Construction and Modeling of a Variable Collective Pitch Coaxial UAV

Jinqiang Cui1, Fei Wang1, Zhengyin Qian2, Ben M. Chen2 and Tong H. Lee2 1NUS Graduate School for Integrative Sciences & Engineering, National University of Singapore, Singapore, Singapore 2Department of Electrical & Computer Engineering, National University of Singapore, Singapore, Singapore

Keywords: Coaxial Helicopter, Unmanned Aerial Vehicle, Flapping Dynamics, Model Identiﬁcation.

Abstract: This paper describes the construction and modeling of a coaxial unmanned aerial vehicle for in-forest op- eration. The bare helicopter platform is upgraded and mounted with an onboard navigation system, which includes central processing units and sensors such as inertial measurement unit, camera and scanning laser range finder. The model structure of the helicopter is formulated, in which the model of rotor thrust and roll- pitch dynamics are described in details. The flapping dynamics of the rotor and the stabilizer bar are presented and lumped into a state-space model. The parameters of the state-space model are identified in frequency domain using CIFER. Time domain verification with a new set of flight data exhibits excellent agreement with the prediction of the identified model.

1 INTRODUCTION form. In this paper, we first describe the mechanical With the rapid development of unmanned aerial ve- structure of the coaxial helicopter and the onboard hicles (UAVs), a wide range of platforms have been navigation system in section 2. In section 3, we first developed. Model-scale helicopter is one of the more present the model structure of the coaxial helicopter, popular type due to its vertical take-off and landing then we derive the dual rotor thrust empirically based capability. A single rotor UAV based on Yamaha R- on the near-hover flight assumption. The flapping dy- 50 with a rotor diameter of 3.07m has been devel- namics of the rotor and stabilizer bar are presented oped by Carnegie Mellon Univerisity (Mettler et al., separately before they are lumped into a state-space 1999; Mettler, 2002) and the linear UAV models for model. Following this, the lumped system is identi- hover and cruise flight have been identified. A com- fied in frequency domain and verified in time domain. prehensive nonlinear model for a similar small-scale Section 4 concludes the paper. single-rotor UAV has been presented by researchers in National University of Singapore (Cai et al., 2012). A micro coaxial indoor UAV (muFly) with a rotor di- 2 PLATFORM DEVELOPMENT ameter of 0.34m has been modeled and identified by researchers in ETH Zürich (Schafroth et al., 2010). Now muFly is commercially available from Skybotix 2.1 Bare Helicopter (CoaX), which can be an ideal platform for indoor op- eration and advanced controller design (Fankhauser The ‘Kaa-350’ is a coaxial helicopter made in Ger- et al., 2011). many according to the design of full scale coaxial he- In our research scope, we intend to developa UAV licopter from the Kamov design bureau. This heli- that is capable of flying through the forest. Thus the copter has a rotor diameter of 0.7m and weighs 990g platform has to be compact enough to fly among tree without battery. Its rotor head is equipped with in- trunks. Compared to single rotor helicopters, coax- tegrated hinges and shock resistant dampers. With ial helicopters produce better lift efficiency by avoid- the recommended configuration of motor, electronic ing power losses from the tangential airflow. What’s speed controller (ESC) and blades, it can fly safely more, coaxial helicopter is also inherently more stable with a total weight of 2.3kg. The mechanical struc- than single rotor helicopters. Therefore, we choose a ture of ‘Kaa-350’ is shown in Fig. 1. The rotor blades coaxial helicopter as the main frame of our UAV plat- are not assembled in order to better illustrate the struc-

286 Cui J., Wang F., Qian Z., Chen B. and Lee T.. Construction and Modeling of a Variable Collective Pitch Coaxial UAV. DOI: 10.5220/0004039502860291 In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 286-291 ISBN: 978-989-8565-22-8 Copyright c 2012 SCITEPRESS (Science and Technology Publications, Lda.) ConstructionandModelingofaVariableCollectivePitchCoaxialUAV

Upper Rotor Tail Servo GPS IMU Magnetometer

Stabilizer bar Servo Controller Head lock Laser Control To pSwashpla te Scanner Gumstix Multiplexer

Lower Ro tor

Camera Vis ion Gumstix Receiver Three Servos Yaw Contr ol to swashplate LionHub Lower Swashplate WiFi 2.4GHz radio Moto r ESC

Headlock Ground Control Station Manual Control Gyroscope Figure 2: Avionic System Conﬁguration.

munication is established between the two gumstix

units. The control gumstix also reads the outputs Figure 1: Description of bare helicopter. of onboard sensors and generates autonomous control signals which are passed to the servo controller ture. The helicopter consists of two contrarotating ro- and fed into the multiplexer. The multiplexer has two tors: the upper rotor and the lower rotor. The pitch an- 4-channel input ports and one 4-channel output port. gles of the two rotors are controlled by the top swash- Manual control signals from the pilot are transmitted plate and the lower swashplate respectively. The two to the receiver via 2.4GHz radio and fed into the mul- swashplates are always parallel to each other since tiplexer. The outputs of multiplexer are connected to they are connectedby three linkages which rotate with the three servos controlling the swashplates and the the top swashplate. The upperrotor is equippedwith a headlock gyro mixer. The headlock gyro mixer mixes stabilizer bar through a Bell-Hiller mixer which also the yaw control signal and the output of the headlock influences the cyclic pitch of the upper rotor blade. gyroscope to generate a composite yaw control signal The upper rotor and lower rotor are driven by the that controls the yaw servo. The multiplexer is in- same brushless DC electric motor powered by a 3-cell dispensable since the helicopter may encounter unex- lithium-polymer battery through the ESC. The rota- pected situations during flight where an instant switch tion speed of the upper rotor and the lower rotor are to manual control is required to save the helicopter. thus always the same. Collective and cyclic inputs During manual flight or autonomous flight, helicopter from servos are transferred to the lower swashplate states and sensor outputs are logged online and crit- and top swashplate simultaneously, resulting in dy- ical information are transferred to ground station via namic movement of the helicopter in heave direction WiFi communication. Control command from ground or pitch-roll direction. The yaw direction control is station could also be transmitted to the helicopter in realized by changing the collective pitch of the lower autonomous flight mode. Fig. 3 shows the completed rotor. UAV platform operating in the air.

2.2 Onboard System

The helicopter gains autonomous capability provided that it is equipped with an onboard navigation system. This system consists of various sensors and signal processing units. As shown in Fig. 2, the avionic system includes sensors such as inertial measurement unit (IMU), magnetometer, GPS, scanning laser range ﬁnder and camera. The central processing units are two gumstix (Overo Fire) units. One gumstix imple- ments the autonomous control of the helicopter while the other gumstix is responsible for processing im- age sequences captured by the camera. Serial com- Figure 3: Helicopter ﬂying in the air.

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Upper rotor ௨௣ ௨௣ flapping dynamics Vwind ܽ ǡ ܾ Forces and Moments Upper rotor ݑǡ ݒǡ ݓ ߜ௖௢௟ Fb 6ͲDOF ௟௔௧ Fuselage + ݔǡ ݕǡ ݖ ߜ rigid Ͳbody Kinematics Mb dynamics ௟௢௡ Lower rotor ߶ǡ ߠǡ ߰ ߜ mg Headlock controller ௣௘ௗ ௣௘ௗҧ ߜ ߜ ݌ǡ ݍǡ ݎ r Lower rotor flapping dynamics ܽௗ௪ ǡ ܾ ௗ௪ Figure 4: Model Structure Overview.

3 MODELING AND PARAMETER our results in the modeling and identiﬁcation of the IDENTIFICATION roll-pitch dynamics in this paper.

3.1 Model Structure 3.2 Thrust Formulation

The UAVmodel structure is shown in Fig. 4. The col- It is a very complex issue to address the coaxial rotor aerodynamics. A comprehensive survey (Coleman, lective input δcol controls the collective pitch angles of both upper and lower rotors through the two paral- 1997) has covered the major aerodynamic experi- ments and computational models dealing with coax- lel swashplates. The cyclic inputs δlat and δlon tilt the upper and lower swashplates and generate flapping ial rotor systems. It covered issues of separation dis- motion for both rotors, causing the longitudinal and tance, load sharing between rotors, wake structure, lateral movements of the helicopter. The yaw chan- solidity effects, swirl recovery, and the effects of hav- ing no tail rotor. (Lim et al., 2009) investigated the nel control δped is first mixed with the output of the headlock gyro (PI controller) before it is applied on ground and rotor spacing effects and Reynolds num- the collective pitch of the lower rotor. The model is ber scaling effect by comparing three rotor configu- denoted in a compact form as follows, rations, concluding that the coaxial rotor spacing effect on hover performance was minimal for the rotor x˙ = f(x,u,w) , (1) spacing larger than 20% of the rotor diameter. Re- where searchers (Kim and Brown, 2008; Kim and Brown, x = (xyzuvw φ θ ψ 2006) at Glasgow University has developed a Vor- ticity Transport Model (VTM) to study the aerody- T pq r aup bup adw bdw r f ) , namics of coaxial rotor systems. They stated that the T u = (δlat δlon δcol δped) , state-of-the-art computational modeling of helicopter aerodynamics had managed to model the interactive ω ω ω T w = ( u v w) . aerodynamic flow field associated with a coaxial ro- x is the state vector, u is the input vector, δcol, δlat , tor system. δlon and δped are the collective, lateral, longitudinal Since the designed UAV will work at near-hover and pedal inputs to the whole system. ww stands for condition, we decide to first extract an empirical rela- the wind disturbance velocity. The overall dynamics tionship between dual rotor thrust Tmr and collective of the helicopter could be separated into three sub- input δcol. A test bench is utilized to facilitate a series systems: the roll-pitch dynamics, the yaw dynamics of tests where the dual rotor thrust and collective input and the heave dynamics. The roll-pitch dynamics, are recorded simultaneously. Fig. 5 shows the results capturing the angular responses of helicopter to the of five tests performed on two fully charged batteries. cyclic inputs, constitutes the core of helicopter dy- After fitting the results using the least square method namics (Mettler et al., 1999). Thus we mainly present and averaging the five groups of coefficients, a linear

288 ConstructionandModelingofaVariableCollectivePitchCoaxialUAV

Dual Rotor Force vs Collective Input 21 by removing the higher order terms of the Tip-Path- Plane (TPP) equation, the remaining ﬁrst-order rotor 20.5 dynamics could be expressed as: τ ˙ τ θ 20 rbi = −bi − r p + Baai + cyc,bi , (8) τra˙i = −ai − τrq + Abbi + θcyc,ai , (9) 19.5 where

Force(N) 19 8Kβ A = −B = , (10) b a γ Ω2 dw mrIβ,mr 18.5 Test 1 with battery 1 Test 2 with battery 1 −1 16 8emr Test 1 with battery 2 18 τr = 1 − , (11) Test 2 with battery 2 γrΩmr 3Rmr Test 3 with battery 2 ρ 4 17.5 cmrClα,mrRmr −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 γr = . (12) δ (−1,1) Iβ col ,mr

Figure 5: Thrust of dual rotor against collective input. ai and bi (i represents {up,dw}) are the first-order TPP flapping angles in the longitudinal and lateral relationship is obtained as: directions for upper and lower rotors. τr and γr are the flapping time constant and the lock number of the T = K δ + T , (2) mr t col 0 rotor blades respectively, Iβ,mr is the blade moment of inertia. θ and θ are the longitudinal and where K = 10.09N and T = 20.812N. cyc,a cyc,b t 0 lateral cyclic pitch of rotor blade. The approximate For near-hover flight, the direction of the rotor formulation in Eq.(8-9) characterizes the crucial TPP thrust can be assumed to remain perpendicular to the responses with respect to cyclic control inputs and he- rotor tip-path-plane. The projections of main rotor licopter motion. thrust on the helicopter body axes are defined as: 3.3.2 Stabilizer Bar Flapping Dynamics Xmr = −Tmr sinas , (3) Ymr = Tmr sinbs , (4) The stabilizer bar, which is attached to the upper main Zmr = −Tmr cosas cosbs . (5) rotor shaft via a free-teetering hinge, can be regarded as a secondary rotor. It consists of two paddles and The moments generated by the main rotor are: a steel rod. The stabilizer bar is not designed to produce thrust or moment on the main hub, whereas its L = (Kβ + T H ) sin(b ), (6) mr mr mr s main function is to adjust the helicopter dynamics via Mmr = (Kβ + Tmr Hmr) sin(as), (7) the Bell-Hiller mixer by augmenting the cyclic pitch command of the upper rotor. It serves as a feed- where Kβ is the spring constant, Hmr is the distance from center of gravity (CG) to the middle of two ro- back system which increases the helicopter robustness against wind gust and turbulence (Cai et al., 2011). tor planes, as and bs are the equivalent longitudinal and lateral flapping angles respectively. The torques The flapping dynamics of stabilizer bar can be ex- from upper rotor and lower rotor are balanced when pressed as two first-order differential equations: no heading change is required. 1 Clon c˙s = −q − cs + δlon , (13) τsb τsb 3.3 Flapping Dynamics 1 Dlat d˙s = −p − ds + δlat , (14) τsb τsb 3.3.1 Bare Rotor Flapping Dynamics where τsb is the stabilizer bar flapping time constant, and it can be calculated as One way to represent the rotor dynamics is to regard it as a rigid disc which can tilt about the longitudi- τ 16 sb = γ Ω , (15) nal and lateral axes. Detail description of the rotor sb mr equations are extremely complicated. Here, a sim- where γsb is the stabilizer bar Lock number: plified formulation is adopted, where the rotor forces ρ 4 4 and moments are expressed as a polynomial function csbClα,sb Rsb − rsb γsb = . (16) of the rotor state variables (Mettler, 2002). Moreover, Iβ,sb

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The free-teetering hinge does not constrain the flap- 3.3.4 Roll-Pitch Dynamics Identification ping of stabilizer bar, thus there is no coupling between the longitudinal and lateral flapping motions. The flapping dynamics identification makes full use The augmented rotor cyclic pitch of upper rotor can of a toolkit called CIFER developed by the U.S. be expressed as Army and NASA specifically for rotorcraft applica- tions (Mettler et al., 1999). It incorporates a range of θcyc,aup = Alonδlon + Ksbcs , (17) θ δ utilities to support the various steps of the identifica- cyc,bup = Blat lat + Ksbds , (18) tion process. Flight tests featuring frequency-sweep where Ksb is the ratio of rotor blade cyclic pitch to input in the longitudinal and lateral directions are per- stabilizer bar flapping. formed multiple times. During the flights, the control inputs and the helicopter angular rates are recorded 3.3.3 Lumped Flapping Dynamics online with a sampling rate of 50Hz. CIFER identi- fies the model parameters by searching for the best- In this coaxial helicopter configuration, the upper ro- fit parameters to match frequency responses between tor and the lower rotor receive the same cyclic input δ δ the flight test data and the hypothetic model. Fig. 6 ( lon, lat ) since the top swashplate and bottom swash- shows the on-axis pitch angular rate response with re- plate are always parallel. To minimize the overall spect to longitudinal input. The coherence level re- complexity of the model, the two counter rotating ro- mains above 0.6 up to 30rad/s. This good coherence tor discs are treated as one equivalent rotor disc with indicates the good linearity of the helicopter in hover respect to flapping motions. Thus there exists only flight (Tischler and Remple, 2006). Time domain ver- two equivalent flapping angles (as, bs). This assump- ification is also performed with another flight test data tion producesaccurate results which are shown in sec- which is not used in the identification process. Fig.7 tion 3.3.4. Combining Eq. 8-18, the lumped flapping shows excellent agreement between the model simu- dynamics subsystem could be represented in the fol- lation and the flight data in both longitudinal direc- lowing state space model: tion. The same process is applied to the lateral direc- x˙ = Ax + B u, (19) tion where the roll dynamics is identified in frequency y˙ = Cx, (20) domain and verified in time domain. Table. 1 lists the where values of the identified parameters together with their Cramer-Rao percent and insensitivity. The Cramer- 0 0 0 L b Rao percent and insensitivity are less than 15% and  0 0 Ma 0  1 A 5% respectively, indicating the high accuracy of the A = b , (21)  0 −1 − τ τ  identified parameter.  B 1 δ −− q  a  lon Experiment −1 0 −  20 Simulation  τ τ  0 0 0 0 0 Magnitude (DB) −20 B   (22) 1 2 = ′ , 10 10 0 Alon B′ 0  0  lat  −100 10 0 0 C = , (23) Phase (deg) −200 01 0 0 1 2 10 10 1.2 1 p 0.8 q δlat (t − τlat ) p 0.6

x =  , u = , y = , (24) Coherence a δ (t − τ ) q 0.4 s lon lon 0.2 1 2 b  10 10  s Frequency(Rad/Sec) mgHmr + Kβ mgHmr + Kβ Figure 6: Comparison of frequency response from longitu- Lb = , Ma = . (25) dinal input to pitch angular rate. Jxx Jyy The rotor spring constant Kβ, the lateral and longi- ′ ′ tudinal control derivatives Blat , Alon, the lateral and longitudinal control delay τlat , τlon, and the equiva- 4 CONCLUSIONS AND FUTURE lent flapping time constant τ are to be identified via WORK frequency domain identification in section 3.3.4. The coupling term Ab and Ba are neglected. In this paper we have presented our current progress

290 ConstructionandModelingofaVariableCollectivePitchCoaxialUAV

Table 1: Parameters identiﬁed from CIFER. Cramer-Rao Parameter Insensitivity(%) Physical meaning Percent(%) −2 Lb = 675.8s 7.171 2.433 Lateral rotor spring derivative −2 Ma = 794.7s 7.525 2.589 Longitudinal rotor spring derivative τ = 0.068s 9.301 3.537 Equivalent ﬂapping time constant ′ Alon = 0.898rad/s 4.152 1.962 Longitudinal control derivative ′ Blat = 1.069rad/s 4.157 1.935 Lateral control derivative τlat = 0.03355s 12.08 4.477 Lateral control delay τlon = 0.03390s 12.17 4.440 Longitudinal control delay Kβ = 11.5029Nm NA NA Rotor spring constant

2 Experiment Guowei Cai from NUS Temasek Laboratories for the 1 Simulation constructive discussion and genuine help. We would

0 also like to thank ‘Temasek Defence Systems Insti-

q (rad/s) tute’ for funding the project. −1

−2 0 2 4 6 8 10 12

1.5 REFERENCES 1 0.5 Cai, G., Chen, B. M., and Lee, T. H. (2011). Unmanned

lon 0

δ Rotorcraft Systems. Springer, London. −0.5 Cai, G., Chen, B. M., Lee, T. H., and Lum, K.-Y. (2012). −1 Comprehensive nonlinear modeling of a miniature un- −1.5 0 2 4 6 8 10 12 manned helicopter. Journal of the American Heli- Time(s) copter Society, 57(1):1–13. Figure 7: Time domain verification of longitudinal input to Coleman, C. P. (1997). A survey of theoretical and experi- pitch angular rate. mental coaxial rotor aerodynamic research. Technical report, NASA Ames Research Center. regarding the development and modeling of a coaxial Fankhauser, P., Bouabdallah, S., Leutenegger, S., and Sieg- wart, R. (2011). Modeling and decoupling control of UAVplatform. For platform construction, the payload the coax micro helicopter. In Proc. of the IEEE/RSJ capability of the bare coaxial helicopter is guaranteed International Conference on Intelligent Robots and by careful selection of the key components such as Systems (IROS). motor, blade and ESC. The onboard avionic system Kim, H. and Brown, R. (2006). Coaxial rotor performance is designed and assembled onto the helicopter frame and wake dynamics in steady and manoeuvring flight. using mechanical dampers. For modeling of the heli- In American Helicopter Society 62nd Annual Forum copter, the model structure of the platform has been Proceedings, volume 62, page 20. Kim, H. and Brown, R. (2008). Modelling the aerodynam- laid out. The coaxial rotor thrust has been empir- ics of coaxial helicopters–from an isolated rotor to a ically derived. More importantly, the roll-pitch dy- complete aircraft. In Proceedings of the EU-Korea namics of the helicopter are formulated. Through fre- Conference on Science and Technology, pages 45–59. quency domain identification in CIFER, the equiva- Lim, J. W., McAlister, K. W., and Johnson, W. (2009). lent flapping time constant and spring constant are Hover performance correlation for full-scale and fine-tuned. Time domain verification using a new set model-scale coaxial rotors. Journal of the American of test data has validated the fidelity of the identi- Helicopter Society. Mettler, B. (2002). Identification Modeling and Charac- fied roll-pitch dynamics. Future research work will teristics of Miniature Rotorcraft. Kluwer Academic focus on the modeling of heave dynamics and yaw Publisher, Nowell, MA. dynamics which will produce a complete model. Ad- Mettler, B., Tischler, M. B., and Kanade, T. (1999). System ditional effort will be made to study the coaxial rotor identification of small-size unmanned helicopter dy- wake structure so that an optimal coaxial configura- namics. In American Helicopter Society 55th Annual tion could be achieved. Forum Proceedings, volume 2, pages 1706–1717. Schafroth, D., Bermes, C., Bouabdallah, S., and Siegwart, R. (2010). Modeling and system identification of the mufly micro helicopter. Journal of intelligent & ACKNOWLEDGEMENTS robotic systems, 57(1):27–47. Tischler, M. and Remple, R. (2006). Aircraft and rotorcraft system identification: Engineering Methods with The authors would like to thank Dr. Feng Lin and Dr. Flight Test Examples. AIAA.

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