This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters IEEE ROBOTICS AND AUTOMATION LETTERS PREPRINT VERSION ACCEPTED JANUARY, 2021 Flying with Damaged Wings: The Effect on Flight Capacity and Bio-inspired Coping Strategies of A Flapping Wing Robot Zhan Tu, Fan Fei, Limeng Liu, Yiming Zhou, and Xinyan Deng Abstract—Insects wings are subject to wear and tear from collisions and environmental disturbances during flight They can tolerate both symmetrical and asymmetrical wing damages while maintaining flight capability to some extent Drawing inspiration from nature’s adaptation capabilities, we investigated the consequences of wing damage on a flapping wing micro air vehicle by quantifying the changes in wing kinematics, lift generation, control torque offset, and aerodynamic damping variations in flight tests with intact and damaged wings For the proposed vehicle, the wing damage affected the lift generation significantly Compared to the intact wings, the damaged ones result in increased stroke angle amplitude in order to compensate for lift loss and torque imbalance, which causes an increase in power consumption accordingly Furthermore, asymmetric damages usually require a larger amount of additional control effort for flight stabilization compared to symmetric cases In addition, aerodynamic damping varies as the wing areas change All these aspects pose challenges in flight control An adaptive controller is proposed to cope with the wing damage induced detrimental effects on flight capacity Flight tests were conducted to validate the control performance As a result, the robot can effectively overcome such challenges even in the case of a maximum unilateral lift loss of up to ≈22% Such a result matches the performance of hovering hawkmoths, which can handle torque asymmetry up to 22.3±7.8% To the best of our knowledge, this is the first demonstration of FWMAVs to handle significant wing asymmetry in hover flight Index Terms—Biologically Inspired, Flapping Wing, Micro Aerial Vehicle, Wing Damage, Adaptive Control I Introduction For aerial vehicles, wing damages can cause serious aerodynamic and flight stability consequences Studies on traditional fixed-wing and rotary-wing aircraft show that the lifting surface loss and control surface loss typically results in lift generation and flight stability challenges [1]–[3], and therefore causes the drop in flight capacity As a result, active and passive solutions have been proposed to solve the corresponding flight control and safety issues [4]–[7] Manuscript received October, 15, 2020; Revised January, 3, 2021; Accepted January, 24, 2021 This paper was recommended for publication by Editor Xinyu Liu upon evaluation of the associate editor and reviewers’ comments This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.(Corresponding Author: Zhan Tu; Xinyan Deng.) Zhan Tu is with Institute of Unmanned System, Beihang University, Beijing 100083, China, and also with the School of Mechanical Engineering, Purdue University, W Lafayette, IN 47907, USA Email: zhantu@buaa.edu.cn Fan Fei is with Amazon.com, Inc, Seattle, WA 98109, USA, and also with the School of Mechanical Engineering, Purdue University, W Lafayette, IN 47907, USA Email: ffnc1020@gmail.com Limeng Liu, Yiming Zhou, and Xinyan Deng are with the School of Mechanical Engineering, Purdue University, W Lafayette, IN 47907, USA Email: liu1936@purdue.edu; zhou663@purdue.edu; xdeng@purdue.edu Digital Object Identifier (DOI): Fig (a) Schematic representation of the treatments applied to each individual moth and their corresponding wing kinematics (top view), taken from [17], [20] (b) Bio-inspired wing damage test on a hovering FWMAV Meanwhile, Flapping Wing Micro Air Vehicles (FWMAVs) could be more sensitive to wing damage due to their unsteady aerodynamics and underactuation characteristics To date, a number of FWMAVs have achieved stable flight [8]–[15], and a systematic investigation on wing damage is needed In nature, flying insects also undergo unavoidable wing wear and tear due to collisions and environmental disturbances They are able to compensate effectively for such damage to some extent For example, biological studies have been conducted to investigate the wing damage consequences to flight performance and the corresponding solutions in flying animals [16]–[20] It was found that insects are able to alter their wing kinematics or flight muscles asymmetrically to deal with wing damage consequences For example, hawkmoths can tolerate up to 20% wingtip loss [17], [20] Their particular adaption strategy of wing damage is shown in Fig 1(a) Flight resiliency under wing area loss enables the animals to counter the environmental factors causing wing wear and tear, e.g., dense branches and bushes in forest, or object collisions caused by windy conditions To find out whether similar adaptation principles could be adopted for FWMAVs and their effect on flight efficiency and performance, we systematically conducted wing damage experiments on a bio-inspired flying robot based on our previous design [15] The results of this study will inform us on both the system resilience and the coping strategies for wing area loss, especially when the vehicle navigates in confined and cluttered environment In addition, it will also provide important insight into the improvement of flight control A preferred prerequisite on such robotic platforms to imitate 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters IEEE ROBOTICS AND AUTOMATION LETTERS PREPRINT VERSION ACCEPTED JANUARY, 2021 flying creatures’ resilience lies in its bio-inspired decoupled wings It is critical because the robot needs to be able to adapt to asymmetric wing damage by varying wing kinematics independently, which is a key component as observed in the coping strategies in flying animals In this work, the test platform is an FWMAV with independently actuated wings, as shown in Fig For each wing, the motion kinematics is independently controlled by a motor To quantify the impact of wing damage, we fabricated several intact and damaged wings as shown in Fig 2(a) The first set-#1 is a pair of intact wings The other two pairs have different degrees of artificial damages Detailed morphological differences between three pairs of wings are summarized in Table I Similar to the hawkmoth study illustrated in Fig 1(a), various pairing schemes of these wings were equipped on the test platform to investigate the impact of both symmetric and asymmetric wing area reductions In particular, we systematically studied the following aspects of the wing damage effect: lift drop, control torque offset, and aerodynamic damping changes The overall negative effects results in the unique flight control challenges which have been rarely studied on FWMAVs With the knowledge of the wing tearing effects, a targeted nonlinear controller is proposed to cope with such challenges The effectiveness of the proposed controller has been validated with systematic flight experiments As a result, the controller can ensure a stable flight even if there is a severe lift gap (>22%) between the two wings To the best of our knowledge, this is the first demonstration of FWMAVs to handle significant wing asymmetry in hover flight This work provides an important contribution to the understanding of the flight capacity change of FWMAVs with damaged wings The proposed study procedure, qualitative results, and flight control solution can be a valuable reference and potentially be generalized to other flapping wing systems with similar aerodynamic principles, aiding the design and control of such bio-inspired flying vehicles The rest of the article is organized as follows Section II introduces the test platform and its dynamics model Section III analysis the effects of wing damage on the test platform Section IV presents the controller design that addresses the corresponding control challenges caused by wing damage Section V shows the experimental flight results of the proposed vehicle under different wing damage scenarios Section VI summarizes this work Fig (a) Demonstration of the test wings: #1-intact wings, #2-damaged wings, bilateral 5% wingtip area loss, #3-damaged wings, bilateral 10% wingtip area loss (b) Illustration of the test platform, which can equip asymmetric wings The clipped wing area is outlined with red line segments around the wingtip to about 45◦ The onboard electronic system consists of two power regulators, a microcontroller, an inertial measurement unit (IMU), and two motor drivers The detailed design of each module can be found in [15] The proposed platform employs just two actuators for 6-DoF flight control Wing kinematic modulation technique is used to generated control torque The particular wing kinematics is adjusted by a sinusoidal motor voltage input, namely: voltage amplitude 𝑉; the differential voltage amplitude of two motors 𝛿𝑉; the voltage bias 𝑉0 ; the split-cycle parameter 𝛿𝜎 [15] A typical motor input 𝑉𝑖𝑛 is 𝑉 sin II Test Platform Description and Modeling 𝑉𝑖𝑛 = 𝑉 sin 𝜔𝑛 𝑡 2𝜎 + 𝑉0 𝜔𝑛 𝑡−2 𝜋 2(1−𝜎) + 𝑉0 𝜎 𝑓 ≤ 1𝑓 if ≤ 𝑡 ≤ if 𝜎 𝑓 ≤𝑡 (1) A Test Platform The test platform in this study is based on a dual-motor actuated FWMAV proposed in [15] It is capable of equipping asymmetric wings as shown in Fig 2(b) The wingspan of such a vehicle with intact wings is about 170mm and the weight is about 12.5g Inspired by the flying animals, it is designed with decoupled wings, i.e., each wing is driven by a dc motor independently Motor power efficiency is optimized by reduction gears and torsional springs The wing is designed to passively rotate due to the aerodynamic and inertial loading [21] The Angle-of-Attack (AoA) of the wings is optimized where 𝜔 𝑛 = 2𝜋 𝑓 and 𝑓 is wingbeat frequency, 𝑡 is time According to the defined four control inputs above, the vehicle can generate lift and 3-axis control torque In particular, lift 𝑓 𝑧 = 𝐾𝑢1 𝑢 where 𝑢 = 𝑉𝑖𝑛 − 𝑉𝑠0 and 𝑉𝑠0 denotes motor driver starting voltage; roll torque 𝜏𝑥 = 𝐾𝑢2 𝑢 + 𝜏𝑥0 , 𝑢 = 𝛿𝑉; pitch torque 𝜏𝑦 = 𝐾𝑢3 𝑢 + 𝜏𝑦0 , 𝑢 = 𝑉0 ; and yaw torque 𝜏𝑧 = 𝐾𝑢4 𝑢 + 𝜏𝑧0 , 𝑢 = 𝛿𝜎 𝐾𝑢1,2,3,4 are linearized input coefficients, and 𝜏𝑥0 , 𝜏𝑦0 , 𝜏𝑧0 are the mechanical imperfection induced trim condition 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters TU et al.: FLYING WITH DAMAGED WINGS: THE EFFECT ON FLIGHT CAPACITY AND BIO-INSPIRED COPING STRATEGIES OF A FLAPPING WING ROBOT ˆ high-speed camera wing kinematics position & attitude Vicon camera (6 in total) ψ, r φ, p PC z θ, q power estimation asymptotic load x III Effect of Wing Damage y Fig Illustration of the flight test setup B Vehicle Dynamics With the coordinate defined in Fig 3, the test vehicle can be modeled by 𝑚 𝒑 = 𝑹 𝒇𝑛 − 𝑚 𝒈 + 𝒇 𝑑 + 𝒅 𝒑 𝑱 𝝎 = 𝝉𝑛 − 𝝎 × 𝑱𝝎 + 𝝉𝑑 + 𝒅𝝎 , (2) where 𝑚 is the total mass; 𝒑 = [𝑥, 𝑦, 𝑧] 𝑇 is the vehicle position in the inertial frame; 𝜼 = [𝜙, 𝜃, 𝜓] 𝑇 is the attitude angle of the vehicle; 𝑹(𝜼) is the rotation matrix; 𝒑 = 𝑹𝒗 𝒃 wherein 𝒗 𝒃 = [𝑢, 𝑣, 𝑤] 𝑇 is the translational velocity in the body frame; 𝒇𝑛 = [0, 0, 𝑓 𝑧 ] 𝑇 ; 𝒈 = [0, 0, 9.8𝑚/𝑠2 ] 𝑇 is the gravity acceleration vector; 𝑱 is the inertia matrix of the vehicle; 𝝎 = [ 𝑝, 𝑞, 𝑟] 𝑇 is the vehicle angular velocity; 𝝉𝑛 = [𝜏𝑥 , 𝜏𝑦 , 𝜏𝑧 ] 𝑇 ; 𝒅 𝒑 and 𝒅𝝎 denote external disturbances; 𝒇 𝑑 and 𝝉𝑑 indicate a unique aerodynamic phenomenon in FWMAVsflapping counter forces/torques (FCFs/FCTs) induced additional damping wrenches [22], [23] The stroke-averaged 𝒇 𝑑 and 𝝉𝑑 are given by 𝒇 𝑑 = 𝑹𝑫 (𝒄 𝒑 )𝒗 𝒃 + 𝑹𝑫 (𝒄 𝒑 , 𝑑 𝑠 )𝝎, 𝝉𝑑 = 𝑫 (𝒄 𝒑 , 𝑑 𝑠 )𝒗 𝒃 + 𝑫 (𝒄 𝒑 , 𝒄𝜼 , 𝑑 𝑠 )𝝎, and normal force coefficient, respectively; 𝑑𝑑𝜓𝑡ˆ𝑤 is the nondimensional flapping velocity FCFs/FCTs has been particularly considered in this work because it directly related to the wings’ morphological change and affects the control bandwidth (3) where 𝑫 1,2,3,4 are damping coefficient matrix in terms of 𝒄 𝒑 = [𝑐 𝑥 , 𝑐 𝑦 , 𝑐 𝑧 ], 𝒄𝜼 = [𝑐 𝜙 , 𝑐 𝜃 , 𝑐 𝜓 ], and 𝑑 𝑠 , where 𝑑 𝑠 is the offset between the stroke plane and the center of gravity The expanded form of 𝑫 1,2,3,4 is given by the equation (17) in [15] At near-hovering condition, 𝒄 𝒑 and 𝒄𝜼 are derived by 𝑑 𝜓ˆ 𝑤 |, 𝑐 𝑥 = 2𝜌 𝑎 𝑅 2𝑤 𝑐Ψ ¯ 𝑤0 𝜔 𝑛 𝑟ˆ11 𝐶𝐷 cos2 (𝜓 𝑤 )| 𝑑 𝑡ˆ 𝑑 𝜓ˆ 𝑤 𝑐 𝑦 = 2𝜌 𝑎 𝑅 2𝑤 𝑐Ψ ¯ 𝑤0 𝜔 𝑛 𝑟ˆ11 𝐶𝐷 sin2 (𝜓 𝑤 )| |, 𝑑 𝑡ˆ 𝑑 𝜓ˆ 𝑤 𝑑𝐶 (𝛼) | 𝛼0 cos(𝛼0 )| |, ¯ 𝑤0 𝜔 𝑛 𝑟ˆ11 𝑁 𝑐 𝑧 = 𝜌 𝑎 𝑅 𝑤 𝑐Ψ 𝑑𝛼 𝑑 𝑡ˆ (4) ˆ𝑤 𝑑 𝜓 𝑑𝐶 (𝛼) 𝑁 | 𝛼0 cos(𝛼0 ) cos2 (𝜓 𝑤 )| 𝑐 𝜙 = 𝜌 𝑎 𝑅 𝑤 𝑐Ψ ¯ 𝑤0 𝜔 𝑛 𝑟ˆ3 |, 𝑑𝛼 𝑑 𝑡ˆ 𝑑𝐶 (𝛼) 𝑑 𝜓ˆ 𝑤 𝑐 𝜃 = 𝜌 𝑎 𝑅 4𝑤 𝑐Ψ ¯ 𝑤0 𝜔 𝑛 𝑟ˆ33 𝑁 | 𝛼0 cos(𝛼0 ) sin2 (𝜓 𝑤 )| |, 𝑑𝛼 𝑑 𝑡ˆ 𝑑 𝜓ˆ 𝑤 |, ¯ 𝑤0 𝜔 𝑛 𝑟ˆ33 𝐶𝐷 | 𝑐 𝜓 = 2𝜌 𝑎 𝑅 4𝑤 𝑐Ψ 𝑑 𝑡ˆ where 𝜌 𝑎 is the air density; 𝑅 𝑤 is the wing length; 𝑐¯ is wing mean chord length; 𝑟 𝑛𝑛 means the n-order dimensionless moment of wing area; 𝑡ˆ = 𝜔 𝑛 𝑡 is the non-dimensional time; Ψ 𝑤0 is the nominal stroke amplitude; 𝛼 and 𝛼0 are the effective and geometric AoA, respectively; 𝐶𝐷 and 𝐶 𝑁 are the drag In order to determine the effect of wing damage on the test FWMAV, modeling, analysis, and flight test validation were conducted Quasi-steady model [24] was used to estimated the aerodynamic forces and torques For cross-validation, the corresponding experimental force/torque measurement and free flight experiments were performed The flight test setup is illustrated in Fig 3, which has a high-speed top-view camera to capture the instantaneous wing kinematics and a motion capture system-Vicon to provide the vehicle’s posture and position feedback The motor current is sensed by onboard sensing resistors for power consumption estimation These records can be utilized to systematically evaluate the particular flight capacity changes under different wing tear scenarios In this section, we first determine the damage threshold that could cause insufficient lift generation on the proposed platform The result will guide the fabrication of the test wings Then, modeling and experimental verification were performed to evaluate lift loss, control torque offset, and aerodynamic damping changes, respectively A Design of Artificial Wing Damage Based on the Quasi-steady model, as the bilateral wing area loss goes up to about 15.6%, the proposed vehicle can barely generate sufficient lift force for stable flight Nevertheless, in actual flight tests, the vehicle cannot perform stable liftoff when the clipped area exceeds 15% as shown in the attached video A time sequential result is shown in Fig On the other hand, 15% asymmetry also causes unmanageable flight due to the severe control torque offset It is notable that some flying animals such as hawkmoth can tolerate wing damage up to 20% [17], [20] Compared to the test vehicle, hawkmoth may benefit from its wing materials, flexibility, and multiple groups of flight muscles for more elaborate wing kinematics Based on the 15% threshold, three pairs of wings were fabricated for testing, covering 0%, 5%, 10% wing area loss These wings are shown in Fig 2(a) and their specific parameters are summarized in Table I Note, each wing was clipped vertically at wingtip from the leading-edge to the trailing-edge, similar to the methods adopted in biological studies on hawkmoth wings [17], [20] Clipping in this way is because the distal wingtip area is the most vulnerable area which suffers wear and tear in unavoidable collisions In addition, due to higher wingtip velocity, wingtip area generally produces significant larger aerodynamic lift force and control torques than the other wing area, which subsequently causes obvious flight capacity drop and stability issues as discussed in the following subsections B Effect of Wing Damage on Lift Generation Based on the wings listed in Table I, we first check their respective lift generation capability without flight control Such 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters IEEE ROBOTICS AND AUTOMATION LETTERS PREPRINT VERSION ACCEPTED JANUARY, 2021 0.25 Intact wing (#1) 5% clipped (#2) 10% clipped (#3) 0.2 0.15 -1 -2 0.1 10 12 V (V ) 14 16 Fig Insufficient lift to takeoff with 15% loss of wing area 𝑅𝑤 70.0mm 66.2mm 62.6mm 𝑐¯ 21.2mm 21.3mm 21.5mm 0.1 0.2 V (V ) 0.2 TABLE I Parameters of Test Wings Wing area loss 0% bilateral 5% bilateral 10% -1 0.4 0.5 Test wings #1 #2 #3 -3 -2 0 𝑟ˆ2 0.5296 0.5295 0.5293 Aspect ratio 3.3 3.1 2.9 -0.2 -0.5 -2 -0.4 -1 V0 (V) -0.6 -0.2 -0.1 Fig Static force/torque measurement using wing #1, #2, #3, respectively an open-loop result can be used to determine the linearized input coefficients 𝐾𝑢1,2,3,4 for the controller design followed later An ATI Nano-17 force/torque transducer was used for measurement The result is shown in Fig As the wing damage intensifies, the maximum lift of the vehicle decreases severely Besides the falling actuation capability, it also brings a control problem: The linearized control input coefficient 𝐾𝑢1 mentioned in Section II varies, represented by 𝛼𝑧 𝐾𝑢1 , where 𝛼𝑧 ∈ [0, 1] This varying coefficient needs to be reconsidered in the controller design Compared to the open-loop test, the actual maximum lift of the vehicle in free flight could be further limited since additional control effort is required to ensure stability Such effective maximum lift can be roughly obtained from a lifting load test The vehicle was programmed to lift as much payload as it can while maintaining flight stability Inspired by the biological test [20], an asymptotic varying load, e.g., a string of small aluminum beads was used in this test Each bead weighs about 0.3g During the test, the vehicle performed vertical takeoff and gradually lifted the aluminum beads midair until it lost stability, which is shown in the attached video The instantaneous wing kinematics and power consumption were recorded The averaged results of five flight trials are summarized in Table II, including the free flight and load lift cases The vehicle with a pair of intact wings, i.e., #1, demonstrates the baseline performance From Table II, the actual maximum payload capacity drops severely with respect to the increment of wing damage, which matches the lift loss result obtained by static force measurement Compared to the intact wing’s performance, just 10% of wing tip area loss will cause more than three times effective payload capacity reduction of the proposed FWMAV, which indicates that such damage affects the lift generation significantly In order to compensate for such lift drop, the stroke amplitude and total energy consumption of the damaged wings increase accordingly Note, in controlled flight, the proposed asymptotic load does not generate significant instantaneous impact on the vehicle In addition, at near-hovering condition, the payload brings a downward shift of the center of gravity, which enhances the passive stability of the system as introduced in [15] section IV.C As demonstrated in the attached video, during the load lifting test, the vehicle demonstrates stable flight straight upwards with minor attitude and position drift TABLE II Cost of Symmetric Wing Damage Wing type Wing area loss Hover voltage Power consumption Stroke amplitude (left / right) Control Control Control Control Payload input 𝑢1 input 𝑢2 input 𝑢3 input 𝑢4 Capacity #1 #2 0% bilateral 5% Hovering without payload 10.90V 11.63V 5.05W 6.15W 142.2◦ 142.2◦ ◦ /141.0 /142.2◦ Load lifting 13.957V 12.564V 0.157V 0.227V 0.397V 0.358V 0.08 0.06 6.3g 3.9g #3 bilateral 10% 12.80V 6.21W 152.9◦ /154.5◦ 12.139V 0.331V 0.587V 0.09 2.1g C Effect of Wing Damage on Control Torque As shown in Fig 5, the control torque generation of the vehicle is limited by the wing damage In general, as the wing area loss becomes severe, the control torques in all three axes decreased to a certain degree Similar to the lift generation, the respective variation of their input coefficients 𝐾𝑢2,3,4 should be reconsidered in the controller design as well In terms of such performance drop, it is expected that the asymmetry of the left and right wings could lead to control challenges inevitably A proper control method is preferred to counter such wing asymmetry induced flight stability issue 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters TU et al.: FLYING WITH DAMAGED WINGS: THE EFFECT ON FLIGHT CAPACITY AND BIO-INSPIRED COPING STRATEGIES OF A FLAPPING WING ROBOT Besides the torque generation, as shown in Fig 5, the effective control effort is also affected by the trim condition, i.e., 𝜏𝑥0 , 𝜏𝑦0 , 𝜏𝑧0 For instance, compared to the other wing pairs, the #2 wings’ obvious yaw trim variation would significantly impact its overall control performances since the limited negative yaw torque shrinks the overall flight envelope Such control performance limitation is demonstrated in Section V.A In fact, for the proposed FWMAV, yaw torque generation is always weak due to the split-cycle control method (corresponding to downstroke and upstroke asymmetries in left and right wings) Even in the case of intact wing test, yaw torque is the most limited one among those of the three rotational axes Such a limitation is further exacerbated by the loss of wing area and the wing fabrication induced trim condition, resulting in the unmanageable yaw control drifting eventually D Effect of Wing Damage on Vehicle Dynamics For FWMAVs, wing damage induces wings’ morphological changes and the consequent kinematics changes Based on the vehicle dynamics presented in Section II.B, such changes could greatly affect aerodynamic damping during the flight An interesting trade-off of the flapping wing system is that when the wing length reduced, the stroke velocity amplitude Ψ 𝑤0 𝜔 𝑛 increases correspondingly in order to maintain stable flight On the proposed vehicle, only Ψ 𝑤0 increases since 𝜔 𝑛 is invariant As the wing damage becomes severe, the overall trend of 𝒄 𝒑 and 𝒄𝜼 keeps decreasing For example, the estimated 𝒇 𝑑 and 𝝉𝒅 in open-loop condition are illustrated in Fig 6, where the intact wings produce the strongest additional damping effect, as expected The initial condition of this estimation is an ideal hover flight with initial 𝝎 = [0.01, 0.01, 0.01] rad/s2 The control input and trim condition are from Table II Since there is no flight control in this case, 𝒇 𝑑 and 𝝉𝒅 diverge quickly as the attitude becomes unstable Based on Fig 6, such intact wings response can guide the controller design to compensate for this unique additional damping wrench effect 0.05 0.1 0.15 0.2 0.02 0.01 0 -5 -0.01 -10 -0.02 0.05 0.1 0.15 0.2 0.15 0.2 10 -4 Intact wing 5% clipped 10% clipped -15 0.05 0.1 Time (s) 0.15 0.2 (5) where 𝓂 = 𝑚/𝛼𝑧 is the equivalent vehicle mass, 𝑢 = 𝑉, Δ𝑧 is the lumped system uncertainty For altitude control, control error is defined by 𝑒𝑧 = 𝑧 − 𝑧𝑑 , 𝑒 𝑧 = 𝑒 𝑧 + 𝑘 𝑧1 𝑒 𝑧 = 𝑧 − 𝑧 𝑒𝑞 (6) where 𝑒 𝑧 is the altitude tracking error, 𝑧 𝑑 is the z-axis control reference, 𝑒 𝑧 is an auxiliary speed tracking error, 𝑘 𝑧1 is a positive control gain, and 𝑧 𝑒𝑞 is the equivalent tracking target 𝑒 𝑧 → when 𝑒 𝑧 converges to An integral sliding surface is given by ∫ 𝑠 𝑧 = 𝑒 𝑧 + 𝑘 𝑧2 𝑒 𝑧 𝑑𝜏, (7) where 𝑘 𝑧2 is a positive control gain Based on 𝑠 𝑧 , the altitude error dynamics is given by 𝓂𝑠 𝑧 = 𝐾𝑢1 · 𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝜃 · 𝑢 − 𝓂𝑔 + Δ𝑧 − 𝓂𝑧 𝑒𝑞 + 𝓂𝑘 𝑧2 𝑒 𝑧 (8) 𝓂 ˆ = 𝛾𝑧 𝜑𝑧 𝑠𝑧 , -1 𝓂𝑧 = 𝐾𝑢1 · 𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝜃 · 𝑢 − 𝓂𝑔 + Δ𝑧 , 0.01 IV Flight Control Based on Section III, the main control challenge in this study is from the wing damage induced control effort change and the potential asymmetrical force and torque brought by it Such actuation performance uncertainty induced stability issue can be addressed by targeted control strategy as presented below As mentioned in Section III, damaged wing causes control input coefficient varying To avoid the change of controller structure and the repeated gain tuning, the varying actuation performance can be lumped into vehicle dynamics change For example, the lift reduction can be equivalent to the increase of the modeled mass of the vehicle Consequently, the altitude dynamics of the vehicle with damaged wings is 0.02 0.005 system zeros and poles location at hovering condition, which determines the maximum control bandwidth of the vehicle [15] In this study, #3 wing provides overall smaller (≈86%) 𝒄 𝒑 than #1 wing According to that, the increased system sensitivity challenges the transient performance of the flight control with #3 wing equipped In order to counter the lift loss caused by wing damage, parameter adaptation is essential in control law design A feasible adaptation law is given by 10 -3 0.015 0.05 0.1 Time (s) Fig Estimated additional damping wrench induced by flapping wings Although 𝒄 𝒑 and 𝒄𝜼 demonstrated limited impact on total lift and control torques according to Fig 6, they dominant the (9) where 𝓂 ˆ is the estimated model parameter for control, 𝛾 𝑧 is the adaptation rate, 𝜑 𝑧 is a regressor 𝓂 ˆ ∈ [𝑚 𝑚𝑖𝑛 , 𝑚 𝑚𝑎𝑥 ], where the 𝑚 𝑚𝑖𝑛 is designed to slightly less than the vehicle’s original weight, and 𝑚 𝑚𝑎𝑥 is obtained by the result of the lifting load test mentioned in Section III.B The estimation error is defined by 𝓂 ˜ = 𝓂 − 𝓂 ˆ Propose an extended Lyapunov function as : 1 𝑉𝑧 (𝑒 𝑧 , 𝓂) ˜ = 𝓂𝑠2𝑧 + 𝓂 ˜ (10) 2𝛾 𝑧 𝓂 Design 𝜑 𝑧 = −(𝑔 + 𝑧 𝑒𝑞 − 𝑘 𝑧2 𝑒 𝑧 ), 𝑢1 = − [𝑘 𝑧3 𝑠 𝑧 + 𝜑 𝑧 𝓂 ˆ + 𝜆 𝑧 𝑠𝑔𝑛(𝑠 𝑧 )], 𝐾𝑢1 𝑐𝑜𝑠𝜙𝑐𝑜𝑠𝜃 (11) 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters IEEE ROBOTICS AND AUTOMATION LETTERS PREPRINT VERSION ACCEPTED JANUARY, 2021 Fig Stable hovering with symmetric damaged wings The clipped wing area is outlined with red line segments around the wingtip (a), (b), and (c) top figures are the time sequence result which respects the flying test using the wings #1, #2, #3 The bottom ones are the corresponding flight trajectory The gray dashed lines are the control references where 𝑘 𝑧3 is a positive control gain Thus, 𝑉𝑧 = −𝑘 𝑧3 𝑠2𝑧 − (𝜆 𝑧 |𝑠 𝑧 | − Δ𝑧 𝑠 𝑧 ) In this case, the lumped system uncertainty Δ𝑧 mainly depends on the aerodynamic damping and external disturbances To let 𝑒 𝑧 converge to asymptotically, 𝜆 𝑧 ≥ Δ𝑧 should be guaranteed The knowledge of 𝒇 𝑑 and 𝝉𝑑 can aid the design of 𝜆 𝑧 For instance, in this work, the upper bound of 𝒇 𝑑 and 𝝉𝑑 can be estimated as demonstrated in Fig In indoor test, 𝜆 𝑧 can be tuned with such particular model-based result in the absence of external disturbances The attitude controller follows a similar control scheme Due to the underactuation characteristics of the test platform, the 𝜙 and 𝜃 are coupled to 𝑦 and 𝑥 axes, respectively Different from our previous maneuver controller presented in [25], the attitude reference 𝜙 𝑑 and 𝜃 𝑑 are given from a position PID control law directly Such a method can effectively attenuate the undesired oscillation induced by the the sensing error and avoid the multiple derivative of the state feedback In practice, this method works reasonably well on FWMAVs with damaged wings because they generally suffer from actuation limitation and high sensitivity issues in flight control Attitude control errors is defined by V Flight Test Results In order to validate and the proposed controller, flight tests were conducted to cover all of the combinations with the fabricated wings shown in Fig In particular, two categories of flight test were performed, i.e., flying with symmetrical wing damage and with asymmetrical wing damage During the test, the vehicle is commanded to perform a stable hover flight The control reference is at 𝒑 = [0, 0, 350𝑚𝑚] and 𝜼 = [0◦ , 0◦ , 0◦ ] A Symmetric Wing Damage Sample flight tests are illustrated in Fig By taking advantages of the proposed flight controller, even under the severe wing area loss, i.e., flying with #3 wing, the vehicle can still maintain overall stable flight Such results demonstrate that 𝒆𝜼 = 𝜼 − 𝜼 𝒅 , 𝛽1 −𝑞𝑟 𝑞𝑟 −1 0 𝛽2 −𝑝𝑟 −1 , 𝝋𝜼 = 𝑝𝑟 (13) −𝑝𝑞 𝑝𝑞 𝛽3 0 −1 [𝑢 , 𝑢 , 𝑢 ] 𝑇 = −𝑲𝒖2,3,4 −1 [𝒌 𝜼3 𝒔𝜼 + 𝝋𝜼 𝒥ˆ + 𝝀𝜼 𝒔𝒈𝒏(𝒔𝜼 )], 0.2 Intact wing (#1) 5% clipped (#2) 10% clipped (#3) 0.1 u4 𝒆𝜼 = 𝒆𝜼 + 𝒌 𝜼1 𝒆𝜼 = 𝜼 − 𝜼𝒆𝒒 (12) ∫ Given the 𝒔𝜼 = 𝒆𝜼 + 𝒌 𝜼2 𝒆𝜼 𝒅𝝉, where 𝒌 𝜼2 is a diagonal gain matrix The model parameter is 𝒥ˆ = [ 𝐽ˆ𝑥 𝑥 , 𝐽ˆ𝑦 𝑦 , 𝐽ˆ𝑧𝑧 , 𝜏ˆ𝑥0 , 𝜏ˆ𝑦0 , 𝜏ˆ𝑧0 ] At hovering condition, let 𝒥ˆ = 𝜸𝜼 𝝋𝜼 𝒔𝜼 and 𝜼𝒆𝒒 − 𝒌 𝜼2 𝒆𝜼 = [𝛽1 , 𝛽2 , 𝛽3 ] 𝑇 , the adaptation regressor and control input are where 𝑲𝒖2,3,4 is a diagonal input coefficient matrix, 𝒌 𝜼3 is a positive diagonal gain matrix, 𝝀𝜼 > 𝚫𝝎 wherein 𝚫𝝎 is dominated by flapping induced aerodynamic damping in the absence of external disturbances -0.1 Time (s) Fig Illustration of the yaw control input, corresponding to Fig 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters TU et al.: FLYING WITH DAMAGED WINGS: THE EFFECT ON FLIGHT CAPACITY AND BIO-INSPIRED COPING STRATEGIES OF A FLAPPING WING ROBOT Fig Stable hovering flight with asymmetrically damaged wings The clipped wing area is outlined with red lines segments around the wingtip (a) and (b) respect to the flying test result using wing combination of 1L+3R, 3L+1R From left to right, there are time sequence result, flight trajectory, and key parameter adaptation The gray lines are the control references the proposed controller can respond to the parametric change caused by wing damage effectively Note, in these cases, the estimated model rarely converges to its true changes since the reference does not match the Persistent Excitation (PE) condition In general, the results of symmetric wing damage can be fairly expected As presented in Section III, the incompleteness of wings is directly related to the vehicle’s actuation capability, which determines the overall control performance accordingly For example, in Fig 7(b) and (c), due to the wing damage, the altitude control shows obvious steady state error though the proposed control law has already compensated lift loss to some extent To demonstrate the effectiveness of the proposed controller, several comparative tests were conducted on the same setup with a cascade PID control The results are shown in the attached video With intact wings, two test controllers show equal stable flight performance However, with the incremental of the wing damage, the performance of the PID controller has been severely affected When the bilateral wing damage reaches 10%, PID control cannot even guarantee stable liftoff Compared to the other degree of freedoms, yaw-axis control is special for such direct-drive FWMAV under wing damage Yaw control performance majorly depends on the perfection of wing up/down stroke rather than the wing area loss For instance, in Fig 7(b), we intend to show a yaw drifting result as a representative case In fact, based on Fig 5, the overall yaw control effort generated by #3 wing is less than that of #2 wing However, due to the obvious yaw torque offset of the #2 wings as investigated in Section III.C, its effective yaw control effort is limited Consequently, as shown in Fig 8, the control effort of #2 wing drawn from split cycle is nearly saturated in this case By comparison, there is no obvious saturation issue on the other two cases, thus, they demonstrate better yaw control performance As a result, as the hover regime shown in Fig 7, the root mean square errors of yaw tracking of the flight trial (b) is 95.057◦ , significantly larger than that of flight trial (a) and (c), which are 4.804◦ and 9.497◦ , respectively B Asymmetric Wing Damage Unlike symmetric wing damage, asymmetric wing damage poses significant stabilization challenges Relying on the proposed controller with parameter adaptation, the test platform is able to maintain stable flight even with a severe lift imbalance (>22%) between the two wings, i.e., flying with 10% wing asymmetry During the asymmetric wing damage test, different pairing methods of the test wings were performed In this section, we mainly focus on the most representative cases, namely, as the wing asymmetry reaches 10% The averaged results of flight trails are summarized in Table III Here, #1 Left-side wing paired with #3 Right-side wing is abbreviated as "1L+3R", similarly hereinafter The results of two typical flight scenarios are illustrated in Fig Referring to Table III, the vehicle generates asymmetric wing kinematics to maintain stability with the proposed control law Such a method is fairly intuitive and consistent with that observed in biological experiments [17] However, the accompanying large differential stroke amplitude will shrink the flight envelope, especially on the roll-axis As shown in Table III, when the wing asymmetry reaches 10%, the roll control input surges up significantly compared to that of the symmetry wings Such a phenomenon brings the inspiration back to the controller design, namely, higher saturation of roll 2377-3766 (c) 2021 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information Authorized licensed use limited to: RMIT University Library Downloaded on March 10,2021 at 01:29:24 UTC from IEEE Xplore Restrictions apply This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters IEEE ROBOTICS AND AUTOMATION LETTERS PREPRINT VERSION ACCEPTED JANUARY, 2021 TABLE III Cost of Asymmetric Wing Damage Wing type 1L+3R Wing area loss 0% + 10% Hovering without payload Hover voltage 11.99V Power consumption 6.131W Stroke amplitude 128.3◦ (left / right) /155.1◦ Load lifting Control input 𝑢1 12.391V Control input 𝑢2 1.730V Control input 𝑢3 0.741V Control input 𝑢4 0.120 Payload capacity 3.5g 3L+1R 10% + 0% 11.59V 6.055W 149.3◦ /117.6◦ 12.342V -1.746V 0.505V 0.112 3.5g and pitch control input is able to withstand the weakened flight capacity caused by wing damage Due to such imbalanced actuation capability, stable flight becomes a challenging task As shown in Fig 9, the proposed controller enables the sustained stable flight of the vehicle even facing severe asymmetric wings Actually, referring to the test illustrated in Fig 9, the robot undergoes significant position drift during liftoff due to the imbalanced roll torque In addition, the wing asymmetric caused yaw torque offset also affects heading angle stabilization in hover Despite, the flight control can cope with such defective aspects properly and maintain the overall stability during the flight As shown in Fig 9, the proposed adaptation scheme can respond to these unexpected imperfections immediately, which plays an important role in the tracking error convergence VI Conclusion In this paper, we studied the consequences of wing damage to the flight capacity of an FWMAV Three sets of test wings were fabricated, including a pair of intact wings, and two pairs of damaged wings with different degrees of artificial damages Utilizing these wings and their different combinations, we systematically studied the cost of the vehicle facing both symmetrical and asymmetrical wing damages as well as their impact on flight capacity, covering three main aspects: lift loss, control torque offset, and aerodynamic damping change Such impacts result in several specific control challenges To cope with these challenges, an adaptive controller is proposed The experimental results show that, with the proposed flight control law, the test vehicle can maintain stability by modulating the different kinematics of the wings to respond to such undesired wing damages, a strategy similar to that observed in hovering hawkmoths The proposed study procedures and control methods can help guide the wing design and flight control of bio-inspired flying robots operating in real 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Xplore Restrictions apply ... Automation Letters TU et al.: FLYING WITH DAMAGED WINGS: THE EFFECT ON FLIGHT CAPACITY AND BIO- INSPIRED COPING STRATEGIES OF A FLAPPING WING ROBOT Fig Stable hovering flight with asymmetrically damaged. .. 10.1109/LRA.2021.3059626, IEEE Robotics and Automation Letters TU et al.: FLYING WITH DAMAGED WINGS: THE EFFECT ON FLIGHT CAPACITY AND BIO- INSPIRED COPING STRATEGIES OF A FLAPPING WING ROBOT ˆ... Automation Letters TU et al.: FLYING WITH DAMAGED WINGS: THE EFFECT ON FLIGHT CAPACITY AND BIO- INSPIRED COPING STRATEGIES OF A FLAPPING WING ROBOT Besides the torque generation, as shown in Fig 5, the