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Bioinspired Feathered Flapping Wing UAV Design for Operation in Gusty Environment

Bioinspired Feathered Flapping Wing UAV Design for Operation in Gusty Environment Hindawi Journal of Robotics Volume 2021, Article ID 8923599, 14 pages https://doi.org/10.1155/2021/8923599 Research Article Bioinspired Feathered Flapping Wing UAV Design for Operation in Gusty Environment S. H. Abbasi , A. Mahmood, and Abdul Khaliq Department of Electrical and Computer Engineering, SS CASE IT, Islamabad, Pakistan Correspondence should be addressed to S. H. Abbasi; abbasi882@gmail.com Received 29 July 2021; Accepted 27 August 2021; Published 13 September 2021 Academic Editor: L. Fortuna Copyright © 2021 S. H. Abbasi et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (e flight of unmanned aerial vehicles (UAVs) has numerous associated challenges. Small size is the major reason of their sensitivity towards turbulence restraining them from stable flight. Turbulence alleviation strategies of birds have been explored in recent past in detail to sort out this issue. Besides using primary and secondary feathers, birds also utilize covert feathers deflection to mitigate turbulence. Motivated from covert feathers of birds, this paper presents biologically inspired gust mitigation system (GMS) for a flapping wing UAV (FUAV). GMS consists of electromechanical (EM) covert feathers that sense the incoming gust and mitigate it through deflection of these feathers. A multibody model of gust-mitigating FUAV is developed appending models of the subsystems including rigid body, propulsion system, flapping mechanism, and GMS-installed wings using bond graph modeling approach. FUAV without GMS and FUAV with the proposed GMS integrated in it are simulated in the presence of vertical gust, and results’ comparison proves the efficacy of the proposed design. Furthermore, agreement between experimental results and present results validates the accuracy of the proposed design and developed model. Significant degradation in performance of UAVs has 1. Introduction been observed in the presence of high gusts and intense Attitude control is a serious concern for UAVs operating turbulence [7–12]. Furthermore, one of the major reasons of in the atmospheric boundary layer (ABL). (is ABL re- UAV loss at low altitudes operations is adverse winds [13]. gion is best suitable for UAV applications in Intelligence, Researches have indicated the loss of these UAVs is the result Surveillance, and Reconnaissance (ISR) missions. ABL, of lacking feedback from the sensors and huge time delay in however, is considered as highly turbulent as shown in transmission of data from the UAV to the pilot’s control Figure 1 [1, 2]. system [14]. (erefore, to continue stable UAV operation in (e aircrafts flying in this region experience abrupt and these turbulent regions, a GMS is inevitable to optimize the severe gusts that can cause fast disturbances in orientation, aircraft’s stability while decreasing danger of crashing. attitude, position, and speed. (e interaction of airflow with After the Wright brothers’ first journey, numerous flight ground obstacles changes due to various factors comprising controllers have been designed to tackle these turbulent size, density, shape, and permeability. (e Department of airflows. (e first ever GMS was developed in 1914 [15], after Land Resources has investigated the turbulence modes that, many attempts have been made to design an auton- present in forested regions. It was revealed that the forests omous GMS, including study by the Bristol Company 1949 are the key turbulence source due to their patchy surface. In [16], Douglas Firm 1950 [17], and NACA 1952 [18, 19]. addition, the trees also disturb the profile of the turbulent (e use of the Global Positioning System (GPS) and flow because of drag in close vicinity to the tree line [3–5]. autopilot modules have reduced pilot workload and im- (e Matterhorn, Switzerland, shows turbulence in moun- proved safety while operating in gusty weather. Each sub- tainous ranges by the snow that is trapped within the wind system is interlinked with the UAV’s central flight computer shear in vicinity of the summit [6]. and empowers the flight crew to closely assess the desired Package Delivery Surveilance 2 Journal of Robotics active flow control and therefore reduce flight instability [28]. By producing these jets, the boundary layer remains attached in gusty wind conditions thereby enabling the UAV to maintain stability. However, since the size of SJAs is large Updraft Downdraft enough to be incorporated in UAVs, their exploration for small scale aircrafts remains an open field for researchers. Similarly, vortex generators that produce microvortices on the surface of wing in order to avoid boundary layer sep- aration are also the variant of active GMS techniques for larger aircrafts [29]. However, due to size constraints, their applicability for UAVs remains a major question. Shear Layer Yeo et al. [30] have proposed flow aware wing design combining aerodynamic, computational, electrical, and mechanical elements to have improved flight during tur- bulent flows. Each wing is upgraded with an independent Vortices processor in order to actuate a dedicated control surface. Numerical simulation results have verified that the flow aware design of wings show a 22% decrease in roll angle Figure 1: Airflow around buildings [1]. deviancies and 18% drop in roll rate deviations in presence of turbulence. Blower and Wickenheiser in [20] have presented pri- flight path. Resultantly, preemptive actions can be taken mary- and secondary-feathers-inspired biomimetic flow sensors for fixed wing UAVs and discovered their suitability prior to facing bad weather and turbulent airflow to reduce gusting intensity, resulting in precautionary modifications in for usage as an active GMS. (e design showed significant improvement in stability characteristics of UAVs; however, heading and altitude [20]. Several other designs have been made to advance UAV their usage for FUAVs has not been discussed and leaves an open gap for researchers. avionics to attain higher performance in the turbulent airflows. Study in [21] presented the advanced avionics for (e detailed study of birds has revealed an interesting UAVs that can achieve stabilization performance similar to fact that during high turbulent airflows and gusty winds, large-sized aircrafts. A Micro Architecture and Control birds take on an intermittent flight, i.e., nonflapping phase. (MARC) avionics design is developed having substantial (e covert feathers during these intermittent gliding flights improvements in weight constraints and power consump- get activated to alleviate gusts as shown in Figure 2 [31]. tion of UAVs. Inspired by the biological covert feathers of birds, this research presents a novel distributed GMS for FUAV. GMS In addition to the aforementioned design efforts, during the last decade bioinspiration has also emerged as a comprises EM covert feathers integrated in flapping wings of UAV. GMS activates only at the time of turbulent airflows to breakthrough for solutions to many impending engineering problems. Researchers have carried out in-depth study of mitigate gust, while at all other instants it remains tightly birds that fly successfully close to the ground as well as in attached with wing to retain airfoil overall profile. It provides forests in turbulent conditions. Biologically inspired UAVs various flight advantages, including better maneuverability are not new [22–25]. Several bioinspired flow sensors have and enhanced stability during adverse wind environments. been developed to date to alleviate turbulence. (ese include Preliminary version of this research is presented by Particle Image Velocimetry (PIV), Light Detection and authors in [32, 33] in which only the development of GMS Ranging (LiDAR), Laser Doppler Anemometry (LDA), and and its effectiveness is studied by incorporating it in a rigid RADAR. However, since these sensors have large size, wing and performing simulations. (e efficacy of the pro- posed design by modeling the complete FUAV having GMS therefore they cannot be incorporated into UAVs. Researchers in [26] have studied the latest trends in installed in it needed to be ascertained. (erefore, the substantial enhancement of current research is as follows. reactive inertial sensors. Results obtained proved huge time delays and slow response while using single sensors for flight First, we present comprehensive model of a complete FUAV control during gusty airflows and necessitated the use of comprising the main body and its allied accessories. (ese multisensor systems for attitude control. Another research accessories include flapping mechanism, wings, and the [27] showed that conventional reactive attitude sensors have propulsion system which comprises battery, motor, and the very slow response times for attitude control during tur- gear box. Second, GMS is incorporated in the model of bulent environments. (ey presented a solution to the FUAV and a complete multibody model of gust-mitigating FUAV is presented. We utilize bond graph modeling (BGM) above-mentioned delays and developed novel bioinspired sensors, which provide phase advanced information of for developing the complete model and for performing simulations of gust-mitigating FUAV. 20-SIM software is disturbances thereby improving response time of actuators. Synthetic jet is another method for gust alleviation. used in this research for modeling. Furthermore, we gen- erate state space equations for in-depth analysis of internal (ese jets when combined into the wing extend the flight envelope of the aircraft to higher angles of attack through dynamics. Lastly, we simulate multibody model to check its Indoor Surveilance Journal of Robotics 3 Covert feathers deflecting in resultantly the EM feathers rotating to allow strong gusts to response to oncoming gust transpire through the airframe with little impedance. Figure 4 illustrates EM covert feather’s internal working. (e flap rotates as a response to incident gust and gives signal to PZT that is acting as a sensor through mechanical linkage and spring. After receiving gust signal, the PZT now acts as an actuator and produces an output signal equivalent to gust experienced and gives it to controller which in turn generates desired control output. (is control output, i.e., current, is forwarded to voice coil actuator. Voice coil ac- tuator moves out the shaft inside it and applies force on the flap that deflects out of the wing. Consequently, the gust flows through the EM covert feathers with very minimal Figure 2: Deflection of covert feathers during turbulence [31]. interaction with the wing’s cross-sectional area. Every EM covert feather is having a closed loop feedback accuracy and efficacy and also compare results with pub- design. (e GMS has a separate control and is not dependent lished experimental researches for validation of proposed on the main UAV controller. (is design allows local data scheme. analysis and control, thereby decreasing response times (e remaining paper is organized as follows. In Section 2, compared to traditional present day gust alleviation designs the design of gust-mitigating FUAV is presented. Section 3 that have delayed reaction times. During larger turbulence, covers the creation of bond graph model (BGM) of FUAV multiple feathers actuate since single feather response is not subsystems leading to the formulation of a multibody model enough. (is minimizes stress on a single EM feather, since of complete gust-mitigating FUAV. To validate the accuracy the incoming gust is spread over a certain region of the wing of proposed design and to check its correctness, comparison instead of concentration on a single point. of results with experimental studies and subsequent discus- sions are carried out in Section 4. (e final section includes 3. Bond Graph Formulation and Derivation of conclusions and future work. Dynamic Equations 2. FUAV Design Modeling is the process of interpreting scientific problems from an application field into tractable mathematical for- (e prototype FUAV under study is Festo’s Smart Bird [34]. mulations including its construction and working. (is (e Festo bird is having 2.2 m wing span and 0.28 m chord formulation of model helps in developing scientific un- length. Dynamic model of the system under investigation derstanding which assists in testing the effects of changes in a can be developed considering that the FUAV is composed of system and offers insight, solutions, and direction beneficial subsystems namely the main body, motors, the flapping for the original application. A mathematical model generally mechanism, rigid wings, and GMS. defines a system by a set of equations and variables that form (e flapping system comprises main structure, rigid relationships between the variables. Modeling renders so- beam wings, two DC motors driven by two batteries, and lutions by providing clear understandings into complex pair of crank rod mechanisms. A sketch of this flapping systems. [36]. mechanism is illustrated in Figure 3. (e flapping system Bond graph models are a domain independent graphical also consists of an arm added to slider bar as well as to wings depiction of dynamic behavior of physical systems. Meaning to generate the motion perpendicular to wing surface. (e by the systems from various domains, i.e., electrical, me- top angular velocity of wing is about 12 rad/s. chanical, hydraulic, thermodynamic, acoustical, etc., is la- (e proposed GMS consists of 16 biomimetic EM covert beled in the same way. (e basic concept is that bond graphs feathers. Eight are incorporated in the wing’s top surface and work on energy exchange between various domains. Simi- eight on the wing’s bottom surface. Single EM covert feather larities between domains are nothing more than just comprises flap, hinge, mechanical linkage, spring, piezo- mathematical equations being analogous, i.e., the utilized electric transducer (PZT), controller, and the voice coil physical concepts are the same. Bond graph modeling is a actuator. (e piezoelectric transducers having small size and potent tool for modeling engineering systems, particularly multiple functionalities are utilized in EM feathers due to the when diverse physical domains are present. Additionally, size limits of wings. Moreover, PZTs can have dual func- bond graph submodels can be reused smartly, since bond tionality at the same time, i.e., acting as sensors as well as graph models are noncausal. If the submodels are seen as actuators. objects, we can easily say that the bond graph modeling is a (e FUAV wing is composed of a skeletal structure type of object-oriented modeling of physical systems [37]. equipped with ribs and spars to carry loads. (e design of GMS ensures the wings to retain the airfoil’s overall shape throughout flapping phases as EM covert feathers remain 3.1. Main Body BGM. (e FUAV’s main body is taken as 6 firmly attached to wings. At the time of high turbulence, DOF rigid body which can perform both rotational and FUAV resorts to intermittent flight and GMS activates translational motion. (e analysis of motion of rigid body in 4 Journal of Robotics wing Hinge point Up stroke angle Crank-rod mechanism Down stroke angle Connecting rod (Link 2) Gear no. 2 Gear no. 1 Figure 3: Sketch of present flapping mechanism [35]. analytical solution of these Euler’s equations can be found in Flap certain cases; however, their general solution cannot be found [37]. Finally, using these six equations, the BGM of the main body is formed. PZT Mechanical Spring y Linkage z (3) p � F + mω − mω , x x z y m m P P z x _ (4) p � F + mω − mω , y y x z m m Voice Coil Controller y _ (5) p � F + mω − mω , z z y x m m Figure 4: Electromechanical covert feather. PJ PJ pJ � τ + J ω − J ω , (6) x x y y z z space produces equations given below based on Newton’s J J z y second law of motion [37]: PJ PJ zp x z (1) pJ � τ + J ω − J ω , (7) F � + ω × p, y y z z x x J J zt x z zpJ PJ PJ τ � + ω × pJ, (2) _ pJ � τ + J ω − J ω . (8) z z x x y y zt J J y x where p is linear momentum, p is angular momentum, F is Figure 5 shows the final BGM of the main body with a the force acting on the body, τ is the torque, and ω is the angular velocity of the main body. (ese two equations, i.e., general motion in 3 dimensional space. Six state space equations are obtained from the above-mentioned BGM (1) and (2), derived from Newton’s second law of motion, help attain the Euler’s equation given in (3)–(8). (e because the number of energy storing elements is 6. (e state LR DC motor Flapping angle (θ) Journal of Robotics 5 :m F V x x :J mω x ω mω x y MGY 1 MGY J ω J ω y y z z MGY MGY m m K K K τ τ z y 11 MGY ω ω z ‧ y ‧ J ω p x x p j j z y II :J K :J z y V V y z F F y 1 MGY 1 z ‧ ‧ p mω p y x z I :m :m Figure 5: BGM of the main body of FUAV. at one end. In this case, the wing’s vertical displacement at variables comprise generalized momentum p , p , p , p , p , x y z jx jy and p at every inertia element. the end point is calculated by [37, 38] jz y � l sin θ, (9) 3.2. DC Motors BGM. (e DC motors are powered by a where y is the displacement, θ is the flapping angle, and l is battery source and are used to change electrical energy into the wing span respectively. (e effort and flow relation can mechanical energy. It comprises an electromechanical be described as follows [39]: coupling and the armature which further consists of in- V � (lcos θ)ω, ductance and resistance elements. (e back EMF of the (10) motors is presented as a gyrator in the BGM [37]. (e BGM x cos θ􏼁 F � τ, of the DC motor is developed using the above-mentioned where V is the vertical direction velocity, F is the force, and description and is presented Figure 6. y τ is the torque, respectively. Figure 8 demonstrates the BGM of wing under vertical force, which is gust (Sf). l cosθ and 3.3. Flapping Mechanism BGM. (e flapping motion of the x cos θ are the transformer modulus relating translational FUAV under study is attained through slider crank mecha- quantities to rotational quantities. nism. (is mechanism comprises two rods linked together and an arm which is hinged at 90 angles to the rotating shaft. 3.5. BGM of Gust Mitigation System (GMS). In this section (e reciprocating movement is transmitted to and received BGM of a GMS is presented. Detailed development of BGM from this shaft and is used for conversion of rotational motion of GMS starting from single electromechanical (EM) covert into reciprocating motion and also vice versa. Input to the feather will not be discussed as the same has been extensively crank rod, i.e., velocity, is applied as a source of flow. (e _ investigated in previous work [32, 33]. corresponding BGM is shown in Figure 7. 1-junction (1J) is BGM of EM covert feather is shown in Figure 9. (e used for depicting the motion of the crank. (e inertia of the overall order of the model is eight since there are eight crank about its axis is shown as I element and the linear energy storing elements. (ere is one disturbance input, i.e., velocity of the connecting rod as (1x, _ 1y _), whereas I elements S (source of flow) which depicts gust incident on the feather. show the mass of connecting rod. 1-junction(1α _ ) and And there are two controllable inputs, i.e., MSf (modulated modulated transformers (MTF) are used for rotational mo- source of flow) and MSe (modulated source of effort). (ese tion of the link [37]. Furthermore, two inertial elements inputs form part of input vector u(t). MS is actually the representing mass and mass moment of inertia of the e force applied on the linkage, whereas MSf is the current components are dovetailed to the corresponding junctions. being input to the voice coil actuator. (e BGM obtained is used to formulate state space 3.4. Rigid Beam Wing BGM. Dynamics of the wings are equations given as (11)–(19). (e state variables comprise modeled as a rigid beam in transverse motion that is pivoted generalized momentum p , p , p at every inertia element 1 2 3 6 Journal of Robotics R I R I Se 1GY 1 R R1 Se GY Figure 6: BGM of a DC motor. T (θ) :m MTF 1 I MTF 2 I1 J : I T (θ) :m MTF 1 I θ 2 MTF1 I2 Sf Sf1 T (θ) :j MTF 1 I 2 MTF2 I3 T (θ) :m MTF 1 I slider MTF3 I4 Figure 7: BGM of a flapping mechanism. I I1 Gain Integrate1 ʃ Integrate Se MTF 0 MTF 0 I x cosθ V F ω lcosθ 1 y Figure 8: BGM of a wing. and generalized displacement q , q , q , q at every com- 1 2 3 4 q_ � · p , (14) pliance element. State variable q is the state of displacement 2 2 sensor used in the bond graph. _ p � q , (15) p � ic · p + ic · q , (11) 3 5 1 3 3 1 1 q � S − p − p , (16) q_ � · p , (12) 3 f 2 1 1 2 l · I I m R ic ic 1 1 m _ q_ � p − q , p � p + q − q − q − q , (17) (13) 4 2 4 2 3 3 1 2 4 I C l l C C C 1 2 1 2 Journal of Robotics 7 GUST SPRING PIEZO STACK MECHANICAL Sf C1 I2 C2 C3 Sf C I C C LINKAGE I1 m I 0 q TF 1 1 1 TF 0 f R FLAP MSe MSe1 MSf MSf IC IC COTROLLABLE INPUTS VOICE COIL Figure 9: BGM of EM feather. 3.7. Nonlinear Dynamic Modeling. In this research, the scope q_ � p . (18) 5 2 remains only to simulate vertical gust which produces the lift l · I force in the FUAV. (is lift force is integrated in BGM as Figure 10 shows the BGM of GMS comprising 16 EM flow source (S ). (e aerodynamic lift force being incident covert feathers. on the wings of FUAV produces upward movement, i.e., z direction. (e modulated transformer, i.e., MTF, is utilized in the BGM as shown in Figure 11 for conversion of wing 3.6. Complete BGM of a Gust-Mitigating FUAV. To study the motion into FUAV’s displacement in z direction. efficacy and correctness of the proposed GMS after incorpo- (e comprehensive modeling of Gust-mitigating FUAV ration in both wings of FUAV, the complete BGM of the by integrating all aerodynamic and structural elements is FUAV comprising main body and GMS incorporated rigid complicated. For simplification, certain assumptions are wings driven by two DC motors and slider crank flapping made that include neglecting a wide range of aerodynamic mechanism is taken into account. (e complete BGM of the forces encountered by FUAV being explored in the latest Gust-Mitigating FUAV is developed by joining the BGM of the studies, i.e., thrust, drag, wing’s wake, rotational inertia, subsystems presented in previous sections using appropriate circular rotation, rotational lift, leading edge vortex, viscous junctions and is illustrated in Figure 11. It is important to friction, and added mass. Also, we model flapping wing as a mention here that complete BGM of gust-mitigating FUAV rigid beam, and further insight into the wing’s flexibility has been reduced to 8 EM covert feathers per wing to avoid remains out of scope of the present work. Moreover, modeling complexity, since complete FUAV model comprising nonlinearity due to inherent system imperfections giving th 16 feathers per wing results in 260 order model and is rise to hidden dynamics and the associated control strategy challenging to simulate. Moreover, this reduced model presents to optimally utilize these nonlinearities for positive impact a baseline and is sufficient to prove efficacy of the proposed on the overall system as presented by [40] remains open for GMS design. Further research can be carried out to find out research. Addition of several boundary conditions, various optimal numbers of feathers that can be added in a wing. input forces and moments, extra degrees of freedoms and (e BGM in Figure 11 helps us compute state space of moreover incorporation of flexibility, and altering the wing’s gust-mitigating FUAV. (e state matrix x(t) contains vibrational modes need to be further explored. Also, os- generalized momentum of inertia elements and generalized cillations rise in the FUAV by means of unmodeled non- displacement of compliance elements. (ere are 17 dis- linearities, and delays leading to dominant scenarios of turbance inputs depicting gusts which are applied to each bifurcations and chaos as studied in [35] are out of the scope EM covert feather. Additionally, gust is applied to rigid wing of the present research. as well as a source of flow, i.e., S at 0 junction and this also forms part of the disturbance input vector. (ere are 34 4. Results Validation and Discussion controllable inputs including 2 sources of efforts (S ) rep- resent the DC motors, 16 are displayed as modulated flow In order to ascertain the correctness of BGM of gust- source, i.e., MS , and 16 are presented as modulated effort mitigating FUAV developed in the above section, we use source, i.e., MS . (ese 34 controllable inputs form part of three vertical gust speeds (35 m/s, 25 m/s, 15 m/s) on three the input vector u(t). (e final state matrix A comes out to feathers (feather no 1, feather no 2, and feather no 3) in- be of 132 ×132 order, input gain matrix B comes out to be of stalled on the right wing of FUAV. Figure 12 depicts the 132 × 34 order, and the output gain matrix C comes out to be voice coil actuator current of these 3 EM feathers. (e peak of 34 ×132 order. values currently depicted in the figure are in correct range 8 Journal of Robotics Figure 10: BGM of 16 EM feathers GMS. and are directly proportional to the gust force being applied It can be clearly seen that the gust-mitigating FUAV has on feathers. Figure 13 depicts the flapping angle of FUAV successfully alleviated the gust to 32% because of the ac- given in radians. tuation of EM covert feathers installed on the wing as ex- In order to prove efficacy of the proposed design, two pected. (e GMS-installed FUAV has displaced only 11.2 m simulation scenarios are considered. First the FUAV in comparison to 16.5 m displacement for the model without without GMS is simulated by applying 25 m/s gust on its GMS. Likewise, the roll angle of FUAV with GMS has re- wing, and movement in z direction is observed. Second, duced to 0.21 rad in comparison to 0.31 rad for the model the same gust is applied on the FUAV with GMS installed without GMS. (e above-mentioned results confirm the in it and the corresponding motion in z direction is an- anticipated utility of the proposed gust-mitigating FUAV alyzed. (e displacement in z direction of both the design. Moreover, it is pertinent to mention here that, in the simulation scenarios is illustrated in Figure 14. (e preliminary version of this research by authors in [32, 33], corresponding roll angles of FUAVs in both scenarios are the installation of GMS in the rigid wing helped mitigate the also shown in Figure 15. gust up to 50% and here in this research the mitigation in Journal of Robotics 9 Figure 11: BGM of a complete gust-mitigating FUAV. Voice coil actuator current (amp) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 –0.1 0 0.5 1 1.5 2 2.5 3 time (s) Feather 1 at gust speed 35 m/s Feather 2 at gust speed 25 m/s Feather 3 at gust speed 15 m/s Figure 12: Voice coil actuator current. Flapping Angle (rad) 0.5 –0.5 –1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 time Figure 13: Flapping angle of FUAV. y 10 Journal of Robotics Vertical Displacement (m) 0 123456789 10 time (s) With GMS Without GMS Figure 14: Displacement of FUAV in vertical direction. Roll Angle (rad) 0.4 0.3 0.2 0.1 0 123456789 10 time (s) Without GMS With GMS Figure 15: Roll angle of FUAV (with and without GMS). Forward Velocity (m/s) 0 123456789 10 time (s) Present Experimental Figure 16: Comparison of forward velocities in present work and experimental research [41]. complete FUAV is 32% which is exactly within the antici- summarized in Table 1. Very close agreement among the pated range. results of FUAV with GMS and FUAV without GMS, ac- Figure 16 shows the comparison of forward velocities of quired in current work and experimental findings, endorses FUAV in present research and study by [41]. Furthermore, accuracy and validity of the proposed design. results attained in current study are compared to the For further insight into model internal dynamics, gust findings of experimental research by [41] and are speed on the right wing (S ) is used as input and force f Journal of Robotics 11 Table 1: Comparison between present work and experimental research. Z displacement (m) Without GMS 16.5 Current work With GMS 11.2 Experimental [41] 16.9 Linear System Pole Zero Plot 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.8 0.9 –50000 –100000 –150000 –150000 –100000 –50000 0 Re Figure 17: Pole-zero (PZ) plot. Table 2: Parameters of model. Component Description Values Motors Voltage source Electrical 7.2 V Armature resistance of the motors Electrical 5.1Ω Gyrator ratio of motors Electrical 0.00813 Damping of motors Mechanical 0.00068 N-s/m Mass of motors Mechanical 0.021 kg Gears Ratio of gears Mechanical 0.112 Flapping mechanism Mass moment of inertia of crank Mechanical 0.009 kg/m Transformer ratio of connecting rod Mechanical 2 Transformer ratio of linkages Mechanical 1 Mass of connecting rod Mechanical 0.03 kg Mass moment of inertia of connecting rod Mechanical 0.006 kg/m Rigid beam wing Mass of rigid beam Mechanical 0.4 kg Mass moment of inertia of rigid beam Mechanical 0.024 kg/m Transformer ratio of rigid beam Mechanical 1 Main body Mass of body Mechanical 0.15 kg Mass moment of inertia (J , J , J ) Mechanical 0.002,0.004,0.003 kg/m x y z Gust speed Mechanical 25 m/s GMS Flap Mass of flap Mechanical 0.018 kg Mass of skeletal structure Mechanical 0.098 kg Gust velocity on feather Mechanical 25 m/s Voice coil actuator Im 12 Journal of Robotics Table 2: Continued. Component Description Values Inductance Electrical 0.89 H Stiffness Mechanical 0.589 kN/m Piezoelectric stack Resistance between amplifier and PZT Electrical 5Ω Mass of stack Mechanical 0.008 kg PZT spring stiffness Mechanical 0.024 kN/m −7 PZT equivalent capacitance Electrical 1.5 ×10 F Coupling ratio Electrical 0.478 Spring Spring stiffness Mechanical 0.03 kN/m Mechanical linkage Transformer ratio Mechanical 0.2 acting on wing (I ) is used as output. Linearizing the model Abbreviations for this input and output in 20-SIM software generates nd GMS: Gust mitigation system 132 order model. Figure 17 illustrates pole-zero plot of BGM: Bond graph model the model and displays that multiple poles are at origin and FUAV: Flapping wing UAV some of the poles are in the right half plane and thus the GAS: Gust alleviation system system is unstable. Moreover, step response indicates di- PZT: Piezoelectric transducer verging response further endorsing the internal unstable EM: Electromechanical dynamics of the system under study, whereas in the system UAV: Unmanned aerial vehicle in which GMS was installed in rigid wing in the prelim- UAS: Unmanned aircraft system inary version of this research in [32, 33], the internal CFD: Computational fluid dynamics dynamics were stable. Sf: Source of flow (e values of elements of BGM of gust-mitigating FUAV Se: Source of effort presented in Figure 11 are shown in Table 2. It must be noted MSf: Modulated source of flow that elements of all the 16 EM feathers are the same as one MSe: Modulated source of effort EM feather and are described in detail in previous work [33]. TF: Transformer GY: Gyrator 5. Conclusions SJA: Synthetic jet actuators. We propose a design of a new Gust Mitigation System (GMS) for flapping wing UAV (FUAV) inspired from covert Data Availability feathers of birds. We develop a complete Bond Graph Model (BGM) of a FUAV containing the main rigid body, flapping (e data that support the findings of this study are available system, GMS-installed wings, and the power system com- from the corresponding author upon reasonable request. prising of the battery, motor, and a gear combination. Addition of electromechanical (EM) covert feathers on the Conflicts of Interest top and bottom wing surfaces of FUAV decreases the gusting (e authors have confirmed no potential conflicts of interest forces being exerted on FUAV body and thereby offers a with respect to the research, authorship, and/or publication novel strategy of active gust mitigation for FUAVs. of this article. Simulations performed reveal hierarchal response gen- eration capability of feathers and also the unstable internal dynamics. (e results further show successful mitigation of References gust to 32% and therefore validate the effectiveness of the [1] S. Watkins, M. (ompson, B. Loxton, and M. 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Bioinspired Feathered Flapping Wing UAV Design for Operation in Gusty Environment

Journal of Robotics , Volume 2021 – Sep 13, 2021

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Copyright © 2021 S. H. Abbasi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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10.1155/2021/8923599
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Abstract

Hindawi Journal of Robotics Volume 2021, Article ID 8923599, 14 pages https://doi.org/10.1155/2021/8923599 Research Article Bioinspired Feathered Flapping Wing UAV Design for Operation in Gusty Environment S. H. Abbasi , A. Mahmood, and Abdul Khaliq Department of Electrical and Computer Engineering, SS CASE IT, Islamabad, Pakistan Correspondence should be addressed to S. H. Abbasi; abbasi882@gmail.com Received 29 July 2021; Accepted 27 August 2021; Published 13 September 2021 Academic Editor: L. Fortuna Copyright © 2021 S. H. Abbasi et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (e flight of unmanned aerial vehicles (UAVs) has numerous associated challenges. Small size is the major reason of their sensitivity towards turbulence restraining them from stable flight. Turbulence alleviation strategies of birds have been explored in recent past in detail to sort out this issue. Besides using primary and secondary feathers, birds also utilize covert feathers deflection to mitigate turbulence. Motivated from covert feathers of birds, this paper presents biologically inspired gust mitigation system (GMS) for a flapping wing UAV (FUAV). GMS consists of electromechanical (EM) covert feathers that sense the incoming gust and mitigate it through deflection of these feathers. A multibody model of gust-mitigating FUAV is developed appending models of the subsystems including rigid body, propulsion system, flapping mechanism, and GMS-installed wings using bond graph modeling approach. FUAV without GMS and FUAV with the proposed GMS integrated in it are simulated in the presence of vertical gust, and results’ comparison proves the efficacy of the proposed design. Furthermore, agreement between experimental results and present results validates the accuracy of the proposed design and developed model. Significant degradation in performance of UAVs has 1. Introduction been observed in the presence of high gusts and intense Attitude control is a serious concern for UAVs operating turbulence [7–12]. Furthermore, one of the major reasons of in the atmospheric boundary layer (ABL). (is ABL re- UAV loss at low altitudes operations is adverse winds [13]. gion is best suitable for UAV applications in Intelligence, Researches have indicated the loss of these UAVs is the result Surveillance, and Reconnaissance (ISR) missions. ABL, of lacking feedback from the sensors and huge time delay in however, is considered as highly turbulent as shown in transmission of data from the UAV to the pilot’s control Figure 1 [1, 2]. system [14]. (erefore, to continue stable UAV operation in (e aircrafts flying in this region experience abrupt and these turbulent regions, a GMS is inevitable to optimize the severe gusts that can cause fast disturbances in orientation, aircraft’s stability while decreasing danger of crashing. attitude, position, and speed. (e interaction of airflow with After the Wright brothers’ first journey, numerous flight ground obstacles changes due to various factors comprising controllers have been designed to tackle these turbulent size, density, shape, and permeability. (e Department of airflows. (e first ever GMS was developed in 1914 [15], after Land Resources has investigated the turbulence modes that, many attempts have been made to design an auton- present in forested regions. It was revealed that the forests omous GMS, including study by the Bristol Company 1949 are the key turbulence source due to their patchy surface. In [16], Douglas Firm 1950 [17], and NACA 1952 [18, 19]. addition, the trees also disturb the profile of the turbulent (e use of the Global Positioning System (GPS) and flow because of drag in close vicinity to the tree line [3–5]. autopilot modules have reduced pilot workload and im- (e Matterhorn, Switzerland, shows turbulence in moun- proved safety while operating in gusty weather. Each sub- tainous ranges by the snow that is trapped within the wind system is interlinked with the UAV’s central flight computer shear in vicinity of the summit [6]. and empowers the flight crew to closely assess the desired Package Delivery Surveilance 2 Journal of Robotics active flow control and therefore reduce flight instability [28]. By producing these jets, the boundary layer remains attached in gusty wind conditions thereby enabling the UAV to maintain stability. However, since the size of SJAs is large Updraft Downdraft enough to be incorporated in UAVs, their exploration for small scale aircrafts remains an open field for researchers. Similarly, vortex generators that produce microvortices on the surface of wing in order to avoid boundary layer sep- aration are also the variant of active GMS techniques for larger aircrafts [29]. However, due to size constraints, their applicability for UAVs remains a major question. Shear Layer Yeo et al. [30] have proposed flow aware wing design combining aerodynamic, computational, electrical, and mechanical elements to have improved flight during tur- bulent flows. Each wing is upgraded with an independent Vortices processor in order to actuate a dedicated control surface. Numerical simulation results have verified that the flow aware design of wings show a 22% decrease in roll angle Figure 1: Airflow around buildings [1]. deviancies and 18% drop in roll rate deviations in presence of turbulence. Blower and Wickenheiser in [20] have presented pri- flight path. Resultantly, preemptive actions can be taken mary- and secondary-feathers-inspired biomimetic flow sensors for fixed wing UAVs and discovered their suitability prior to facing bad weather and turbulent airflow to reduce gusting intensity, resulting in precautionary modifications in for usage as an active GMS. (e design showed significant improvement in stability characteristics of UAVs; however, heading and altitude [20]. Several other designs have been made to advance UAV their usage for FUAVs has not been discussed and leaves an open gap for researchers. avionics to attain higher performance in the turbulent airflows. Study in [21] presented the advanced avionics for (e detailed study of birds has revealed an interesting UAVs that can achieve stabilization performance similar to fact that during high turbulent airflows and gusty winds, large-sized aircrafts. A Micro Architecture and Control birds take on an intermittent flight, i.e., nonflapping phase. (MARC) avionics design is developed having substantial (e covert feathers during these intermittent gliding flights improvements in weight constraints and power consump- get activated to alleviate gusts as shown in Figure 2 [31]. tion of UAVs. Inspired by the biological covert feathers of birds, this research presents a novel distributed GMS for FUAV. GMS In addition to the aforementioned design efforts, during the last decade bioinspiration has also emerged as a comprises EM covert feathers integrated in flapping wings of UAV. GMS activates only at the time of turbulent airflows to breakthrough for solutions to many impending engineering problems. Researchers have carried out in-depth study of mitigate gust, while at all other instants it remains tightly birds that fly successfully close to the ground as well as in attached with wing to retain airfoil overall profile. It provides forests in turbulent conditions. Biologically inspired UAVs various flight advantages, including better maneuverability are not new [22–25]. Several bioinspired flow sensors have and enhanced stability during adverse wind environments. been developed to date to alleviate turbulence. (ese include Preliminary version of this research is presented by Particle Image Velocimetry (PIV), Light Detection and authors in [32, 33] in which only the development of GMS Ranging (LiDAR), Laser Doppler Anemometry (LDA), and and its effectiveness is studied by incorporating it in a rigid RADAR. However, since these sensors have large size, wing and performing simulations. (e efficacy of the pro- posed design by modeling the complete FUAV having GMS therefore they cannot be incorporated into UAVs. Researchers in [26] have studied the latest trends in installed in it needed to be ascertained. (erefore, the substantial enhancement of current research is as follows. reactive inertial sensors. Results obtained proved huge time delays and slow response while using single sensors for flight First, we present comprehensive model of a complete FUAV control during gusty airflows and necessitated the use of comprising the main body and its allied accessories. (ese multisensor systems for attitude control. Another research accessories include flapping mechanism, wings, and the [27] showed that conventional reactive attitude sensors have propulsion system which comprises battery, motor, and the very slow response times for attitude control during tur- gear box. Second, GMS is incorporated in the model of bulent environments. (ey presented a solution to the FUAV and a complete multibody model of gust-mitigating FUAV is presented. We utilize bond graph modeling (BGM) above-mentioned delays and developed novel bioinspired sensors, which provide phase advanced information of for developing the complete model and for performing simulations of gust-mitigating FUAV. 20-SIM software is disturbances thereby improving response time of actuators. Synthetic jet is another method for gust alleviation. used in this research for modeling. Furthermore, we gen- erate state space equations for in-depth analysis of internal (ese jets when combined into the wing extend the flight envelope of the aircraft to higher angles of attack through dynamics. Lastly, we simulate multibody model to check its Indoor Surveilance Journal of Robotics 3 Covert feathers deflecting in resultantly the EM feathers rotating to allow strong gusts to response to oncoming gust transpire through the airframe with little impedance. Figure 4 illustrates EM covert feather’s internal working. (e flap rotates as a response to incident gust and gives signal to PZT that is acting as a sensor through mechanical linkage and spring. After receiving gust signal, the PZT now acts as an actuator and produces an output signal equivalent to gust experienced and gives it to controller which in turn generates desired control output. (is control output, i.e., current, is forwarded to voice coil actuator. Voice coil ac- tuator moves out the shaft inside it and applies force on the flap that deflects out of the wing. Consequently, the gust flows through the EM covert feathers with very minimal Figure 2: Deflection of covert feathers during turbulence [31]. interaction with the wing’s cross-sectional area. Every EM covert feather is having a closed loop feedback accuracy and efficacy and also compare results with pub- design. (e GMS has a separate control and is not dependent lished experimental researches for validation of proposed on the main UAV controller. (is design allows local data scheme. analysis and control, thereby decreasing response times (e remaining paper is organized as follows. In Section 2, compared to traditional present day gust alleviation designs the design of gust-mitigating FUAV is presented. Section 3 that have delayed reaction times. During larger turbulence, covers the creation of bond graph model (BGM) of FUAV multiple feathers actuate since single feather response is not subsystems leading to the formulation of a multibody model enough. (is minimizes stress on a single EM feather, since of complete gust-mitigating FUAV. To validate the accuracy the incoming gust is spread over a certain region of the wing of proposed design and to check its correctness, comparison instead of concentration on a single point. of results with experimental studies and subsequent discus- sions are carried out in Section 4. (e final section includes 3. Bond Graph Formulation and Derivation of conclusions and future work. Dynamic Equations 2. FUAV Design Modeling is the process of interpreting scientific problems from an application field into tractable mathematical for- (e prototype FUAV under study is Festo’s Smart Bird [34]. mulations including its construction and working. (is (e Festo bird is having 2.2 m wing span and 0.28 m chord formulation of model helps in developing scientific un- length. Dynamic model of the system under investigation derstanding which assists in testing the effects of changes in a can be developed considering that the FUAV is composed of system and offers insight, solutions, and direction beneficial subsystems namely the main body, motors, the flapping for the original application. A mathematical model generally mechanism, rigid wings, and GMS. defines a system by a set of equations and variables that form (e flapping system comprises main structure, rigid relationships between the variables. Modeling renders so- beam wings, two DC motors driven by two batteries, and lutions by providing clear understandings into complex pair of crank rod mechanisms. A sketch of this flapping systems. [36]. mechanism is illustrated in Figure 3. (e flapping system Bond graph models are a domain independent graphical also consists of an arm added to slider bar as well as to wings depiction of dynamic behavior of physical systems. Meaning to generate the motion perpendicular to wing surface. (e by the systems from various domains, i.e., electrical, me- top angular velocity of wing is about 12 rad/s. chanical, hydraulic, thermodynamic, acoustical, etc., is la- (e proposed GMS consists of 16 biomimetic EM covert beled in the same way. (e basic concept is that bond graphs feathers. Eight are incorporated in the wing’s top surface and work on energy exchange between various domains. Simi- eight on the wing’s bottom surface. Single EM covert feather larities between domains are nothing more than just comprises flap, hinge, mechanical linkage, spring, piezo- mathematical equations being analogous, i.e., the utilized electric transducer (PZT), controller, and the voice coil physical concepts are the same. Bond graph modeling is a actuator. (e piezoelectric transducers having small size and potent tool for modeling engineering systems, particularly multiple functionalities are utilized in EM feathers due to the when diverse physical domains are present. Additionally, size limits of wings. Moreover, PZTs can have dual func- bond graph submodels can be reused smartly, since bond tionality at the same time, i.e., acting as sensors as well as graph models are noncausal. If the submodels are seen as actuators. objects, we can easily say that the bond graph modeling is a (e FUAV wing is composed of a skeletal structure type of object-oriented modeling of physical systems [37]. equipped with ribs and spars to carry loads. (e design of GMS ensures the wings to retain the airfoil’s overall shape throughout flapping phases as EM covert feathers remain 3.1. Main Body BGM. (e FUAV’s main body is taken as 6 firmly attached to wings. At the time of high turbulence, DOF rigid body which can perform both rotational and FUAV resorts to intermittent flight and GMS activates translational motion. (e analysis of motion of rigid body in 4 Journal of Robotics wing Hinge point Up stroke angle Crank-rod mechanism Down stroke angle Connecting rod (Link 2) Gear no. 2 Gear no. 1 Figure 3: Sketch of present flapping mechanism [35]. analytical solution of these Euler’s equations can be found in Flap certain cases; however, their general solution cannot be found [37]. Finally, using these six equations, the BGM of the main body is formed. PZT Mechanical Spring y Linkage z (3) p � F + mω − mω , x x z y m m P P z x _ (4) p � F + mω − mω , y y x z m m Voice Coil Controller y _ (5) p � F + mω − mω , z z y x m m Figure 4: Electromechanical covert feather. PJ PJ pJ � τ + J ω − J ω , (6) x x y y z z space produces equations given below based on Newton’s J J z y second law of motion [37]: PJ PJ zp x z (1) pJ � τ + J ω − J ω , (7) F � + ω × p, y y z z x x J J zt x z zpJ PJ PJ τ � + ω × pJ, (2) _ pJ � τ + J ω − J ω . (8) z z x x y y zt J J y x where p is linear momentum, p is angular momentum, F is Figure 5 shows the final BGM of the main body with a the force acting on the body, τ is the torque, and ω is the angular velocity of the main body. (ese two equations, i.e., general motion in 3 dimensional space. Six state space equations are obtained from the above-mentioned BGM (1) and (2), derived from Newton’s second law of motion, help attain the Euler’s equation given in (3)–(8). (e because the number of energy storing elements is 6. (e state LR DC motor Flapping angle (θ) Journal of Robotics 5 :m F V x x :J mω x ω mω x y MGY 1 MGY J ω J ω y y z z MGY MGY m m K K K τ τ z y 11 MGY ω ω z ‧ y ‧ J ω p x x p j j z y II :J K :J z y V V y z F F y 1 MGY 1 z ‧ ‧ p mω p y x z I :m :m Figure 5: BGM of the main body of FUAV. at one end. In this case, the wing’s vertical displacement at variables comprise generalized momentum p , p , p , p , p , x y z jx jy and p at every inertia element. the end point is calculated by [37, 38] jz y � l sin θ, (9) 3.2. DC Motors BGM. (e DC motors are powered by a where y is the displacement, θ is the flapping angle, and l is battery source and are used to change electrical energy into the wing span respectively. (e effort and flow relation can mechanical energy. It comprises an electromechanical be described as follows [39]: coupling and the armature which further consists of in- V � (lcos θ)ω, ductance and resistance elements. (e back EMF of the (10) motors is presented as a gyrator in the BGM [37]. (e BGM x cos θ􏼁 F � τ, of the DC motor is developed using the above-mentioned where V is the vertical direction velocity, F is the force, and description and is presented Figure 6. y τ is the torque, respectively. Figure 8 demonstrates the BGM of wing under vertical force, which is gust (Sf). l cosθ and 3.3. Flapping Mechanism BGM. (e flapping motion of the x cos θ are the transformer modulus relating translational FUAV under study is attained through slider crank mecha- quantities to rotational quantities. nism. (is mechanism comprises two rods linked together and an arm which is hinged at 90 angles to the rotating shaft. 3.5. BGM of Gust Mitigation System (GMS). In this section (e reciprocating movement is transmitted to and received BGM of a GMS is presented. Detailed development of BGM from this shaft and is used for conversion of rotational motion of GMS starting from single electromechanical (EM) covert into reciprocating motion and also vice versa. Input to the feather will not be discussed as the same has been extensively crank rod, i.e., velocity, is applied as a source of flow. (e _ investigated in previous work [32, 33]. corresponding BGM is shown in Figure 7. 1-junction (1J) is BGM of EM covert feather is shown in Figure 9. (e used for depicting the motion of the crank. (e inertia of the overall order of the model is eight since there are eight crank about its axis is shown as I element and the linear energy storing elements. (ere is one disturbance input, i.e., velocity of the connecting rod as (1x, _ 1y _), whereas I elements S (source of flow) which depicts gust incident on the feather. show the mass of connecting rod. 1-junction(1α _ ) and And there are two controllable inputs, i.e., MSf (modulated modulated transformers (MTF) are used for rotational mo- source of flow) and MSe (modulated source of effort). (ese tion of the link [37]. Furthermore, two inertial elements inputs form part of input vector u(t). MS is actually the representing mass and mass moment of inertia of the e force applied on the linkage, whereas MSf is the current components are dovetailed to the corresponding junctions. being input to the voice coil actuator. (e BGM obtained is used to formulate state space 3.4. Rigid Beam Wing BGM. Dynamics of the wings are equations given as (11)–(19). (e state variables comprise modeled as a rigid beam in transverse motion that is pivoted generalized momentum p , p , p at every inertia element 1 2 3 6 Journal of Robotics R I R I Se 1GY 1 R R1 Se GY Figure 6: BGM of a DC motor. T (θ) :m MTF 1 I MTF 2 I1 J : I T (θ) :m MTF 1 I θ 2 MTF1 I2 Sf Sf1 T (θ) :j MTF 1 I 2 MTF2 I3 T (θ) :m MTF 1 I slider MTF3 I4 Figure 7: BGM of a flapping mechanism. I I1 Gain Integrate1 ʃ Integrate Se MTF 0 MTF 0 I x cosθ V F ω lcosθ 1 y Figure 8: BGM of a wing. and generalized displacement q , q , q , q at every com- 1 2 3 4 q_ � · p , (14) pliance element. State variable q is the state of displacement 2 2 sensor used in the bond graph. _ p � q , (15) p � ic · p + ic · q , (11) 3 5 1 3 3 1 1 q � S − p − p , (16) q_ � · p , (12) 3 f 2 1 1 2 l · I I m R ic ic 1 1 m _ q_ � p − q , p � p + q − q − q − q , (17) (13) 4 2 4 2 3 3 1 2 4 I C l l C C C 1 2 1 2 Journal of Robotics 7 GUST SPRING PIEZO STACK MECHANICAL Sf C1 I2 C2 C3 Sf C I C C LINKAGE I1 m I 0 q TF 1 1 1 TF 0 f R FLAP MSe MSe1 MSf MSf IC IC COTROLLABLE INPUTS VOICE COIL Figure 9: BGM of EM feather. 3.7. Nonlinear Dynamic Modeling. In this research, the scope q_ � p . (18) 5 2 remains only to simulate vertical gust which produces the lift l · I force in the FUAV. (is lift force is integrated in BGM as Figure 10 shows the BGM of GMS comprising 16 EM flow source (S ). (e aerodynamic lift force being incident covert feathers. on the wings of FUAV produces upward movement, i.e., z direction. (e modulated transformer, i.e., MTF, is utilized in the BGM as shown in Figure 11 for conversion of wing 3.6. Complete BGM of a Gust-Mitigating FUAV. To study the motion into FUAV’s displacement in z direction. efficacy and correctness of the proposed GMS after incorpo- (e comprehensive modeling of Gust-mitigating FUAV ration in both wings of FUAV, the complete BGM of the by integrating all aerodynamic and structural elements is FUAV comprising main body and GMS incorporated rigid complicated. For simplification, certain assumptions are wings driven by two DC motors and slider crank flapping made that include neglecting a wide range of aerodynamic mechanism is taken into account. (e complete BGM of the forces encountered by FUAV being explored in the latest Gust-Mitigating FUAV is developed by joining the BGM of the studies, i.e., thrust, drag, wing’s wake, rotational inertia, subsystems presented in previous sections using appropriate circular rotation, rotational lift, leading edge vortex, viscous junctions and is illustrated in Figure 11. It is important to friction, and added mass. Also, we model flapping wing as a mention here that complete BGM of gust-mitigating FUAV rigid beam, and further insight into the wing’s flexibility has been reduced to 8 EM covert feathers per wing to avoid remains out of scope of the present work. Moreover, modeling complexity, since complete FUAV model comprising nonlinearity due to inherent system imperfections giving th 16 feathers per wing results in 260 order model and is rise to hidden dynamics and the associated control strategy challenging to simulate. Moreover, this reduced model presents to optimally utilize these nonlinearities for positive impact a baseline and is sufficient to prove efficacy of the proposed on the overall system as presented by [40] remains open for GMS design. Further research can be carried out to find out research. Addition of several boundary conditions, various optimal numbers of feathers that can be added in a wing. input forces and moments, extra degrees of freedoms and (e BGM in Figure 11 helps us compute state space of moreover incorporation of flexibility, and altering the wing’s gust-mitigating FUAV. (e state matrix x(t) contains vibrational modes need to be further explored. Also, os- generalized momentum of inertia elements and generalized cillations rise in the FUAV by means of unmodeled non- displacement of compliance elements. (ere are 17 dis- linearities, and delays leading to dominant scenarios of turbance inputs depicting gusts which are applied to each bifurcations and chaos as studied in [35] are out of the scope EM covert feather. Additionally, gust is applied to rigid wing of the present research. as well as a source of flow, i.e., S at 0 junction and this also forms part of the disturbance input vector. (ere are 34 4. Results Validation and Discussion controllable inputs including 2 sources of efforts (S ) rep- resent the DC motors, 16 are displayed as modulated flow In order to ascertain the correctness of BGM of gust- source, i.e., MS , and 16 are presented as modulated effort mitigating FUAV developed in the above section, we use source, i.e., MS . (ese 34 controllable inputs form part of three vertical gust speeds (35 m/s, 25 m/s, 15 m/s) on three the input vector u(t). (e final state matrix A comes out to feathers (feather no 1, feather no 2, and feather no 3) in- be of 132 ×132 order, input gain matrix B comes out to be of stalled on the right wing of FUAV. Figure 12 depicts the 132 × 34 order, and the output gain matrix C comes out to be voice coil actuator current of these 3 EM feathers. (e peak of 34 ×132 order. values currently depicted in the figure are in correct range 8 Journal of Robotics Figure 10: BGM of 16 EM feathers GMS. and are directly proportional to the gust force being applied It can be clearly seen that the gust-mitigating FUAV has on feathers. Figure 13 depicts the flapping angle of FUAV successfully alleviated the gust to 32% because of the ac- given in radians. tuation of EM covert feathers installed on the wing as ex- In order to prove efficacy of the proposed design, two pected. (e GMS-installed FUAV has displaced only 11.2 m simulation scenarios are considered. First the FUAV in comparison to 16.5 m displacement for the model without without GMS is simulated by applying 25 m/s gust on its GMS. Likewise, the roll angle of FUAV with GMS has re- wing, and movement in z direction is observed. Second, duced to 0.21 rad in comparison to 0.31 rad for the model the same gust is applied on the FUAV with GMS installed without GMS. (e above-mentioned results confirm the in it and the corresponding motion in z direction is an- anticipated utility of the proposed gust-mitigating FUAV alyzed. (e displacement in z direction of both the design. Moreover, it is pertinent to mention here that, in the simulation scenarios is illustrated in Figure 14. (e preliminary version of this research by authors in [32, 33], corresponding roll angles of FUAVs in both scenarios are the installation of GMS in the rigid wing helped mitigate the also shown in Figure 15. gust up to 50% and here in this research the mitigation in Journal of Robotics 9 Figure 11: BGM of a complete gust-mitigating FUAV. Voice coil actuator current (amp) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 –0.1 0 0.5 1 1.5 2 2.5 3 time (s) Feather 1 at gust speed 35 m/s Feather 2 at gust speed 25 m/s Feather 3 at gust speed 15 m/s Figure 12: Voice coil actuator current. Flapping Angle (rad) 0.5 –0.5 –1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 time Figure 13: Flapping angle of FUAV. y 10 Journal of Robotics Vertical Displacement (m) 0 123456789 10 time (s) With GMS Without GMS Figure 14: Displacement of FUAV in vertical direction. Roll Angle (rad) 0.4 0.3 0.2 0.1 0 123456789 10 time (s) Without GMS With GMS Figure 15: Roll angle of FUAV (with and without GMS). Forward Velocity (m/s) 0 123456789 10 time (s) Present Experimental Figure 16: Comparison of forward velocities in present work and experimental research [41]. complete FUAV is 32% which is exactly within the antici- summarized in Table 1. Very close agreement among the pated range. results of FUAV with GMS and FUAV without GMS, ac- Figure 16 shows the comparison of forward velocities of quired in current work and experimental findings, endorses FUAV in present research and study by [41]. Furthermore, accuracy and validity of the proposed design. results attained in current study are compared to the For further insight into model internal dynamics, gust findings of experimental research by [41] and are speed on the right wing (S ) is used as input and force f Journal of Robotics 11 Table 1: Comparison between present work and experimental research. Z displacement (m) Without GMS 16.5 Current work With GMS 11.2 Experimental [41] 16.9 Linear System Pole Zero Plot 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.8 0.9 –50000 –100000 –150000 –150000 –100000 –50000 0 Re Figure 17: Pole-zero (PZ) plot. Table 2: Parameters of model. Component Description Values Motors Voltage source Electrical 7.2 V Armature resistance of the motors Electrical 5.1Ω Gyrator ratio of motors Electrical 0.00813 Damping of motors Mechanical 0.00068 N-s/m Mass of motors Mechanical 0.021 kg Gears Ratio of gears Mechanical 0.112 Flapping mechanism Mass moment of inertia of crank Mechanical 0.009 kg/m Transformer ratio of connecting rod Mechanical 2 Transformer ratio of linkages Mechanical 1 Mass of connecting rod Mechanical 0.03 kg Mass moment of inertia of connecting rod Mechanical 0.006 kg/m Rigid beam wing Mass of rigid beam Mechanical 0.4 kg Mass moment of inertia of rigid beam Mechanical 0.024 kg/m Transformer ratio of rigid beam Mechanical 1 Main body Mass of body Mechanical 0.15 kg Mass moment of inertia (J , J , J ) Mechanical 0.002,0.004,0.003 kg/m x y z Gust speed Mechanical 25 m/s GMS Flap Mass of flap Mechanical 0.018 kg Mass of skeletal structure Mechanical 0.098 kg Gust velocity on feather Mechanical 25 m/s Voice coil actuator Im 12 Journal of Robotics Table 2: Continued. Component Description Values Inductance Electrical 0.89 H Stiffness Mechanical 0.589 kN/m Piezoelectric stack Resistance between amplifier and PZT Electrical 5Ω Mass of stack Mechanical 0.008 kg PZT spring stiffness Mechanical 0.024 kN/m −7 PZT equivalent capacitance Electrical 1.5 ×10 F Coupling ratio Electrical 0.478 Spring Spring stiffness Mechanical 0.03 kN/m Mechanical linkage Transformer ratio Mechanical 0.2 acting on wing (I ) is used as output. Linearizing the model Abbreviations for this input and output in 20-SIM software generates nd GMS: Gust mitigation system 132 order model. Figure 17 illustrates pole-zero plot of BGM: Bond graph model the model and displays that multiple poles are at origin and FUAV: Flapping wing UAV some of the poles are in the right half plane and thus the GAS: Gust alleviation system system is unstable. Moreover, step response indicates di- PZT: Piezoelectric transducer verging response further endorsing the internal unstable EM: Electromechanical dynamics of the system under study, whereas in the system UAV: Unmanned aerial vehicle in which GMS was installed in rigid wing in the prelim- UAS: Unmanned aircraft system inary version of this research in [32, 33], the internal CFD: Computational fluid dynamics dynamics were stable. Sf: Source of flow (e values of elements of BGM of gust-mitigating FUAV Se: Source of effort presented in Figure 11 are shown in Table 2. It must be noted MSf: Modulated source of flow that elements of all the 16 EM feathers are the same as one MSe: Modulated source of effort EM feather and are described in detail in previous work [33]. TF: Transformer GY: Gyrator 5. Conclusions SJA: Synthetic jet actuators. We propose a design of a new Gust Mitigation System (GMS) for flapping wing UAV (FUAV) inspired from covert Data Availability feathers of birds. 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Journal of RoboticsHindawi Publishing Corporation

Published: Sep 13, 2021

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