J Intell Robot SystDOI 10.1007/s10846-013-9987-3

A Novel Actuation Concept for a Multi Rotor UAV

Pau Segui-Gasco · Yazan Al-Rihani ·Hyo-Sang Shin · Al Savvaris

Received: 1 September 2013 / Accepted: 30 September 2013© Springer Science+Business Media Dordrecht 2013

Abstract This paper proposes a novel strategyto improve the performance and fault toleranceof multi-rotor vehicles. The proposed strategyuses dual axis tilting propellers and thus enablesthree different actuation mechanisms, namely, gy-roscopic torques, thrust vectoring and differentialthrusting. Unlike the conventional quadrotor, theproposed strategy offers a wider range of con-trol torques by combining the three actuationmechanisms. Conventional quadrotors cannot bereconfigured if one of rotors fails. However, theproposed strategy is still able to reconfigure thevehicle with complete failure of one rotor and apair of adverse motors. In order to prove this con-cept, a dual axis tilting UAV is first designed andprototyped. Next, a mathematical representationof the prototyped vehicle is modelled and verifiedusing experiments. Then, a control system is de-veloped based on a PD controller and pseudoin-

P. Segui-Gasco · H.-S. Shin (B) · A. SavvarisDepartament of Engineering Physics,Cranfield University, Cranfield MK43 0HT, UKe-mail: h.shin@cranfield.ac.uk

P. Segui-Gascoe-mail: p.seguigasco@cranfield.ac.uk

Y. Al-RihaniKing Abdullah Design an Development Bureau(KADDB), Amman, Jordane-mail: yazan.rihani@kaddb.mil.jo

verse control allocator and validated through testson a rig and flight tests. The tests show that thevehicle is faster than a conventional counterpartand that it can resist the failure of two rotors.Finally, this paper suggests how to lead furthersubstantial improvements in performance.

Keywords Multi-rotor vehicle ·Agility and reliability · Actuation mechanism ·Gyroscopic torques · Thrust vectoring ·Differential thrusting · Control allocation

1 Introduction

In recent years inexpensive lightweight Un-manned Aerial Vehicles (UAV) have prolifer-ated vastly as an alternative to more expensiveand complex manned systems. The operationalexperience of small UAVs has proven that theirtechnology can bring a dramatic impact to bothmilitary and civil arenas. This includes, but notlimited to: obtaining real-time, relevant situa-tional awareness before making contact; helpingcommanders to lead appropriate decision mak-ing; and reducing risk to the mission and op-eration. In R&D many prototype technologies,algorithms and techniques are tested in the, nowubiquitous, quadrotor platform. Quadrotors havebecome very popular due to their simplicity, easeof use and maintenance, and low cost.

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For real applications, quadrotors may becomelarger because they might need to carry morepayloads and/or should be resilient to externaldisturbances such as a wind gust or turbulence.When one tries to scale them up, agility and re-liability become an important issue. As a multi-rotor vehicle scales up there are two main prob-lems that slow down its dynamic response, i.e.,decrease agility of the vehicle. First, as stated by[11], if the vehicle scales up, its inertia builds upand consequently it demands much larger controlmoments to create the same angular accelerationon the airframe. Second, as the weight increases,assuming a constant disc loading, the propellersize increases and hence its inertia. Note that thetorque required for an equivalent angular acceler-ation of the propeller, and hence that of the vehi-cle, scales with the square of the vehicle’s weight.However, the motor torques are constrained bythe maximum amperage of the motors whichis physically limited. Therefore, as the vehicle’sweight increases, the range of attainable angularaccelerations is reduced, and consequently thecontrol bandwidth of the vehicle decreases. Theseare physical boundaries that the conventionalquadrotor has in its performance. If quadrotorsare operated in mission environments where theymight require aggressive and fast manoeuvres, forexample complex urban environments, the agilityissue could become important.

In the conventional quadrotor, if any of theactuators fails, the vehicle is completely de-stabilised because its inherent dependence on thesymmetry of the lift. In order to mitigate thisreliability issue, two approaches were proposed inour previous study [10]: the first approach usespropellers with a variable pitch and the secondapproach shifts the CG. Although both of the pro-posed approaches could reconfigure the controlla-bility in pitch and roll axes, the yaw axis remainsuncontrollable. Hence, the two main issues for alarge quadrotor platform are fault tolerance andagility: When an arm fails, the vehicle is com-pletely uncontrollable; and the control bandwidthof the system dramatically decreases as the weightincreases.

There have been some attempts to overcomethese issues. One naive approach is to increasethe number of rotors. Typical examples include six

rotors, called hexarotors, or eight, named octoro-tors. This approach has several advantages, amongthose are mechanical simplicity and its increasednumber of actuators and hence, its reliability.However, this approach might fail to increase thebandwidth, because the increase in the number ofpropellers must match that in weight to keep theweight carried by each propeller constant. In thiscase, radius and inertia of each propeller shouldbe kept low to maintain the bandwidth high. How-ever, this could imply a possibly unacceptablelarge number of propellers for moderate weights.As a consequence of the number of arms, for thesame payload, they would increase the fraction ofthe structural weight, increasing the inertia, andhence reducing the bandwidth.

Rather than adding more rotors, other ap-proaches involve a variety of actuation devices.As usual with aircraft design, key aspects thatmust be considered are its size and weight. Avery effective approach has been shown by Cutleret al. [4] using propellers with variable pitch. Intheir approach, while the authors manage to keepthe weight down, they increase the bandwidth ofits actuators by almost an order of magnitude.However, the reliability is still an issue, because afailure of an actuator might result in instability. In[9], Control Moment Gyroscopes (CMG) are pro-posed to increase the bandwidth of the actuatorsof the control system merging a thrust vectoringapproach with additional flywheels to use as CMGand a vane system for thrust vectoring. This ap-proach, however, greatly complicates the systemand could significantly increase its weight becausethe aircraft needs to carry the extra weight of theflywheels and the thrust vectoring vane system.Gress [6] came up with the idea of using OpposedLateral Tilting (OLT) as a means of using thegyroscopic effects for governing the pitch attitudeof aircraft, using the propellers as gyroscopes. Inhis latest work [7], OLT is proved to give highercontrol authority than other means of actuationsuch as vaned fans. Also, this concept has been ex-plored by [8], where the authors provide evidenceof the effectivity of this technique in simulation.In [1] these concepts are put into practice withthe vehicle T-Phoenix UAV, providing a detailedmodel and a control strategy for hovering, show-ing experimental evidence of the feasibility of the

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OLT strategy. In another work [12] the authorsprovide also a survey of OLT technology and amore in depth modelling of the tilting phenomena.

The aim of this paper is to find a novel ac-tuation architecture that overcomes the two ma-jor problems with the convectional quadrotors:control bandwidth and fault tolerance. Conven-tional multi-rotors use differential thrusting; mostof tilt rotor vehicles use thrust vectoring; and someother vehicles utilise the gyroscopic torques in[7, 9]. The key idea of the proposed concept isto integrate all these three actuation modes intoone system. This approach is similar to [9], butin a simpler and more integrated way. Insteadof introducing extra devices to use as flywheelsand vanes, the propellers of the vehicle are usedas flywheels themselves by introducing dual axistilting to the propellers. This concept enables ex-ploitation of the three different actuation types.Gyroscopic torques are achieved by using the an-gular momentum and fast tilting of its rotationalaxes. Thrust vectoring is achieved by orientingthe thrust of each propeller independently of thebody. Differential thrusting is obtained by theconventional quadrotor strategy of differential an-gular velocities in the rotors.

In order to prove that the proposed concept isactually able to improve reliability and agility, anew multi-rotor arm concept is developed. Then,a quadrotor UAV, which uses this arm concept togenerate the three actuation mechanisms, is alsodesigned and prototyped. A high fidelity simu-lation model of the novel quadrotor is also de-veloped to assist the understanding of its dynam-

ics and design a control system. Then, a controlsystem is designed based on the classical controltheory and pseudoinverse control allocation. Fur-thermore, a fault tolerant control is developed bymodifying the control effectiveness matrix. Theperformance of the proposed concept and all de-signed controllers is validated through simulation,experiment on a test rig, and flight test. Analysisand discussion of the results focus on verifyingwether the new control system actually increasesthe bandwidth and degree of fault tolerance.

The paper layout is as follows: first the designand prototyping of the quadrotor are presented.Second, an overview of the simulation model isdescribed. Next, the design of the control system isdetailed. Then, the tests performed are described.Finally, an analysis and discussion of the resultsare presented.

2 Prototyping

A realisation of this novel arm concept is shown inFig. 1a. Here we have used commercially availableparts to minimise the number of custom manu-factured parts. This design is based around theservoblock [13] part which serves as a frame tomount a standard size RC servo which allowsit to move the whole arm around its axis. Inthe arm there is mounted another servo which isconnected through a pushpull mechanism to themotor mount which swivels parallel to the servolever. Thus, the propeller rotational axis can befreely configured with the two angles generated by

(a) Novel arm prototype (b) Vehicle prototype

Fig. 1 Arm 3D model and built prototype

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Fig. 2 Platform technical drawing

the servomotors. Henceforth, the naming of thesetwo angles/motions will be named push-pull andservoblock.

The vehicle prototype can be seen in Fig. 1b.The nominal weight of the vehicle is three kilo-grams and its dimensions are illustrated in Fig. 2.All selected and designed components and theirweights are represented in Table 1. The servo-motors used at the servoblock and pushpull arethe HS-7940TH by Hitec. The propellers are threebladed because of the even distribution of its mass

Table 1 Breackdown of components and their weights

Component Weight (g)

IMU(SBG IG-500N) 44IMU voltage level converter 10Flight Computer (chipKIT Max32) 36Servo controller 19GPS antenna 38Wireless (xbee pro) 2Xbee explorer regulated 2BATTERY (LiPo 14,8 V 5350 mAh) 504BATTERY (LiPo 7.4 V 3200 mAh) 185RC receiver(Spectrum) 5Harnesses and connectors 2434x Motor with adapter( MK3638) 4 × 1254x Propeller (3-blade 12 × 6 ) 4 × 454x ESC (Roxxy BL 930-6) 4 × 324x Motor holding bracket 4 × 144x servoblock 4 × 258x servo (HS-7940TH) 8 × 664x Adapters and holders 4 × 304x Aluminum Arm 4 × 158x Clamping hub 8 × 94x Push Pull arm 4 × 94x Arm tip mount 4 × 52x Center plate 2 × 100Landing gear 55Battery holder 41

Total 3057

and inertia, and the model is the master airscrew 3blade 12 × 6 in. The motors used are the brush-less DC outrunners MK3638 by Mikrokopter.The ESC used were the Roxxy Bl Control 930-6from Robbe. The vehicle had two batteries, oneto power the servomotors, a LiPo 7.4 V 2S1P3200 mAh 25 C and another one to power themotors, a LiPo 14.8 V 4S1P 5000 mAh 20 C. Thesensor suite used was an IMU by SBG systems,the IG-500N, this unit has an embedded processorable to output filtered attitude and position dataup to a 100 Hz. All the control software was runon a Max32 board by Digilent, that runs a PIC32,and the servomotors and ESCs were driven bya Parallax Propeller board. The telemetry wasimplemented using XBee modules by Digi.

A more detailed overview of the vehicle designcan be found in the Theses by Al-Rihani [2] andSegui-Gasco [5] or in the paper by the authors [3].Note that, whereas [3] focuses on design and mod-elling of the proposed vehicle, this paper focusesmore on control system design and proof on onthe entire concept.

3 Modelling

In this section a general overview of the mainphenomena involved in the modelling of the actu-ation system is described. This can be found withfurther elaboration on the paper by the authors[3] which is specifically focused on the modellingand simulation of the vehicle. The modelling ofthe actuation phenomena has 3 main parts. Oneis the development of the rigid body relationsof the tilting propeller that describe the torqueas a function of the vehicle motion and the tilt-ing motions. Another one is the characterisationof the propellers in terms of thrust and torquecoefficients, and finally the individual actuatorsthat create the tilting motion, servomotors, andthe motors that vary the propeller’s angular speedare dynamically characterised.

3.1 Gyroscopic Actuation Modelling

The gyroscopic effects are modelled as the reac-tions generated by individual rotors spinning due

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to the vehicle motion and tilt motion of the actua-tors. In other words, it is assumed that each of therotor-propeller assembly, shown in Fig. 3a, doesthe job of a flywheel that, and when tilted, createsthe gyroscopic reaction torques. The relations be-tween the motion of the rotor j and the momentsapplied onto it expressed on the reference frame iare given by the Euler equation:

iM j = iI jiα j + iω j × iI j

iω j (1)

where iM j is the moment in the centre of gravityof the rotor in arm j expressed in reference framei, see Fig. 3b, iI j is the inertia tensor about the CGin the reference frame i, iω j is the total angularvelocity of the body j and iα j is the total angularacceleration of the body j in the reference frame i,i.e. iα j = d

dtiω j.

As can be inferred from Fig. 3b, the vehiclepresents symmetry both around the x-z plane andthe y-z plane. Hence, the development of theequations is the same for all four arms if thereference frame is adequately transformed. Forthis reason, here only the equations with respectto arm 3 will be developed and then, the equationsregarding the remaining arms can be obtainedby an appropriate frame change. Arm 3 will bereferred to, herein, as Standard Arm or Arm 3indifferently.

With the nomenclature stablished in Fig. 4, theangular velocity of the of rotor in arm 3, expressed

Fig. 4 Reference frames used in the development

in terms of reference attached to the motor stator(frame 3), will be given by:

3ω = 3i1 p +3 j1q +3 k1r︸ ︷︷ ︸

Vehicle Motion

+ 3j1η︸︷︷︸

servoblock

+ 3i2γ︸︷︷︸

push pull

+ 3k3�︸ ︷︷ ︸

Motor

(2)

where the vectors ii jij j

ik j represent the unit vec-tors of reference frame j expressed in terms of thereference frame i, see Fig. 4 where the referenceframes are detailed. The angular acceleration isthe derivative of the angular velocity, hence:

3α = d3ω

dt(3)

The inertia tensor of the rotor, Fig. 3a, is sym-metric because of the use of 3-blade propellers,

(a) Spinning Body, motor estator + propeller (b) Arm numbering

Fig. 3 Spinning body and arm numbering illustration

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hence, it does not change with respect of its rota-tion axis. The reference frame 3 is coincident withthe principal inertia axes of the rotor, and so theinertia tensor is constant around those axes andgiven by:

3I =⎡

⎣

Ixx 0 00 Iyy 00 0 Izz

⎤

⎦ (4)

Thus, the moments can be calculated with theEuler equation around the reference frame 3:

3M = 3I3α + 3ω × 3I3ω (5)

Since the interest is the actions that the spin-ning assembly exerts onto the airframe the reac-tions shall be calculated and, also, for convenienceare expressed into the vehicle frame, i.e. refer-ence frame 1. Therefore, introducing and simpli-fying all the expressions above, the moments thatthe spinning body applies onto the airframe inthe reference frame of the vehicle, 1MGyro, aregiven by:

1MGyro = R3to1(−3M) =⎡

⎣

1MGyroX1MGyroY1MGyroZ

⎤

⎦ (6)

where,1MGyroX, 1MGyroY

and 1MGyroZare the

scalar moments in each axis which are specifiedon the Appendix.

Now, taking advantage of the vehicle symmetrythese equations can be transformed to express theaction of any other of the vehicle arms by switch-ing the axes and maintaining the sign criteria inFig. 4. This is done by adding up each individualarm:

1MGyro j= R3to j

1MGyro (7)

where R3to j represent the transform matrix fromarm 3 to the arm j, obviously, because the equa-tions have been developed in arm 3, R3to3 is theidentity. Thus, the total action exerted by the fourdifferent arms will be:

MGyroTotal=

4∑

j=1

1MGyro j(8)

3.2 Thruster Characterisation

The thrust generated by the propellers is modelledby means of constant thrust coefficient given by:

T = ρ A(�R)2CT and Q = ρ A(�R)2 RCQ (9)

Experimentally the coefficients were found to be:CT = 0.013 and CQ = 0.0013.

3.3 Component System Identification

Another vital part of the model is to find thedynamics of the motors and the servomotors be-cause they determine, respectively, the rate ofchange of thrust and the time derivatives of thetilt angles which create the gyroscopic torques. Aseries of experiments were carried out yielding thefollowing transfer functions for each actuator.

GMotor = �ω ( rads )

�τ (0 to 1)= e−0.035s9.19

(1 + 0.16s)(10)

Gservoblock = η (rad)

ηRequested (rad)

= 1228.05

1228.05 + 49.18s + s2(11)

Gpushpull = γ (rad)

γRequested (rad)

= 1212.73

1212.73 + 51.11s + s2(12)

3.4 Thrusting Torques

The thrusters create two main sources of aerody-namic torques. One is the torque created by thethrust and the other is the drag torque. Again forarm 3 they can be expressed as:

MMotor3 = rHub2CG × TMotor + Q

= T

⎡

⎣

l cos(γ ) cos(η) − H sin(γ )

−H cos(γ ) sin(η)

−l cos(γ ) sin(η)

⎤

⎦

± Q

⎡

⎣

cos(γ ) sin(η)

− sin(γ )

cos(γ ) cos(η)

⎤

⎦ (13)

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where H and l are the vertical and lateral sepa-ration of the CG and the propeller hub respec-tively. For the remaining arms the torque is easilycalculated again by projection as done in Eq. 7and, hence, the total aerodynamic moment on thevehicle is:

MMotorTotal =4

∑

j=1

R3to jMMotor3 (14)

4 Control System Design

The vehicle, by its nature, is open loop unstable, soa control system should be properly designed. Thegeneral structure and architecture of the controlsystem is shown in Figs. 5 and 6. The control sys-tem is based on two main components, the controllaw and the control allocator. The control law isa stability augmentation system that receives thepilot commands from the transmitter and the mo-tion information from the IMU sensor and issuesthe required rolling, pitching yawing moments andthrust. The design of the control system is basedon the conventional control theory, especially aPD controller because it is desired to have a con-trol system which is simple to tune and efficientto implement so as to take best advantage of oursophisticated over-actuated system. The architec-ture chosen was a PD-like loop for each axes anda control allocator, see Fig. 6. The designed con-trol allocator, receives the rolling, pitching yawingmoments and thrust and distribute them amongthe 12 actuators. This enables to utilise severalknown advantages, among others: allowance toaccommodate actuator failures and capability tochoose the actuator combination to optimise somecost function, e.g. minimising drag, deflection or

energy consumed. The Weighted Pseudorinversemethod presents these numerous advantages, be-sides its simplicity. For this reason, this method isselected as the control allocator in this study andwill be detailed in the following section.

4.1 Control Allocation

Actuator Model Linearisation The first step todesign a proper control allocator is to under-stand the control effectiveness results from theproposed control actuations. Therefore, the con-trol effectiveness matrix, B, must be found suchthat:

v = [M, N, L, T]T = h(t, x, u) ≈ Bu (15)

where t ≥ 0 is time, x ∈ Rr is the state vector,

u ∈ Rm is the physical actuators input vector and

v ∈ Rn. The function h in the above equation is a

nonlinear function of the time, t, the state vector,x, and the physical control inputs u that mapsthe effects of the physical control inputs and thevehicle motion to the Roll (M), Pitch (N), Yaw(L) moments and thrust (T) domains. Note thatthe mathematical model and PD controller arebased on roll, pitch and yaw moments and thrustdomains as in the conventional modelling andcontrol approaches for aircraft.

To carry out this linearisation some assump-tions were taken. Around the trim point the thrustand torque generated by the propellers is assumedto be linear and proportional to the actuator com-mands. This is a realistic assumption because thecommands to the motors are issued to the ESCin terms of PWM uptime which is linear with thethrust, rather than in terms of angular speed. The

Fig. 5 Main structure ofthe control system

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Fig. 6 Architecture ofthe control system

proportionality constants are defined herein as μ

for the thrust and κ for the torque. Also, anothersimplification is that the deflection angles η and γ

are sufficiently small so that sin(γ ) ≈ γ , sin(η) ≈η, cos(γ ) ≈ 1 and cos(η) ≈ 1. This is reasonablegiven that the maximum deflection of the servosis constrained by the arm clearance and is around10◦. Finally, another further simplification, is thatthe rate of change of the servomotor angle is equalto the average rate of change over the rise partof the response. That is, the commanded angledivided by the rise time, η ≈ η

trand γ ≈ γ

tr.

All these is put together to form the controleffectiveness matrix for the standard arm, (arm 3),with a column for each individual actuator:

BStandard Arm = [

BMotor BServoblock BPush Pull]

(16)

Now the column vector corresponding to eachactuator are developed:Thrusters:

• Thrust T = μm• Drag Torque: Qd = κm• Thrust Torque: Q = lT = lμm

BMotor = BMotorThrust + BMotorDrag + BMotorThrust Torque

=

⎡

⎢

⎢

⎣

000μ

⎤

⎥

⎥

⎦

+

⎡

⎢

⎢

⎣

00

±κ

0

⎤

⎥

⎥

⎦

+

⎡

⎢

⎢

⎣

−lμ000

⎤

⎥

⎥

⎦

=

⎡

⎢

⎢

⎣

−lμ0

±κ

μ

⎤

⎥

⎥

⎦

(17)

Servoblock:

• Thrust vectoring Torque: HT0η and lT0η

• Gyroscopic Torque: J�η ≈ J�η

tr

BServoblock = BServoblockThrust + BServoblockGyro

=

⎡

⎢

⎢

⎣

0HT0

lT0

0

⎤

⎥

⎥

⎦

+

⎡

⎢

⎢

⎣

−J�tr000

⎤

⎥

⎥

⎦

=

⎡

⎢

⎢

⎣

−J�tr

HT0

lT0

0

⎤

⎥

⎥

⎦

(18)

Push Pull:

• Thrust vectoring: HT0γ

• Gyroscopic Torque: J�γ ≈ J�γ

tr

BPush Pull = BPush PullThrust + BPush PullGyro

=

⎡

⎢

⎢

⎣

HT0

000

⎤

⎥

⎥

⎦

+

⎡

⎢

⎢

⎣

0J�tr00

⎤

⎥

⎥

⎦

=

⎡

⎢

⎢

⎣

HT0J�tr00

⎤

⎥

⎥

⎦

(19)

All these three actuators in the standard armput together yield the control effectiveness matrixof the standard arm BStandard Arm.

BStandard Arm = [

BMotor BServoblock BPush Pull]

=

⎡

⎢

⎢

⎣

−lμ −J�tr

HT0

0 HT0J�tr±κ lT0 0

μ 0 0

⎤

⎥

⎥

⎦

(20)

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With the submatrix B known for the standardarm, BStandard Arm, obtaining the B matrix of allthe arms is just a matter of rotating the axes. IfRStandard 2 n is the rotation matrix from the stan-dard arm to Arm n, then:

BArm n = RStd2n BStandard Arm (21)

The last step is to introduce wether the propellersare turningclockwise or anticlockwise in the signs

of κ and � and assembling all the submatrices Bfor each arm to form the final B matrix:

B = [

BArm 1 BArm 2 BArm 3 BArm 4]

(22)

The B matrix represents, then, a linear approx-imation to the forces and moment generated byeach actuator command:

v =

⎡

⎢

⎢

⎣

MNLT

⎤

⎥

⎥

⎦

≈ Bu =

⎡

⎢

⎢

⎢

⎢

⎢

⎣

0 HT0J�

tr0 −HT0

J�

tr−lμ

J�

trHT0 lμ

J�

tr−HT0

lμJ�

tr−HT0 −lμ

J�

trHT0 0 HT0 − J�

tr0 −HT0 − J�

tr−κ lT0 0 κ lT0 0 κ lT0 0 −κ lT0 0μ 0 0 μ 0 0 μ 0 0 μ 0 0

⎤

⎥

⎥

⎥

⎥

⎥

⎦

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

m1

η1

γ1

m2

η2

γ2

m3

η3

γ3

m4

η4

γ4

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

(23)

Note that the B matrix represents the relationbetween the inputs such as servo angle demandsand the throttle and moments. Therefore, theunits in the B matrix are not identical and this maycause some issues due to the different order ofmagnitudes embedded in the unit representationof the inputs. In order to avoid this problem,the B matrix is normalised, so that all the inputsrange from -1 to 1 regardless of whether they aredeflection angles or throttle positions. The newnormalised B matrix will be represented by B.To do so, a matrix E is defined whose diagonalterm is given by the maximum absolute of theactuator limits, that is, Eii = max(|u

¯ i|, |ui|). Thenthe normalised B matrix will be given by: B = BE.Therefore all the inputs will be given by u = E−1uwhich is normalised, i.e., −1 ≤ ui ≤ 1.

Allocator Design The control allocator problemcan be posed as a quadratic minimisation problem:Find a matrix B∗ such that,

minu

1

2uT Wu (24)

subject to vc − Bu = 0 (25)

where u = B∗vc. Note that an analytical solutionof the optimal control allocation problem is givenby the weighted pseudoinverse:

B∗ = W−1 BT(

BW−1 BT)−1

(26)

As shown in Eq. 26 and the optimal solutionof the allocation problem, the weight matrix Wdetermines the characteristics of the optimal so-lution. Thus, the optimal allocation problem inthis study can considered as a problem finding aappropriate weight matrix, W, such that they givea satisfactory blend of the different effectors.

Before determining the weight matrix, differentcontrol actuations must be understood. As ex-pected, from a few tests and analysis, it is con-cluded that the gyroscopic action is fast and decayswith time while the propulsive or motor actionis rather slow but persistent in time. Figure 7visualises the difference. As shown in Fig. 7, thenormalised step response of a gyroscopic pitchingmoment and a propulsive pitching moment areshown together.

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Fig. 7 Normalisedpitching momentresponse generated by themotors following adifferential step and theservo gyroscopic effectsfollowing a step at time 0.Note difference in timescales

In this paper, the weights of the W matrix areselected in a way that they blend both the gyro-scopic effects and the motor action. The higher theelement of an actuator is, the higher the cost it willhave, and the more it will be minimised, i.e., theleast used will be. To do this, a weight wmotor suchthat 0 < wmotor < 1 was added in the elementscorresponding to the motors and a weight wgyro =1−wmotor

2 was added in the elements correspondingto the servos. So that for each arm all the weightswere 1, i.e., 1 = wgyro + wgyro + wmotor.Thus, thelarger wmotor the smaller the use of the motors willbe and the larger the use of the servos will be.Summing up, the weighting matrix is given by:

W =

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

wmotor

wgyro 0wgyro

wmotor

wgyro

0 . . .

wgyro

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

where: wgyro = 1 − wmotor

2

(27)

By selecting wmotor the relation between motor ac-tuation and gyroscopic, or servo actuation, was al-tered. Thus, allowing to blend of the servo “kick”

and the motor actuation to shape the response ofthe actuators. This mixing concept is illustrated inFig. 8.

Several weights were tested by spanning wmotor

from 0 to 1, and the response to a step at time0 in the pitching moment was recorded and nor-malised. The result is shown in Fig. 9. From Fig. 9it can be inferred that too large values of wmotor

yield responses that have a significant overshoot,while small values of wmotor make the responsevisibly slower. Another issue to take into accountis that, the larger the use of the servos, the largeris the likelihood of them being saturated.

As a trade-off between speed and excessiveovershoot, it was concluded that a 15 % of over-shoot would be desirable. To find which was theweight that gave 15 % of overshoot, an interpo-lation from the previous tested weights with itscorresponding overshoots was carried out. Thesolution yielded that the value wmotor that makesthe overshoot 15 % given by wmotor = 0.994.

In Fig. 10 the response to a step with thecombination given by wmotor = 0.994 is shown.In Table 2 all the performance parametersare summarised and compared. It is clear thatthe response with allocator is faster than withdifferential thrusting. This faster response is alsoobvious from the bode plot of both effectorsshown in Fig. 11, where the new actuator suitebrings an order of magnitude improvement inbandwidth.

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Fig. 8 Illustration of the concept of the control allocator as a “mixer” of the two kinds of effectors. Note that all the responsesare normalised

4.2 Controller Tuning

The control law designed was a Proportional-Derivative, PD, loop for each axis independently,that took the readings and issued demands oftorque to the control allocator. The approach fol-lowed to tune the controller gains was a mixtureof model based tuning and testing with the realvehicle on a rig.

A simplified SISO model was produced foreach axis with the structure shown in Fig. 12.From that model a transfer function was obtainedand its characteristics on the frequency domaincould be analysed. Thus, by visualising the fre-quency responses, an informative quantificationof the quality parameters and a clear picture of thetrends, performance indices and stability frontierswas obtained.

Fig. 9 Normalisedpitching momentresponse generated by theallocator for differentweights wmotor rangingfrom 0 to 1. Note the redline when wmotor ≈ 0,thus, being basicallyexecuted by the motorsalone

0.2 0.4 0.6 0.8 1.0Time S

0.5

1.0

1.5

Normalised N 0 1

J Intell Robot Syst

Fig. 10 Resultingallocator withwmotor = 0.994. Blue linesshow the responses forseveral Pitching Moment(N) step commands from0 to 1 Nm. The red linerepresents the responsewhen wmotor ≈ 0. Notethe dashed lines showingthe settling time (95 %)for the two actuatorcombinations

0.0 0.2 0.4 0.6 0.8Time S0.0

0.2

0.4

0.6

0.8

1.0

1.2Normalised N 0 1

However, analytical models only are sim-plification of reality and so several potentially im-portant effects are neglected. In this paper, thoseincluded actuator saturation (specially servomo-tors), processing and communication delays andneglected coupling dynamics because of the SISOapproach. To avoid this, a combined strategy wasdevised. Essentially, the procedure was to findgains that gave desirable characteristics on thefrequency domain and, then, testing them in thereal vehicle on the rig to see its performance.Hence, by testing the gains of the vehicle, the realsensor measurements, processing and communi-cation delays and the full dynamics were takeninto consideration as well.

To easily manipulate the gains and see theimmediate results, a graphical interface was con-structed in Mathematica with two sliders, one forthe KP and one for the KD. With this facilityit was very easy to test and play with the gains,thus, resulting in a deeper understanding of the

Table 2 Comparison of the speed of the response of bothcontrol actions

Allocator Rise T. Settling T. Bandwidth.tr (s) ts (s) ( rad

s )

Combination, 0.024 0.42 100wmotor = 0.994

Motors only 0.52 0.52 6.1wmotor = 0

Improvement 95 % 20 % ≈1600 %

Fig. 11 Frequency response of the different sets ofeffectors. Blue using weighted pseudoinvrese allocator andred using differential thrusting approach

J Intell Robot Syst

Fig. 12 Structure of thePD controller for thepitching dynamics

effects and trends. While, at the same time, itprovided a quantified measure of the quality ofthe response in terms of the Peaks MT and MS.And, more relevantly, it raised awareness on theeffects of possible changes in the gains showingthe trends that each gain introduced on the re-sponse. This was fundamental because in provideda much deeper insight on the suitability of eachcombination of gains than what could have beenachieved by a conventional trial and error tuningon the rig.

To test the controller on the vehicle, it wasattached to a ball joint in a way that it con-strained only the position, thus, allowing the 3angular motions, Roll, Pitch and Yaw to be freeand constraining only the translational motion.The setup of the test rig is illustrated in Fig. 13.The most relevant inconvenience of this setup isthat there exists an offset between the ball andthe vehicle’s centre of gravity. This exerted aninverted-pendulum-like destabilising moment tothe vehicle. Hence, it made vehicle more unstablethan when flying.

Fig. 13 Detail of the ball joint rig

Finally a design was found that for pitch androll with the following gains: KP = 2.5 and KD =0.38. The characteristic parameters of the fre-quency response are:

MT = 1.90dB MS = 3.79dB

ωc = 3.83rad

sdSdω Low Freq

= −20dBdec

(28)

and the stability margins are:

GM = 23.6dB PM = 78.62◦ (29)

5 Test and Design Validation

5.1 Test and Validation on the rig

The validation of the mathematical model is rep-resented in [3] and it is shown that the overall thesimulation model qualitatively follows the trendsof the real vehicle with fidelity. In order to val-idate the proposed concept and tune the controlsystem, a set of typical tests on the ball joint righas been carried out. The sequence followed isdescribed below.

1) Holding the vehicle, a slow throttle rampcommand is sent to the vehicle. Once thenominal rpm have been obtained, the vehicleis released to verify stability.

2) A series of perturbations was introduced totest the controller for disturbance rejection.This was done by pushing the vehicle in eachof axis with a foam handle. A sample recoverysequence is depicted in Fig. 14.

3) Finally, the controller was tested for referencetracking. The time histories for a sample testare presented for each axis see, Fig. 15 forRoll, Fig. 16 for Pitch and Fig. 17 for Yaw.

J Intell Robot Syst

(a) (b) (c)

(d) (e) (f)

Fig. 14 Vehicle recovery after a disturbance test

As shown in Figs. 15, 16 and Fig. 17, theproposed control system works reasonably well,but it shows a considerable overshoot and de-lay. However, a similar tendency was observedin the numerical simulation results once the ballrig effects were introduced [3]. With the ball rigeffects removed, this tendency diminished signifi-cantly, therefore, it is likely that the overshootingis caused by the inverted-pendulum-like momentsintroduced by the ball.

95 100 105

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Time (sec)

Ang

le (

rad)

Roll angle performance on ball joint

Roll commandRoll actual

Fig. 15 Roll angle command tracking at ball joint rig

5.2 Flight Test and Validation

Once the control was tuned and satisfactory per-formance was achieved, the fist flight was at-tempted. The vehicle took-off, see Fig. 18, hov-ered for about minute and then landed. Relevantflight variables of interest were recorded and areshown in this Fig. 19. The data recorded is shownin a series of figures, the data has been organ-ised by axes according to each control loop. For

86 88 90 92 94 96

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Ang

le (

rad)

Pitch angle performance on ball joint

Pich commandPitch actual

Fig. 16 Pitch angle command tracking at ball joint rig

J Intell Robot Syst

100 105 110 115 120

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

Ang

le (

rad)

Yaw angle performance on ball joint

Yaw commandYaw actual

Fig. 17 Yaw angle command tracking at ball joint rig

each axis, the variables shown are the angle com-manded, the actual angle, the angular rate and thetotal moment resulting from the control law. Toevaluate the performance of the controller. Thethrottle history was also monitored, ranging from−50 % to 50 %, −50 % meaning zero throttle and50 % meaning full throttle.

The first flight was the last stage of the vehicleconstruction, hence, it was intended to be just avalidation of the sizing of the vehicle and the sta-bility of the control system. Therefore, no quanti-tative conclusions are extracted from it. Furtherflight testing should imply quantitative compar-isons based on systematic testing to analyse rele-vant variables in order to further validate the sim-ulation model and to improve the control system.However, from it, it can be concluded that thevehicle is stable and able to maintain its attitude,all its systems performed as expected and it hadplenty of control authority.

(a) (b)

(c) (d)

Fig. 18 First Flight: takeoff

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200 210 220 230 240 250 260 270 280 290 300−50

−40

−30

−20

−10

0

10

Time (sec)

−50

% to

50%

Throttle in Flight test

(a)

230 240 250 260 270 280 290

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Pitch angle performance in Flight test

Pich command (rad)Pitch actual (rad)/q (rad/s)/10My (Nm)/10

(b)

(c) (d)

230 235 240 245 250 255 260 265 270 275 280

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Roll angle performance in Flight test

Roll command (rad)Roll actual (rad)p (rad/s)/10Mx (Nm)/10

240 245 250 255 260 265 270 275 280

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time (sec)

Yaw angle performance on in Flight test

Yaw command (rad)Yaw actual (rad)r (rad/s)/10Mz (Nm)/10

Fig. 19 Data recorded during the first flight. Please not the 110 scaling where stated in the legend

6 Analysis and Discussion

There are two main objectives in this study: thefirst one is to improve the performance, and thesecond one to enhance fault tolerance capabilityover that of a conventional quadrotor. In thissection, the performance improvement is verifiedby comparing the response to an identical vehiclewith the conventional actuation. Then, the faulttolerant capabilities are verified experimentallyby switching off the motors in two arms andchecking for stability and disturbance rejection onthe rig.

6.1 Performance Analysis

To put the performance into perspective, it is nec-essary to compare it against a baseline. The aimof this study is to develop an innovative actuatedvehicle, hence, the logical step is to compare itsequivalent conventionally actuated vehicle. Thus,a model of the pitching/rolling dynamics of thesame quadrotor dynamics was developed, but, thistime the function GAcuators was equivalent to adifferential thrust dynamics, i.e., GMotor. In orderto make the systems comparable, the controller ofthis conventional quadrotor was tuned so that its

J Intell Robot Syst

dominant poles laid at the same position of thoseof the gyroscopically actuated vehicle.

Let’s start the comparison with the closed loopfunction peaks:

MT = 1.90dB MS = 3.79dB (30)

MTmotors = 2.07dB MSmotor = 5.76dec (31)

The target for these peaks are MT < 2dB andMS < 6dB. Both peaks are lower using the newactuator suite than in the conventionally actuatedquadrotor. This means that the stability and ro-bustness of the new system has higher safeguardsthan with the conventional quadrotor. In whichthe limits imposed are only met in the case of MS

and they’re violated in the case of MT . This isbetter seen in the Stability Margins:

GM = 23.6dB PM = 78.62◦ (32)

GMmotors = 4.71dB PMmotors = 34.45 (33)

The conventional quadrotor, has a very narrowgain margin, consequence of the violation limit ofMT . And, the phase margin is almost half that

of the new design. Thus, it can be concludedthat an overall better quality of the responseof the new strategy’s actuated quadrotor and ahigher confidence level about its stability has beenachieved. This is because the speed in the actua-tion system has been increased in the new strategyimproving the slow motor dynamics. To comparethe response in terms of speed, the bandwidth ofboth systems is compared:

ωc = 3.83rad

sωcmotor = 2.68

rads

(34)

The speed of the new vehicle is higher with thenew strategy, consequence of the faster actuation.However, this is not the full potential of this con-cept it can be shown that a higher gain designexists that provide an increase on an order of mag-nitude in the control bandwith. However, this highgain design is not feasible because the limitationimposed by the servomotor deflection saturation.Preliminary estimations have shown that a re-design of the rotors to increase its inertia that withan overall vehicle weight overhead below 10 % ofthe total weight, can solve this issue, because if therotor inertia is increased, smaller deflections areneeded to produce the same torques. This remains

(a) (b)

(c) (d)

Fig. 20 Sequence of the two rotor failure test, note the stick in frame c to generate perturbations

J Intell Robot Syst

an open area for future work and a combined iner-tial and aerodynamical design should be carefullylooked at should a more advanced prototype bedeveloped, because, if proven successful, it couldyield an order of magnitude leap in performance.

6.2 Fault Tolerance

This actuator suite was also meant to increase thefault tolerance of the system increasing the num-ber of individual actuator failures that don’t gen-erate a full destabilisation of the system. To ex-plore these features the vehicle was tested againsta two arm failure event. A new control allocatorwas designed by zeroing the columns correspond-ing to those actuators. Then, in the ball joint rigthe vehicle was tested adding perturbations tocheck its stability. A sequence of these tests isshown in Fig. 20, where the vehicle is hovering onthe rig, then two rotors are switched off and someperturbations are generated to check its perfor-mance. Of course, this is not a formal proof of allthe capabilities that this strategy could yield, butrather a quick demonstration that this aspect canbe a fruitful area for exploration in future work.

7 Conclusions

In this paper, a new innovative actuation strategyfor multi rotors has been devised. In order to

prove the proposed concept, a dual axis tiltingUAV is designed and prototyped. Moreover, acontrol scheme based on the classical control the-ory and optimal control allocation is developed af-ter mathematically obtaining a reasonable fidelitymodel of the vehicle. A series of tests on a balljoint rig and flight tests have been undertaken tovalidate the proposed concept and the designedcontrol system. Comparing to a conventional ac-tuation strategy in a quadrotor, i.e., based onvarying propeller rpm, it is evidenced that the newactuation strategy could significantly increase thespeed, performance of the actuator suite, and reli-ability of the quadrotor UAV. The actuators, haveshown an order of magnitude increase in speedwith the current design and the new strategy hasalso shown to be tolerant to actuator faults. How-ever, in order to validate the proposed strategymore rigorously, further tests and analysis of theperformance based on collected data are required.

Appendix

The gyrosocopic reactions of the standard arm aregiven by:

1MGyro = R3to1(−3M) =⎡

⎣

1MGyroX1MGyroY1MGyroZ

⎤

⎦ (35)

where, after some tedious algebra:

1MGyroX= 1

4

(−2Ixxqr+ Iyyqr+ Izzqr + 3Iyy cos(2γ )qr − 3Izz cos(2γ )qr − 4Izz sin(γ )�r + 2Iyyηr + 2Izzηr

+ 2Iyy cos(2γ )ηr − 2Izz cos(2γ )ηr − 2Ixx p − Iyy p − Izz p + Iyy cos(2γ ) p − Izz cos(2γ ) p

− 2Iyy p sin(2γ )γ + 2Izz p sin(2γ )γ − sin(2η)(4(Ixx − Iyy)p sin(γ )� + 2(Iyy − Izz)r sin(2γ )γ

− (2Ixx − Iyy − Izz)(r + p(q + 2η)) − (Iyy − Izz) cos(2γ )(r + p(q + 2η)))

− cos(2η)(4(Ixx − Iyy)r sin(γ )� + 2(Izz − Iyy)p sin(2γ )γ + (2Ixx − Iyy − Izz)( p − r(q + 2η))

+ (Iyy − Izz) cos(2γ )( p − r(q + 2η))) − 2 cos(η)(2(Ixx − Iyy + Izz) cos(γ )�(q + η)

+ (Iyy − Izz) sin(2γ )(q − r + η)(q + r + η) + 2Ixxγ )

− 2 sin(η)(−2(−Ixx + Iyy + Izz) sin(γ )�γ − 2Ixx(q + η)γ + 2(Iyy − Izz) cos(2γ )(q + η)γ

+ 2Izz cos(γ )� − (Iyy − Izz) sin(2γ )(pr − q − η)))

J Intell Robot Syst

1MGyroY= 1

4

( − 2Ixx sin(2η)p2 + Iyy sin(2η)p2 + Izz sin(2η)p2 − 4Ixx cos(2η)rp + 2Iyy cos(2η)rp

+ 2Izz cos(2η)rp − 4Ixx sin(η)γ p + 2Ixxr2 sin(2η) − Iyyr2 sin(2η) − Izzr2 sin(2η) − 2Iyyq − 2Izzq

− 4Ixx cos(η)rγ − 4(Ixx − Iyy − Izz) cos(γ )�(cos(η)p − r sin(η) + γ )

+ 2(Iyy − Izz) sin(2γ )(− sin(η)(qr + p) + cos(η)(pq − r) + 2γ (q + η)) + 4Izz sin(γ )� − 2Iyyη

− 2Izzη − 2(Iyy − Izz) cos(2γ )(q + (cos(η)r + p sin(η))(cos(η)p − r sin(η) + 2γ ) + η))

1MGyroZ= 1

4

( − 2(Iyy − Izz) sin(2γ ) sin(η)p2 − (4(Iyy − Izz) cos(2γ )η sin2(η)+(2(−2Ixx+ Iyy+ Izz) cos2(η)

− (Iyy − Izz) cos(2γ )(cos(2η) − 3))q − 4(Izz + (Iyy − Ixx) cos(2η)) sin(γ )�

+ 2(Iyy − Izz) cos(η) sin(2γ )(r + 2 sin(η)γ ) + 2(Iyy + Izz + (−2Ixx + Iyy + Izz) cos(2η))η)p

− 2Ixxr − Iyyr − Izzr + Iyy cos(2γ )r − Izz cos(2γ )r − 2Iyyr sin(2γ )γ

+ 2Izzr sin(2γ )γ − cos(2η)((−2Ixx + Iyy + Izz + (Izz − Iyy) cos(2γ ))r + 2(Iyy − Izz)r sin(2γ )γ )

− sin(2η)(4(Iyy − Ixx)r sin(γ )� + (2Ixx − Iyy − Izz)(r(q + 2η) − p)

+ (Iyy − Izz) cos(2γ )(r(q + 2η) − p)) − 2 sin(η)(−(Iyy − Izz) sin(2γ )(q + η)2

− 2(Ixx − Iyy + Izz) cos(γ )�(q + η) − 2Ixxγ ) − 2 cos(η)(−2(−Ixx + Iyy + Izz) sin(γ )�γ

− 2Ixx(q + η)γ + 2(Iyy − Izz) cos(2γ )(q + η)γ + 2Izz cos(γ )� + (Iyy − Izz) sin(2γ )(q + η)))

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