]

is the reference signal

For the linear feedback control law, we choose F as

The tracking matrix G = −[C2(A + BF )− 1B]− 1 is then given by

Next, Design a reduced order observer as follows

,ˆ

(4.12)

where xc = [as, bs, rf b]

is the immeasurable state vector and output ˆx includes both themeasurable and recovered immeasurable states The observer matrices Ac, Bc and Cc aregiven by

The final designed inner-loop control law is then obtained by combining the results ofboth steps

Outer-loop Control Law Design

For the outer-loop control law design, we use the dynamic inversion technique since thestrap down equation and position equation are fully known The output signal of this

control loop is the vector rref, which is also the reference signal for the inner-loop controlblock Specifically the outer-loop control law is designed as follows,

The micro-size IMU, which is physically smaller than their bulky counterparts, tends toprovide poorer sensor information During the system identification process, we observedthat there exists a big problem which lowers the system performance The angular rate in-formation from our IMU sensor contains high amplitude noise, which increases the difficulty

of attitude control In our flight experiment, the UAV sometimes fluctuates wildly due tothe noisy gyroscope output This makes it very difficult to choose matrices Q and R whendesigning a feasible flight control law Another problem is that we are subsequently to usethis miniature UAV platform for indoor vision based navigation, where the accurate GPSposition and velocity signals are not available The MIMO modeling method is not possible

to have good application with less accurate and fidelity vision velocity signal Also, weobserved quite often temporary loss or failure in the GPS signals in our flight experiment,which lead to a severe crash These problems motivated us to employee a novel robustcascaded control architecture for the control of the miniature UAV helicopter The basic

idea is to put the attitude control alone in the core inner loop When the GPS temporarilyloss or failure occurs, the autopilot can switch to attitude control only, thereby a crash can

be avoided This architecture is also easy to implement on a vision-based navigation, which

is able to replace the GPS signal when a GPS loss or failure occur

4.4.1 Cascaded Modeling

Lateral and longitudinal fuselage dynamics

We noted that PID controller also works (see e.g [6]), which means physically that theattitude channels (roll, pitch and yaw) of the helicopter from the control surface deflection

to the attitude angular rate is first-order by ignoring the actuator dynamics This is true

in our manual flight tests We also noted in our experiment that there is coupling effectbetween the latitude channel and the longitudinal channel, which is validated in the classicalmodel in (4.5) However, no apparent coupling was observed for the collective pitch channeland the rudder channel We then further concluded there is a second-order plant from theinput servos to the attitude channels This is to say, a direct reduced second order modelcan be identified by ignoring the flapping angles as and bs dynamics and using the servoinputs as the direct input

acceleration of the helicopter movement As such, we can put the velocity and positiontogether in the outerloop with the attitude alone, as the core inner loop control part As theattitude is driven by the servos, the attitude change will induce the inclination of the rotatingmain blade plane which will again induce the acceleration movement of the helicopter Weconclude that there is a relationship between the helicopter movement and the attitudeinclination angles In general, there exists a cascaded system such that the helicoptermovement control works as the outer loop, and the attitude control works as the innerloop The outer loop will generate attitude references for the inner loop in real-time.This can be deduced from the velocity dynamic equations To see the details, thesimplified forward velocity dynamic equation is used as an example:

·

Considering a linear control, we can simply assume there is a virtual value that meets

where f (θ) is a transition coefficient for the asand the virtual pitch angle θr0,

Thus (4.16) can be rewritten as

·

where θr= θ − Xasas/g = θ − (Xasfθ/g)θr0 is the pitch angle rotation reference

Note that the state asis in the same direction of the pitch attitude θ and in the hovering

or near hovering mode We can assume there exists a linear proportional relation betweenthe state as and the pitch angle reference θr0

In the same way, there is a similar relationship in the lateral velocity channel as in (4.19)

·

where φr= φ + Yb sbs/g is the φ angle rotation reference.

The heave dynamic channel as in (4.20)

1) an inner-loop control block for attitude stabilization of the BabyLion;

2) an outer-loop control block to control the position and velocity;

This control scheme has a clear physical meaning Suppose the UAV is hovering, theground station sends a command to fly forward, the UAV will nose down to drive thehelicopter rotating main blade plane to lean forward The aerodynamics will generate aforce to drive the helicopter fly forward For the lateral flight, there is a similar physicalanalogy

With the flight schedule which generates position and velocity references by the board computer or by the ground station in real time, the Babylion UAV will thus follow

on-Figure 4.11: General flight control scheme for UAVs.

the reference accordingly Since our aim for current stage is to realize the automatic control

in hover and near hover conditions, we hereby only focus on the inner and outer-loop controlblocks design

System Identification

Although a PID controller may work for the inner loop attitude control by ignoring thecoupling term in the horizontal plane, we still want to identify the model parameters anddesign an output feedback controller with decoupling factor to improve the actual flightperformance Based on the selected model structure, we carry out the system identification

to obtain the unknown parameters In our scheme, the attitude modeling is quite clearand simple Similar to the identification procedure of HeLion, we first conduct one set ofspecial flight tests to collect necessary input/output data Specifically the pilot manuallyexecutes the chirp signal, which is a sinusoidal signal with smooth increasing frequency overthe interested frequency range, in each of the four helicopter input channels to perturb thehelicopter in roll, pitch, heave and yaw directions sequentially During these perturbationsthe pilot needs to ensure that the hover or near hover conditions, and the least off-axis orcorrelated inputs The input and output data are then recorded for further data analysis,

Table 4.5: Estimated parameters through system identification, cascaded modeling method.

Parameters Identified Value

Model Validation

The model validation procedure is performed in time-domain One comparison result forall necessary BabyLion’s outputs is shown in Figure 4.12 The close agreement betweenthe simulation response and real flight data indicates the identified model is much moreaccurate than the classical MIMO method, which is due to the need of less parameters to

be identified Therefore it is good enough to reflect the BabyLion’s dynamics, and suitablefor the flight control law design which will presented in the next section

120 130 140 150 160 170 180 190 200 210 220

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−1 0 1 2

p simulation

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−1 0 1 2

time: s

φ simulation

b Euler angle and simulation.

Solid line: experimental; Dashed line: simulationFigure 4.12: Verification of the identified model

4.4.2 Control Law Design for BabyLion UAV Helicopter

Based on the identified mathematic model, we proceed to design the flight control law.The general scheme for a flight control system is depicted in Figure 4.10, which consists ofthree hierarchical control loops, i.e., an inner-loop control block for internal stabilization

of the BabyLion, an outer-loop control block to control the position and velocity, and aflight scheduling block which is to navigate BabyLion to follow flight paths generated bythe ground station or predefined by the on-board system In our design scheme, the innerloop control is the core loop for the attitude stabilization, and the outer loop control is forthe motion (velocity and position) stabilization In our control law design and testing, thecontrol law was designed in three stages Firstly, we design the inner loop control law, wherethe roll and pitch attitude control are of the most importance In this stage, although theUAV may drift to one direction with growing speed, it still can control its attitude and keepflying in the horizontal plane Secondly, once the inner loop (attitude) control performance

in flight tests is satisfactory, we design the outer loop velocity control law by tuning thecontrol gain for the best performances In this stage, although the UAV may drift to onedirection, the speed will be controlled to near zero, and the UAV can even hover for morethan ten seconds Lastly, we design the outer loop position control law with special focus

on the position control drift Through these three stages, the UAV will be able to hoverstably

Inner-loop Control Law Design

With the identified attitude control model, we design the attitude control, which is furtherdivided into horizontal plane (roll, pitch) control and heading (yaw) control The atti-tude control is the core loop of the autopilot control system In the attitude control loop,horizontal plane control is most important for hovering and near hovering mode flight

In our system model, only the two horizontal control channels (longitudinal channeland lateral channel) are coupled As such, we can design control laws separately For the

horizontal plane control channels, the control law is designed using the linear quadraticRegulator (LQG) technique We rewrite the identified model as follows



We design a linear feedback law as

where rref = {φ, θ}

is the reference signal

For the linear feedback control law, we choose

and the tracking matrix G = −[C2(A + BF )− 1B]− 1 is given by

Physically, the yaw dynamics could be decoupled from the other channels when thehelicopter is hovering Thus, modeling of the yaw dynamics could become the identification

of a SISO system, which is shown in (4.15)

Based on the flight experiment performance, we place the poles of the resulted loop system at (−4.7765 ± 1.5482j) with the control law [10]

closed-uψ = [−0.4 − 0.1]

ψr



Outer-loop Control Law Design

For the outer-loop control law design we use a output feedback control method , which isspecified in three portions, namely, position control (the proportional part), velocity control(the derivative part), and position integrator (integration part)

For the velocity control, it is a simple proportional control if the three axis GPS velocity

in the NED frame is transferred in the body frame The output signal of this control loop isthe vector Aref, which is used as the reference signal for the attitude control loop We foundour UAV has the best performance with the gain of -0.06 in the longitudinal and lateralaxis and -0.04 in the vertical axis from real flight experience Specifically, the velocity-loopcontrol law is designed as follows

Aref = [ BbKv(AV − AVref) ] , (4.25)

where AV = [u, v, w]

is the horizontal body frame velocity vector, Bb is the transformationmatrix from NED frame to body frame, AV and AVref are the practical and desired velocityvectors in NED frame The final selected outer-loop control gains are given by

For the position control, a simple proportional control is used The output signal of thiscontrol loop is the vector Vref, which is the reference signal for the velocity control block.Specifically the outer-loop control law is designed as follows

Vref = [ AV ] = [ Kp( AP − APc) ] , (4.27)

where AP and APc are the practical and desired position vectors in NED frame

The final selected outer-loop control gains are given by

The outer loop control design has a form of a PID structure, with position control(proportional part), velocity control (derivative part), and position integrator (integrationpart) This form is quite logical by nature For the horizontal plane, the inner loop will trackthe calculated attitude references (provided by the outer loop control) with the respectiveservo as input, while the servo responds directly to the heading error for the rudder control

4.5.1 MIMO Control Method

The designed flight control law is first simulated in MATLAB/SIMULINK for the purpose

of control performance verification The simulation results for hover conditions are shown in

0 2 4 6 8 10 12 14 16 18 20 0

1 2 3

φ θ ψ

p q r

Figure 4.13: Outputs of hovering flight simulation

Figures 4.13 and 4.14 Initially, the BabyLion Helicopter model is given a 1 m/s rightwardspeed due to the possible wind gust, and the designed control law is then executed to retrievethe desired hovering status We note that all of the helicopter states are converted to thehovering trim values with the satisfied settling time Furthermore, all of the input responsesare within the predefined safety operating range of (−0.3 ∼ 0.3) Such results indicatethat our designed controller is applicable for the BabyLion UAV’s practical automatic flightcontrol

Next, we implement the designed control law on our BabyLion UAV helicopter to realizeautomatic hovering Specifically, the pilot took off the BabyLion UAV helicopter manuallyand made it hover at a designated point with suitable altitude and good sight Afterachieving the manual hovering, the pilot switched the BabyLion to automatic hoveringmode by sending a switching signal through the wireless RC link The actual responses,along with the control inputs, are shown in Figures 4.15 and 4.16

Figure 4.15: Outputs of automatic hovering flight test.

80 82 84 86 88 90 92 0.40

Figure 4.16: Control inputs of automatic hovering flight

It can be noted that the BabyLion could hover at the designated point at an accuracy

of (±1, ±2, ±1) m Furthermore, the remaining outputs in 4.15 and control inputs in 4.16stay at their corresponding trim values as expected However, the velocity of the Babylion

is higher than what we expected This is because the attitude control is not good enough.The main reason for the bad attitude control is that the control of MIMO model structuredepends heavily on the rate gyro output, while the performance of the MNAV100CA isinferior than other bulky but accurate IMUs

4.5.2 Cascaded Control Implementation Results

Hovering Flight Test

The cascaded control method can easily adjust the control parameter, thus the dependence

on rate gyro is greatly relieved The flight experiment can be processed in three stages Inthe first stage, the focus is on the attitude control of the UAV Attitude control parameters

are adjusted according to the flight performance, and a good flight performance means thatthe UAV can fly in a horizontal plane Although the velocity may increase gradually sinceboth the velocity and position control are not applied In the second stage, the focus is

on the velocity control As the attitude control is sufficiently good, parameters for thevelocity control can be easily adjusted according to the flight performance A good flightperformance means that the UAV can fly very slowly, although it may hover at a point forseveral seconds, and it may drift slowly as no position control is applied In the third stage,the focus is on the position control After the parameters for the position control is adjustedaccording to flight performance, the UAV should fly stably at a static point with both goodattitude and velocity control

In a hovering test, we implement the designed cascaded robust control law on ourBabyLion UAV helicopter to realize automatic hovering Similarly, the pilot took off theBabyLion UAV helicopter manually and made it hover at a designated point with suitablealtitude and good line of sight After achieving manual hovering, the pilot switched theBabyLion to automatic hovering by sending a switching signal through the wireless RClink The actual responses are shown in Figures 4.17 (a) to (h) It can be noted that theBabyLion could hover stably at the designated point with the small position error of (±1,

±1, ±1.2) m, the slow velocity of (±0.2, ±0.2, ±0.3) m/s and the tiny attitude fluctuation

of (±3o, ±3o, ±3o) As the accuracy of the position and velocity is limited by the GPSresolution, we also used GPS enhancement method to improve the GPS resolution, which

is shown in our paper [60]

Figure 4.18 is picture that shows the UAV in an autonomous flight from a ground-basedcamera

A Circle Flight Trajectory Tracking

To further test the autopilot performance, a 10 m circle path tracking mode is realized Theresult of the horizontal tracking is shown in Figure 4.19 (a) to (h) The output shows the

180 190 200 210 220 230 240 250 0.4

0 20

0 0.5

1

h Magnetometer outputs of automatic hovering flight test.

Figure 4.17: Automatic hovering flight test with cascaded control