A method for modeling failure of flapping wings and actuators of a biomimetic ornithopter

Abstract

The application discloses a modeling method for wing flapping and actuator failure of a bionic flapping-wing aircraft, and comprises the following steps: 1, dynamic analysis under wing damage; 2, force and torque expression under wing damage; 3, force and torque expression under actuator failure; 4, complete dynamic and kinematic model under wing and actuator failure. The application firstly analyzes the important influence of the flapping-wing failure of the bionic flapping-wing aircraft on the aerodynamic force in detail, and firstly systematically analyzes the complete dynamic and kinematic model of the flapping-wing aircraft when the flapping wing and the actuator fail simultaneously.

Description

Technical Field

[0001] This invention relates to the field of biomimetic robot modeling, and in particular to a modeling method for malfunctions in the flapping wings and actuators of a biomimetic flapping-wing aircraft. Background Technology

[0002] Bionic flapping-wing aircraft are currently a hot research topic both domestically and internationally. However, due to the unique flapping motion of their wings during flight, their aerodynamic characteristics differ significantly from fixed-wing or rotary-wing aircraft, resulting in significantly different flight control modes. Existing conventional aircraft flight control methods cannot be directly applied; a new flight control method suitable for small flapping-wing aircraft needs to be developed. However, the vast majority of bionic flapping-wing aircraft developed domestically and internationally are still in their initial stages, only able to achieve some basic flight maneuvers. Whether in terms of flight agility or performance, they are still far from those of real birds or insects. The development of flapping-wing aircraft involves multidisciplinary knowledge, with flight control being its core and key element.

[0003] Stable and reliable flight is paramount for biomimetic flapping-wing aircraft, especially when performing critical missions where flawless flight is essential. However, real-world flight environments are complex and unpredictable, prone to obstacles. Due to the small size and light weight requirements of small flapping-wing aircraft, the materials used for their flapping wings are relatively brittle and thin, making them more susceptible to damage upon impact. Furthermore, the specific size and weight requirements limit the use of high-performance components, while low-performance components are more prone to wear and tear over long-term operation, leading to a higher failure rate. Moreover, some flapping-wing structures have numerous degrees of freedom, reaching dozens or even hundreds, such as the more than 40 degrees of freedom in a bat's flapping wing, which inevitably increases the failure rate. For aircraft in flight, even a minor malfunction can trigger a crash, leading to a fatal disaster. Existing literature lacks a detailed failure model for the flapping wings and actuators suitable for control systems. Therefore, it is crucial to understand the failure mechanisms of flapping wings and actuators and establish detailed failure models to provide a model foundation for control system design. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a modeling method for the failure of flapping wings and actuators in a biomimetic flapping-wing aircraft. Since there is no detailed failure model of flapping wings and actuators available for use in control systems in existing literature, this invention must clarify the failure mechanism of flapping wings and actuators, establish a detailed failure model of flapping wings and actuators, and provide a model basis for control system design.

[0005] To achieve the aforementioned objectives of the invention, the technical solution adopted to solve its technical problems is as follows:

[0006] This invention discloses a modeling method for malfunctions in the flapping wing and actuator of a biomimetic flapping-wing aircraft, comprising the following steps:

[0007] Step 1: Dynamic analysis under wing damage conditions;

[0008] Step 2: Expression of forces and moments under wing damage conditions;

[0009] Step 3: Modeling the failure scenarios of the actuator;

[0010] Step 4: Complete dynamics and kinematics model under the condition of wing and actuator failure.

[0011] Furthermore, step 1 includes the following steps:

[0012] Step 1.1: To construct a failure model for the flapping wing and actuator, it is necessary to establish the flapping wing aerodynamics and conduct an in-depth analytical analysis of its equations. Considering the influence of leading-edge vortex and rotational circulation, an aerodynamic model can be established based on blade element theory:

[0013]

[0014]

[0015]

[0016]

[0017] Among them, L iT L iR D iT and D iR Let ρ represent the translational lift, rotational lift, translational drag, and rotational drag of wing i, respectively; ρ is the air density, α is the angle of attack, and C is the angle of attack. L (α) and C D (α) represents the lift and drag coefficients, respectively; κ i and τ i Let R and c(r) represent the flapping angle and feathering angle of wing i, respectively; the quantities related to the flapping wing area are R and c(r), representing the wing length and the chord length of the cross section, respectively, where i∈{r, l} represents the right wing and the left wing. Then the total force can be expressed as:

[0018]

[0019] in:

[0020]

[0021]

[0022]

[0023]

[0024] and Let these represent the transformation matrices from the wing coordinate system to the system coordinate system for the right and left wings, respectively. For the expression of torque, the translational and rotational center of pressure relative to the fuselage's center of mass position vectors are required.

[0025]

[0026]

[0027]

[0028]

[0029] in,

[0030]

[0031]

[0032] Therefore, torque can be expressed as:

[0033]

[0034] Step 1.2: Establish Failure Loss Rate

[0035] Flapping wing failures can be categorized into wing wear, cracking, and wing area loss. When flapping wing experiences area loss, the integral constant A in the force and moment relationships is related to the flapping wing length and the chord length of the cross section. T A R y CPtrans and y CProt Will be affected, let A. iT，damage A iR，，iamage y iCPtrans，damage and y iCProt，damage The wing malfunctioned and A were respectively T A R y CPtrans and y CProt The corresponding constant;

[0036] For ease of subsequent analysis, the respective loss rates can be defined as:

[0037]

[0038]

[0039]

[0040]

[0041] The above loss rate satisfies the following constraints:

[0042] 0≤μ iT ≤1 (21)

[0043] 0≤μ iR ≤1 (22)

[0044] μ iCPtran s≥0 (23)

[0045] μ iCProt ≥0 (24).

[0046] Furthermore, step 2 includes the following steps:

[0047] Step 2.1: Representation of forces and moments during flapping wing area loss:

[0048]

[0049]

[0050] Furthermore, step 3 includes the following steps:

[0051] Step 3.1: Fault Modeling of the Actuator of the Ornithopter:

[0052] Failures in flapping wing actuators can be categorized into three types: partial failure, jamming, and complete failure. A unified failure model can be established for these three types of failures.

[0053]

[0054] Where v is the control input,

[0055] ρ=diag{ρ1, ρ2,…,ρ m},0≤ρ i ≤1, (28)

[0056] For effectiveness factors;

[0057] ε = [ε1, ε2, ..., ε4] T (29)

[0058] For the actuator to output noise, then ρ i and ε i Different values ​​can be used to define different fault types, including partial failure, complete failure, and jamming fault.

[0059] Furthermore, step 4 includes the following steps:

[0060] Step 4.1: Complete dynamics and kinematic model under the condition of wing and actuator failure:

[0061] The model of the biomimetic flapping-wing aircraft is highly nonlinear and strongly coupled, with significant uncertainties in its aerodynamic parameters, making it difficult to establish an accurate model. Therefore, these unmodeled terms can be treated as additional forces and moments. Based on the above failure analysis of the flapping wing and actuator, and considering the changes in mass, center of gravity, and moment of inertia caused by wing loss, the following complete 6-DOF failure model can be established:

[0062]

[0063] Among them, P n Let V be the position vector of the aircraft in the inertial frame. b Let Φ be the velocity vector in the system, and ω be the attitude and angular velocity vectors, respectively. Let m be the transformation matrix from the system to the navigation system. total and J total Let E(Φ) be the nominal mass and moment of inertia, and E(Φ) be the attitude update transformation matrix. and These represent the force and torque involved in the fault, respectively, where g is the acceleration due to weight. Δm w and ΔJ w These represent the changes in mass and moment of inertia caused by wing losses, Δm. w and ΔJ w These represent the changes in mass and moment of inertia caused by wing losses, respectively. and These represent the sum of unmodeled aerodynamic forces and torques, respectively.

[0064] By employing the above technical solutions, this invention has the following advantages and positive effects compared with the prior art:

[0065] 1. This invention provides the first detailed analysis of the mechanism by which flapping wing failures affect aerodynamics in a biomimetic flapping wing aircraft. It identifies the key constants by which wing failures affect aerodynamics and innovatively introduces scaling factors for each constant, thus laying the foundation for establishing a wing failure model.

[0066] 2. This invention is the first to systematically establish a complete dynamics and kinematics model of a flapping-wing aircraft when both the flapping wing and the actuator fail simultaneously, providing a model basis for subsequent control system design, fault analysis, and fault-tolerant control. Attached Figure Description

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0068] Figure 1 This is a flowchart illustrating a modeling method for malfunctions in the flapping wing and actuator of a biomimetic flapping-wing aircraft according to the present invention.

[0069] Figure 2 This is a schematic diagram of a flapping-wing aircraft according to the present invention;

[0070] Figure 3 This is a schematic diagram of a triangular flapping wing part missing according to the present invention. Detailed Implementation

[0071] The technical solutions in the embodiments of the present invention will be clearly and completely described and discussed below with reference to the accompanying drawings. Obviously, what is described here is only a part of the examples of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0072] like Figure 1-2 As shown, this invention discloses a modeling method for the failure of the flapping wing and actuator of a biomimetic flapping-wing aircraft. It is the first to analyze in detail the significant impact of flapping wing failure on the aerodynamics of a biomimetic flapping-wing aircraft, and the first to systematically analyze the complete dynamics and kinematics model of a flapping-wing aircraft when both the flapping wing and actuator fail simultaneously. The method includes the following steps:

[0073] Step 1: Dynamic Analysis under Wing Damage. When a wing is damaged, the loss of wing area significantly impacts its dynamic parameters. The lift and drag coefficients, as well as the translational and rotational pressure centers, all contain integral constants, which are closely related to the chord length and length of the wing. When the wing area is lost, both the chord length and length undergo significant changes, resulting in substantial dynamic changes. Therefore, it is necessary to thoroughly study the constants related to wing area, analyze their specific analytical expressions, and uncover the mechanism by which the loss of wing area affects dynamics. To facilitate the definition of force and moment expressions under wing damage conditions, this invention innovatively introduces the ratio of the aforementioned integral constants in the healthy condition to those in the case of wing loss, thus providing convenience for subsequent force and moment representations.

[0074] Step 2: Expression of force and moment under wing damage conditions; The expression of force and moment under wing failure conditions is relatively complex. In order to facilitate the expression, the ratio of the above integral constants is introduced, and the force and moment are decomposed, thus successfully expressing the expression of force and moment under failure conditions.

[0075] Step 3: Modeling the failure conditions of the actuator; the failures of the actuator are mainly divided into partial failure, complete failure and jamming. Therefore, a unified actuator failure model is established for the above failures.

[0076] Step 4: Complete Dynamics and Kinematic Model under Wing and Actuator Failure Conditions. This step integrates the failure models of wing damage and actuator failure into a complete failure model. This failure model includes kinematic and dynamic models, providing a foundation for subsequent control system design.

[0077] Furthermore, step 1 includes the following steps:

[0078] Step 1.1: To construct a failure model for the flapping wing and actuator, it is necessary to establish the flapping wing aerodynamics and conduct an in-depth analytical analysis of its equations. Considering the influence of leading-edge vortex and rotational circulation, an aerodynamic model can be established based on blade element theory:

[0079]

[0080]

[0081]

[0082]

[0083] Among them, L iT L iR D iT and D iR Let ρ represent the translational lift, rotational lift, translational drag, and rotational drag of wing i, respectively; ρ is the air density, α is the angle of attack, and C is the angle of attack. L (α) and C D (α) represents the lift and drag coefficients, respectively; κ i and τ i Let R and c(r) represent the flapping angle and feathering angle of wing i, respectively; the quantities related to the flapping wing area are R and c(r), representing the wing length and the chord length of the cross section, respectively, where i∈{r, l} represents the right wing and the left wing. Then the total force can be expressed as:

[0084]

[0085] in:

[0086]

[0087]

[0088]

[0089]

[0090] and Let these represent the transformation matrices from the wing coordinate system to the system coordinate system for the right and left wings, respectively. For the expression of torque, the translational and rotational center of pressure relative to the fuselage's center of mass position vectors are required.

[0091]

[0092]

[0093]

[0094]

[0095] in,

[0096]

[0097]

[0098] Therefore, torque can be expressed as:

[0099]

[0100] Step 1.2: Establish Failure Loss Rate

[0101] For flapping wing failures, they can be categorized into wing wear, cracking, and wing area loss. In-depth analysis reveals that wing wear and localized cracking, due to the unchanged aerodynamic area, have little impact on forces and moments, and therefore generally have little effect on flight performance. This aligns with conclusions from real-world flapping wing biological flight experiments. Therefore, for these two situations, their impact on forces and moments does not require precise modeling and can be treated as additional perturbations. However, for flapping wing area loss, the impact on forces and moments is significant, thus greatly affecting flapping wing flight performance. This must be fully considered during modeling. For symmetrical wing loss, the main impact is on aerodynamics, with generally small moment deviations. However, for asymmetrical cases, not only are aerodynamics affected, but significant moment deviations are also generated, particularly large roll moment deviations. Therefore, special care is needed. When flapping wing area loss occurs, the integral constant A related to the flapping wing length and cross-sectional chord length in the forces and moments... T A R y CPtrans and y CProt Will be affected, let A. iT，damage A iR,damage y iCPtrans，damage and y iCProt，damage The wing malfunctioned and A were respectively T A R y CPtrans and y CProt The corresponding constant;

[0102] For ease of subsequent analysis, the respective loss rates can be defined as:

[0103]

[0104]

[0105]

[0106]

[0107] The above loss rate satisfies the following constraints:

[0108] 0≤μ iT ≤1 (21)

[0109] 0≤μ iR ≤1 (22)

[0110] μ iCPtrans ≥0 (23)

[0111] μ iCProt ≥0 (24).

[0112] Furthermore, step 2 includes the following steps:

[0113] Step 2.1: Representation of forces and moments during flapping wing area loss:

[0114]

[0115]

[0116] Besides impact and torque, flapping wing loss also alters key parameters such as mass, center of gravity, and moment of inertia, introducing new model uncertainties. The modeling of this impact will be discussed later.

[0117] Furthermore, step 3 includes the following steps:

[0118] Step 3.1: Fault Modeling of the Actuator of the Ornithopter:

[0119] For flapping wing actuator failures, such as those involving motors, gears, and transmission devices, three types can be categorized: partial failure, jamming, and complete failure. A unified failure model can be established for these three types of failures.

[0120]

[0121] Where v is the control input,

[0122] ρ=diag{ρ1, ρ2,…,ρ m},0≤ρ i ≤1, (28)

[0123] For effectiveness factors;

[0124] ε = [ε1, ε2, ..., ε4] T (29)

[0125] For the actuator to output noise, then ρ i and ε i Different values ​​can be used to define different fault types, including partial failure, complete failure, and jamming fault.

[0126] Furthermore, step 4 includes the following steps:

[0127] Step 4.1: Complete dynamics and kinematic model under the condition of wing and actuator failure:

[0128] The model of the biomimetic flapping-wing aircraft is highly nonlinear and strongly coupled, with significant uncertainties in its aerodynamic parameters, making it difficult to establish an accurate model. Therefore, these unmodeled terms can be treated as additional forces and moments. Based on the above failure analysis of the flapping wing and actuator, and considering the changes in mass, center of gravity, and moment of inertia caused by wing loss, the following complete 6-DOF failure model can be established:

[0129]

[0130] Among them, P n Let V be the position vector of the aircraft in the inertial frame. b Let Φ be the velocity vector in the system, and ω be the attitude and angular velocity vectors, respectively. Let m be the transformation matrix from the system to the navigation system. total and J total Let E(Φ) be the nominal mass and moment of inertia, and E(Φ) be the attitude update transformation matrix. and These represent the force and torque involved in the fault, respectively, where g is the acceleration due to weight. Δm w and ΔJ w These represent the changes in mass and moment of inertia caused by wing losses, Δm. w and ΔJ w These represent the changes in mass and moment of inertia caused by wing losses, respectively. and These represent the sum of unmodeled aerodynamic forces and torques, respectively.

[0131] Furthermore, if the shape and size of the wing are determined, the loss rate can be calculated. A specific example of calculating the loss ratio corresponding to wing loss is as follows: assuming partial wing loss occurs... Figure 3 ,in,

[0132]

[0133] k1 = c0 / b, k2 = c0 / (Rb), let b = λ0R and Where 0 < λ0 < 1 and λ0 ≤ l ≤ 1, and let R = 15 mm, b = 3 mm and c0 = 4 mm; then the formula for calculating the loss ratio can be expressed as:

[0134]

[0135]

[0136]

[0137]

[0138] Therefore, the loss rates are shown in Table 1:

[0139] Table 1 Loss Rate and l

[0140]

[0141] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A modeling method for malfunctions in the flapping wing and actuator of a biomimetic flapping-wing aircraft, characterized in that, Includes the following steps: Step 1: Dynamic analysis under flapping wing damage conditions; Step 2: Expression of forces and moments under flapping wing damage; Step 3: Modeling the failure scenarios of the actuator; Step 3 includes the following steps: Step 3.1: Fault Modeling of the Actuator of the Ornithopter: For flapping wing actuator failures, there are three types: partial failure, jamming, and complete failure. A unified failure model is established for these three types of failures: (27) in, To control the input, ， (28) For effectiveness factors; (29) For the actuator to output noise, then and Different values ​​are used to define different fault types, including partial failure, complete failure, and jamming fault; Step 4: Complete dynamics and kinematic model under the condition of flapping wing and actuator failure; Step 4 includes the following steps: Step 4.1: Complete dynamics and kinematic model under the condition of flapping wing and actuator failure: The model of the biomimetic flapping-wing aircraft is highly nonlinear and strongly coupled, with significant uncertainties in its aerodynamic parameters, making it difficult to establish an accurate model. Therefore, these unmodeled terms are treated as additional forces and moments, while also considering the changes in mass, center of gravity, and moment of inertia caused by flapping-wing losses. Finally, the following complete 6-DOF fault model is established: (30) in, Let be the position vector of the aircraft in the inertial frame. Let be the velocity vector in the system. and For attitude and angular velocity vectors, The transformation matrix from the system to the navigation system. and For nominal mass and moment of inertia, To update the transformation matrix for attitude, and These are the forces and torques containing the fault, respectively. For weight acceleration, , and These represent the changes in mass and moment of inertia caused by flapping wing loss, respectively. and These represent the sum of unmodeled aerodynamic forces and torques, respectively.

2. The modeling method for the failure of the flapping wing and actuator of a biomimetic flapping-wing aircraft according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: To construct a failure model for the flapping wing and actuator, it is necessary to establish the flapping wing aerodynamics and conduct an in-depth analytical analysis of its equations, considering the influence of leading-edge vortex and rotational circulation, and establish an aerodynamic model based on blade element theory: (1) (2) (3) (4) in, , , and They represent The translational lift, rotational lift, translational drag, and rotational drag of a flapping wing; air density, For the angle of attack, and These are the lift and drag coefficients, respectively. and They are respectively The flapping angle and feathering angle of the flapping wing; quantities related to the flapping wing area are: , , representing the flapping wing length and the cross-sectional chord length, respectively. Representing the right and left flapping wings, the total force is expressed as: (5) in: (6) (7) (8) (9) and Let these represent the transformation matrices from the flapping wing coordinate system to the system as shown for the right and left flapping wings, respectively. For the expression of torque, the translational and rotational center of pressure relative to the fuselage's center of mass position vectors are required. (10) (11) (12) (13) in, (14) (15) Therefore, the torque is expressed as: (16) Step 1.2: Establish Failure Loss Rate Flapping wing failures are categorized into wing wear, cracking, and wing area loss. When wing area loss occurs, the integral constants of the forces and moments related to the wing length and cross-sectional chord length are... , , and Will be affected, set , , and These are the flapping wing malfunctions and , , and The corresponding constant; For ease of subsequent analysis, the respective loss rates are defined as: (17) (18) (19) (20) The above loss rate satisfies the following constraints: (21) (22) (23) (24)。 3. The modeling method for the failure of flapping wing and actuator of a biomimetic flapping-wing aircraft according to claim 1, characterized in that, Step 2 includes the following steps: Step 2.1: Representation of forces and moments during flapping wing area loss: (25) (26)。

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