CN114115323B - Modeling and control method of three-steering engine driven bird-like ornithopter - Google Patents
Modeling and control method of three-steering engine driven bird-like ornithopter Download PDFInfo
- Publication number
- CN114115323B CN114115323B CN202111543956.2A CN202111543956A CN114115323B CN 114115323 B CN114115323 B CN 114115323B CN 202111543956 A CN202111543956 A CN 202111543956A CN 114115323 B CN114115323 B CN 114115323B
- Authority
- CN
- China
- Prior art keywords
- wing
- flapping
- ornithopter
- coordinate system
- angle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 45
- 230000009194 climbing Effects 0.000 claims abstract description 6
- 230000009189 diving Effects 0.000 claims abstract description 5
- 239000011159 matrix material Substances 0.000 claims description 15
- 230000033001 locomotion Effects 0.000 claims description 12
- 230000001133 acceleration Effects 0.000 claims description 10
- 230000007704 transition Effects 0.000 claims description 9
- 239000013256 coordination polymer Substances 0.000 claims description 7
- 238000013459 approach Methods 0.000 claims description 6
- 230000005484 gravity Effects 0.000 claims description 6
- 238000009499 grossing Methods 0.000 claims description 6
- 230000009466 transformation Effects 0.000 claims description 5
- 229910052799 carbon Inorganic materials 0.000 claims description 4
- 238000006243 chemical reaction Methods 0.000 claims description 4
- 238000012546 transfer Methods 0.000 claims description 4
- 230000008569 process Effects 0.000 claims description 3
- 238000004804 winding Methods 0.000 claims description 3
- 239000011664 nicotinic acid Substances 0.000 abstract description 13
- 230000009471 action Effects 0.000 abstract description 9
- 230000008859 change Effects 0.000 abstract description 6
- RZVHIXYEVGDQDX-UHFFFAOYSA-N 9,10-anthraquinone Chemical compound C1=CC=C2C(=O)C3=CC=CC=C3C(=O)C2=C1 RZVHIXYEVGDQDX-UHFFFAOYSA-N 0.000 abstract description 5
- 238000013461 design Methods 0.000 abstract description 5
- 230000008878 coupling Effects 0.000 abstract description 2
- 238000010168 coupling process Methods 0.000 abstract description 2
- 238000005859 coupling reaction Methods 0.000 abstract description 2
- 230000005540 biological transmission Effects 0.000 description 2
- 238000004891 communication Methods 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 210000003462 vein Anatomy 0.000 description 2
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 1
- 241000238631 Hexapoda Species 0.000 description 1
- 239000004677 Nylon Substances 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 239000004744 fabric Substances 0.000 description 1
- 238000009434 installation Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 238000005459 micromachining Methods 0.000 description 1
- 229920001778 nylon Polymers 0.000 description 1
- 238000005096 rolling process Methods 0.000 description 1
- 238000007514 turning Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
- G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64C—AEROPLANES; HELICOPTERS
- B64C33/00—Ornithopters
- B64C33/02—Wings; Actuating mechanisms therefor
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
Landscapes
- Engineering & Computer Science (AREA)
- Aviation & Aerospace Engineering (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Toys (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention discloses a modeling and control method of a three-steering-engine-driven bird-like ornithopter, which is based on the three-steering-engine independently-controlled bionic ornithopter, establishes a kinetic model of the three-steering-engine-driven bird-like ornithopter, and designs a flight control scheme based on the model. The flapping wing aircraft can change the frequency of wing flapping to lift the lift and thrust of the aircraft, and change the posture of the pitching angle of the aircraft by changing the balance position of the wing flapping, so as to realize the flying actions of rapid diving, climbing and the like of the aircraft. Meanwhile, the flapping wing aircraft can realize steering action by changing the torsion angle of the tail wing. The flight control system generates a flight command of plane constant-speed flight according to the navigation information, and the position and gesture control system generates steering engine driving signals according to the flight command and the established pneumatic model. The control of the pitch angle, the yaw angle and the roll angle of the ornithopter is realized under the condition that the power of the ornithopter is in low coupling, so that the position control of the ornithopter is realized.
Description
Technical Field
The invention belongs to the technical field of control of flapping-wing aircrafts, relates to the design of a power model building and control system of a bionic flapping-wing aircrafts with three steering engines independently driving wings and tail wings, and in particular relates to a modeling and control method of a bird-like flapping-wing aircrafts with three steering engines driving.
Background
Flapping wing flight is a flight mode commonly adopted by natural flight organisms, and flapping wing flying robots (FMAVs) manufactured according to the design of birds and insect flight principles integrate micro-electromechanical system sensors, micro drives and micro machining technologies, and are attracting attention of more and more control researchers in the field of aviation. The flapping wing aircraft integrates the study contents of the supervision courses of aerodynamics, control engineering, mechanical design, electronic technology, new energy sources, new materials and the like, the development of the flapping wing aircraft is brought by the technical progress of multiple disciplines, and meanwhile, the development of various disciplines is promoted by the wide application and urgent requirements of the flapping wing aircraft, so that the flapping wing aircraft has wide potential application in military and civil fields due to strong agility, benign concealment and high flight efficiency.
Bionic ornithopters have evolved significantly over the last decade. Today's bionic ornithopters can be classified into micro ornithopters (FWMAVs) and large bird bionic ornithopters according to the wing size. Because of the rigid wings and the high-frequency flapping motion, the wings of the micro flapping-wing aircraft can realize high-frequency flapping, hover in the air can be realized, the self-attitude can be controlled on 6 degrees of freedom, and autonomous flight can be realized, but the micro bionic flapping-wing aircraft has poor external interference resistance. Compared with a miniature ornithopter, the large bionic ornithopter has strong power and higher load. But large bird flapping wing aircraft have large wings, low flapping frequency and can not be stationary in the air. The transmission structure of the current large-scale bird-imitating ornithopter mostly adopts the design of a motor, a pull rod and a gear, the mechanical structure is complex, the flexibility is low, the weight of the aerocraft is large, the dynamics model is simple, and the agility of the aerocraft is low. The bionic ornithopter driven by the steering engine can not completely and rapidly control the self posture of the aerocraft, improve the performance of the aerocraft and finish the flight task.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a modeling and control method of a three-steering engine driven bird-like flapping-wing aircraft, which establishes a pneumatic model of the flapping-wing aircraft, and realizes the control of the pitching angle, the yaw angle and the rolling angle of the flapping-wing aircraft under the condition that the power of the aircraft is in low coupling by actively adjusting the balance positions of two wing flapping and the torsion angle of a tail wing, so as to realize the position control of the flapping-wing aircraft.
The wings of the bird-like flapping-wing aircraft are flexible wings, are symmetrically distributed on two sides of a fuselage, are independently driven by two steering engines respectively, and provide power for up-and-down flapping of the wings. The tail wing is independently driven by a third steering engine, and the flight direction is changed through the rotary tail wing.
A modeling method of a three-steering engine driven bird-like ornithopter specifically comprises the following steps:
step one: calculating the speed coordinate system (x) of the ornithopter v ,y v ,z v ) Air lift experienced by the lower fuselageAnd resistance->
Wherein V is ∞ Representing speed in forward flight and aerodynamic liftIs perpendicular to the velocity V ∞ And point to y v Positive axis direction, air resistance->Direction and velocity V of (2) ∞ Is opposite in direction, ρ represents air density, S Wing Representing the airfoil area of the wing. C (C) L And C D The dimensionless coefficients of the air lift force and the air resistance are respectively, and the value is related to the flight attack angle alpha:
the sideslip angle beta of the ornithopter during flight is small and is not considered. Recording Euler angle vector of ornithopter asWherein γ represents the roll angle, ψ represents the yaw angle, +.>The pitch angle is expressed, so the flight attack angle α can be written as:
wherein θ v Representing the speed and inclination of the flapping wing aircraft as it is flown.
Step two: calculating the speed coordinate system (x) of the ornithopter v ,y v ,z v ) The lower part is subjected to aerodynamic force v F air ：
Conversion to body coordinate system (x b ,y b ,z b ) Under the action of aerodynamic force b F air The method comprises the following steps:
wherein R is v2b Is a velocity coordinate system (x v ,y v ,z v ) To the body coordinate system (x b ,y b ,z b ) A transition matrix of the transition. Since the slip angle β is negligible, β=0.
Step three: in the body coordinate system (x b ,y b ,z b ) The motion trail of the flapping wing aircraft is designed to simulate the simplified bird flight actions, and the flapping function theta (t) is in a sine form:
θ(t)＝Θ Flap sin(2πft)+B (6)
wherein Θ is Flap The flutter amplitude of the wing is expressed, f represents flutter frequency, and B represents the balance position plane of the wing and the plane x of the fuselage b o b z b An included angle between the two.
Microminiaturizing a wing airfoil from inside to outside along a wing span directionDividing the strips, and calculating the flapping force of each micro strip after dividing to obtain the average flapping thrust F of one wing in one flapping period FlapThrust And average flapping lift force F FlapLift ：
Wherein v is flap Representing flapping speed of wing, C T,f And C L,f The flapping lift coefficient and the flapping thrust coefficient are respectively represented, and dA represents the area of one micro band. Since the flutter function θ (t) is a sinusoidal function, equation (7) can be further simplified to:
F FlapThrust ＝k T f 2
F FlapLift ＝k L f 2 (8)
wherein k is T And k L Respectively representing the thrust coefficient and the lift coefficient. Average flapping thrust F FlapThrust And average flapping lift force F FlapLift Acting on the aerodynamic centre CP of the wing, the average flapping thrust F FlapThrust And x b The direction of the axis is kept consistent, and the average flapping lift force F FlapLift Is perpendicular to the fuselage and is directed to y b The axis is in the positive direction.
Flapping wing aircraft in body coordinate system (x b ,y b ,z b ) The lower flapping wing has the power of b F W For average flapping thrust F on two wings FlapThrust And average flapping lift force F FlapLift Is a combination of:
distance between pneumatic center CP and wing rootThe distance is zeta and the distance between the wing and the gravity center is zeta. Because the wings are symmetrically moved, the aerodynamic center of the two wings is combined with the coordinate b P W The method comprises the following steps:
b P W ＝[ξ ζcosB 0] T (10)
further obtaining aerodynamic moment generated by double wings of the ornithopter b M W The method comprises the following steps:
b M W ＝ b P W × b F W (11)
roll moment τ of a flapping wing aircraft, which is generated by torsion of the tail wing tail The expression of (2) is:
τ tail ＝k γ sin(θ tail )||V ∞ || 2 S tail (12)
wherein k is γ Is the roll moment coefficient, θ tail Is the torsion angle of the tail wing, S tail Representing the tail wing area.
Further obtain the body coordinate system (x b ,y b ,z b ) Moment vector under b M is:
step four: the ornithopter obtained according to the formula (5) and the formula (9) is arranged in a body coordinate system (x b ,y b ,z b ) Lower aerodynamic force b F is:
b F＝ b F air + b F W (14)
further obtain the course coordinate system (x r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r F：
Wherein R is b2r Is the body coordinate system (x b ,y b ,z b ) Direction route coordinate System (x r ,y r ,z r ) The transfer matrix of the transformation, r F x 、 r F y 、 r F z respectively, are the navigation path coordinate systems (x r ,y r ,z r ) Lower aerodynamic force r F is at x r Axis, y r Axis, z r The components in the three directions of the axis, r F x direction and velocity V of (2) ∞ The projection directions of the flapping wing air vehicle are the same in the horizontal plane, and the speed of the flapping wing air vehicle in the horizontal plane is controlled; r F y direction inertial coordinate system (x) i ,y i ,z i ) Middle y i The direction of the shaft is consistent, and the shaft is used for controlling the speed of the ornithopter in the vertical direction; r F z is perpendicular to the velocity V ∞ The projection on the horizontal plane is used for controlling the lateral acceleration of the horizontal speed of the ornithopter, so that the course of the ornithopter is changed.
Step five: since the sideslip angle β=0, the course coordinate system (x r ,y r ,z r ) Lower navigational bias angle psi v =ψ. Obtaining an inertial coordinate system (x) according to equation (15) i ,y i ,z i ) Aerodynamic force of lower flapping wing aircraft i F is:
wherein R is r2i Course coordinate system (x) r ,y r ,z r ) To an inertial coordinate system (x i ,y i ,z i ) A transition matrix of the transition.
Thus in the inertial coordinate system (x i ,y i ,z i ) The dynamic model of the ornithopter is as follows:
wherein, represent derivative.For the position vector of the mass centre of the ornithopter +.>For the velocity vector of the mass centre of the ornithopter +.>Representing a fuselage angular velocity vector, wherein ω x 、ω y 、ω z Respectively represent the airframe winding x b Shaft angular velocity and fuselage wind y b Shaft angular velocity and fuselage windup z b Shaft angular velocity. />The gravity vector, m, represents the mass of the ornithopter and g represents the gravitational acceleration. />Indicating external disturbance force->Representing the total disturbance moment of the ornithopter>Representing the moment of inertia of the ornithopter. />A transformation matrix from the euler angular velocity of the body to the rotation angular velocity of the body is represented.
A control method of a three steering engine driven bird-like ornithopter specifically comprises the following steps:
step one: the flutter amplitude of the wing is kept constant. The outer ring position controller will generate a corresponding outer ring desired force output signal based on the reference three-dimensional path information and the position information of the ornithopter itself and transmit it to the command generator.
For the outer ring position controller, first, the reference three-dimensional path information is defined as P d Position tracking error e p ＝P d P, slip-form surface of the position ring s P ：
Wherein c P ＝diag[c P1 c P2 c P3 ]，c Pi >0,i＝1,2,3，diag[]Representing a diagonal matrix. Slip form surface s P For the exponential approach law, in order to reduce buffeting, a hyperbolic tangent function is selected for the sliding mode switching function to carry out smoothing treatment:
wherein ε P >0，k tP >0，k P >0。
Further get position controller u F The method comprises the following steps:
step two: the command generator generates a desired velocity dip from the outer ring desired force output signal, and then substitutes the outer ring desired force output signal and the desired velocity dip into a course coordinate system (x r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r In the expression F, the corresponding expected gesture signal and expected flutter frequency are solved through Newton's method.
Step three: the inner ring gesture controller generates a desired moment signal according to the desired gesture signal obtained in the second step and the gesture signal of the inner ring gesture controller b M u And transmitted to a command generator, which generates a desired torque signal based on the desired torque signal b M u Resolving to obtain wing flutter frequency, wing flutter balance position information and tail torsionAnd (3) turning the angle, transmitting the angle to three steering engine controllers as control information, and controlling the steering engine to drive the wing and the tail wing.
For an inner loop attitude controller, define the desired attitude signal as q d The attitude tracking error is e q ＝q d Q, slip form surface s of attitude ring q The method comprises the following steps:
wherein c q ＝diag[c q1 c q2 c q3 ]，c qi >0, i=1, 2,3. Slip form surface s q For the exponential approach law, in order to reduce buffeting, a hyperbolic tangent function is selected for the sliding mode switching function to carry out smoothing treatment:
wherein ε>0，k tq >0，k q >0。
Further obtain the inner ring attitude controller u q The method comprises the following steps:
in the sinusoidal flapping movement process of the wing, the average flapping position of the wing is the wing balance position and is in parallel with the plane x of the fuselage b o b z b The included angle between the two is B. When the wing is in equilibrium position in the plane x of the fuselage b o b z b In the upper part, B>0, the aerodynamic center of the wing equilibrium position is located in the plane x of the fuselage b o b z b Above, in the flapping thrust F FlapThrust Is generated in the body coordinate system (x b ,y b ,z b ) Lower edge z b The pitch moment of the shaft in the clockwise direction reduces the pitch angle of the ornithopter and makes a diving motion. When the wing is in equilibrium position in the plane x of the fuselage b o b z b In the lower part, B<0, the aerodynamic center of the wing equilibrium position is located in the plane x of the fuselage b o b z b Below, at the flapping thrust F FlapThrust Is generated in the body coordinate system (x b ,y b ,z b ) Lower edge z b The pitching moment of the shaft in the anticlockwise direction increases the pitch angle of the ornithopter and makes climbing motion.
The invention has the following beneficial effects:
a bionic ornithopter based on independent control of three steering engines establishes a kinetic model of the bionic ornithopter, and a flight control scheme is designed based on the model. The flapping wing aircraft can change the frequency of wing flapping to lift the lift and thrust of the aircraft, and change the posture of the pitching angle of the aircraft by changing the balance position of the wing flapping, so as to realize the flying actions of rapid diving, climbing and the like of the aircraft. Meanwhile, the flapping wing aircraft can realize steering action by changing the torsion angle of the tail wing. The flight control system generates a flight command of plane constant-speed flight according to the navigation information, and the position and gesture control system generates steering engine driving signals according to the flight command and the established pneumatic model. Different from the traditional modeling scheme, the modeling scheme of the bionic ornithopter can be used for modeling according to the characteristics of steering engine driving, the two-team flight state can be changed through the change of the flapping balance position of the wing, meanwhile, the relation between the sliding mode control scheme of the position and the gesture and the pneumatic model can be matched, and the accurate horizontal constant-speed flight control and the vertical acceleration and deceleration control of the bionic ornithopter can be realized through the change of the gesture and the flapping power of the bionic ornithopter, so that the flight action is completed.
Drawings
FIG. 1 is a schematic illustration of the structure of the ornithopter;
FIG. 2 is a block diagram of a control system for an ornithopter;
FIG. 3 is a schematic illustration of the aerodynamic center position of the ornithopter;
FIG. 4 is a flow chart of a method of controlling a ornithopter;
FIGS. 5 (a) and (b) are schematic views of the flapping-wing aircraft in a nose down state;
fig. 6 (a) and (b) are schematic diagrams of the flapping wing air vehicle in climbing state.
Detailed Description
The invention is further explained below with reference to the drawings;
the bird-like ornithopter is shown in fig. 1, and comprises wings 1, a tail wing 5, a fuselage 6 and a control system 8. The length of the fuselage 6 is 0.3m. The wing 1 comprises a wing stick 2, a wing pulse 3 and a wing surface 4. The wing rods 2 and the wing veins 3 are light carbon rods, and the wing surfaces 4 are unfolded and fixed on the wing rods 2 and the wing veins 3. The airfoil 4 adopts PC35 nylon cloth, the length of a single airfoil is 0.475m, the chord length is 0.3m, and the airfoil area is 0.3125m 2 The aspect ratio of the two wings was 3.8. The tail wing 5 is of a triangle structure with the area of 0.075m 2 . The wing and the tail wing of the ornithopter are simple in structure, light in weight and strong in tearing resistance, meanwhile, certain flexibility can be maintained, enough power is provided for the ornithopter, and the ornithopter has certain wind interference resistance.
The control system 8 comprises a hardware system 7, a power supply 10 and a steering engine. Wherein the hardware system 8 and the power supply 10 are fixed on the machine body 6, and the installation position balances the front and rear weight of the machine body. The steering engine comprises an flapping wing steering engine 9 arranged at the head of the fuselage 6 and an empennage steering engine 11 arranged at the tail. The two wings are symmetrically arranged on two sides of the fuselage 6 and controlled by the flapping wing steering engine 9. The flapping wing steering engine 9 is a high-pressure metal steering engine KST320, the weight is 20g, and the working flapping angle reaches 190 degrees. In order to ensure power and reduce the overall quality of the ornithopter, the tail steering engine 11 adopts a blue sword AF D30T-3.3-MG micro steering engine, the weight is 7.2g, and the stroke angle is 120 degrees, so that the tail can twist within a range of +/-60 degrees, and the heading of the ornithopter is controlled.
As shown in fig. 2, the hardware system 7 integrates an attitude sensor module, a navigation module, a wireless communication module, a steering engine driving module and a battery. The hardware system 7 can output control information to the steering engine according to the state information of the ornithopter and the input mission planning information, and drive the wings and the tail wings to execute the flight mission. In the hardware system 7, the MCU is an STM32F407 microprocessor, the attitude sensor adopts an MPU6050 six-axis sensor comprising a three-axis acceleration sensor and a three-axis gyroscope sensor, the navigation module is an M8Q-5883GPS compass module and an BMP320 barometer sensor, and the steering engine driving module comprises three PWM output modules for driving the steering engine to run. The wireless communication module is a 2.4G data transmission module NRF24L01, and is used for transmitting signals to an aircraft and an upper computer or a remote controller on the ground.
Based on the characteristics of steering engine driving, modeling a flight power system of the ornithopter to obtain a dynamic model, and specifically comprises the following steps:
step one: during the flight of the ornithopter, the airframe is influenced by the air lift force and the resistance, and the speed coordinate system (x v ,y v ,z v ) Air lift experienced by the lower fuselageAnd resistance->
Wherein V is ∞ Representing speed in forward flight and aerodynamic liftIs perpendicular to the velocity V ∞ And point to y v Positive axis direction, air resistance->Direction and velocity V of (2) ∞ Is opposite in direction, ρ represents air density, S Wing Representing the airfoil area of the wing. C (C) L And C D The dimensionless coefficients of the air lift force and the air resistance are respectively, and the value is related to the flight attack angle alpha:
the sideslip angle beta of the ornithopter during flight is small and is not considered. Recording Euler angle vector of ornithopter asWherein γ represents the roll angle, ψ represents the yaw angle, +.>The pitch angle is expressed, so the flight attack angle α can be written as:
wherein θ v Representing the speed and inclination of the flapping wing aircraft as it is flown.
Step two: calculating the speed coordinate system (x) of the ornithopter v ,y v ,z v ) The lower part is subjected to aerodynamic force v F air ：
Conversion to body coordinate system (x b ,y b ,z b ) Under the action of aerodynamic force b F air The method comprises the following steps:
wherein R is v2b Is a velocity coordinate system (x v ,y v ,z v ) To the body coordinate system (x b ,y b ,z b ) A transition matrix of the transition. Since the slip angle β is negligible, β=0.
Step three: in the body coordinate system (x b ,y b ,z b ) The motion trail of the flapping wing aircraft is designed to simulate the simplified bird flying action,the flutter function θ (t) is sinusoidal:
θ(t)＝Θ Flap sin(2πft)+B (6)
wherein Θ is Flap The flutter amplitude of the wing is expressed, f represents flutter frequency, and B represents the balance position plane of the wing and the plane x of the fuselage b o b z b An included angle between the two.
Dividing the tiny strips of the wing surface of the wing from inside to outside along the wing span direction of the wing, and then calculating the flapping force of each tiny strip after dividing so as to obtain the average flapping thrust F of one wing in one flapping period FlapThrust And average flapping lift force F FlapLift ：
Wherein v is flap Representing flapping speed of wing, C T,f And C L,f The flapping lift coefficient and the flapping thrust coefficient are respectively represented, and dA represents the area of one micro band. Since the flutter function θ (t) is a sinusoidal function, equation (7) can be further simplified to:
F FlapThrust ＝k T f 2
F FlapLift ＝k L f 2 (8)
wherein k is T And k L Respectively representing the thrust coefficient and the lift coefficient. Average flapping thrust F FlapThrust And average flapping lift force F FlapLift Acting on the aerodynamic centre CP of the wing, the average flapping thrust F FlapThrust And x b The direction of the axis is kept consistent, and the average flapping lift force F FlapLift Is perpendicular to the fuselage and is directed to y b The axis is in the positive direction.
Flapping wing aircraft in body coordinate system (x b ,y b ,z b ) The lower flapping wing has the power of b F W For average flapping thrust F on two wings FlapThrust And average flapping lift force F FlapLift Is a combination of:
as shown in fig. 3, the span length of a single wing is a, the chord length is b, the distance between the aerodynamic center CP and the wing root of the wing is ζ, and the center of gravity o of the wing b Is a distance xi. Because the wings are symmetrically moved, the aerodynamic center of the two wings is combined with the coordinate b P W The method comprises the following steps:
b P W ＝[ξ ζcosB 0] T (10)
further obtaining aerodynamic moment generated by double wings of the ornithopter b M W The method comprises the following steps:
b M W ＝ b P W × b F W (11)
roll moment τ of a flapping wing aircraft, which is generated by torsion of the tail wing tail The expression of (2) is:
τ tail ＝k γ sin(θ tail )||V ∞ || 2 S tail (12)
wherein k is γ Is the roll moment coefficient, θ tail Is the torsion angle of the tail wing, S tail Representing the tail wing area.
Further obtain the body coordinate system (x b ,y b ,z b ) Moment vector under b M is:
step four: the ornithopter obtained according to the formula (5) and the formula (9) is arranged in a body coordinate system (x b ,y b ,z b ) Lower aerodynamic force b F is:
b F＝ b F air + b F W (14)
further obtain the course coordinate system (x r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r F：
Wherein R is b2r Is the body coordinate system (x b ,y b ,z b ) Direction route coordinate System (x r ,y r ,z r ) The transfer matrix of the transformation, r F x 、 r F y 、 r F z respectively, are the navigation path coordinate systems (x r ,y r ,z r ) Lower aerodynamic force r F is at x r Axis, y r Axis, z r The components in the three directions of the axis, r F x direction and velocity V of (2) ∞ The projection directions of the flapping wing air vehicle are the same in the horizontal plane, and the speed of the flapping wing air vehicle in the horizontal plane is controlled; r F y direction and inertial coordinate system (x i ,y i ,z i ) Middle y i The direction of the shaft is consistent, and the shaft is used for controlling the speed of the ornithopter in the vertical direction; r F z is perpendicular to the velocity V ∞ The projection on the horizontal plane is used for controlling the lateral acceleration of the horizontal speed of the ornithopter, so that the course of the ornithopter is changed.
Step five: since the sideslip angle β=0, the drift angle ψ in the course coordinate system v Obtain inertial coordinate system (x) according to equation (15) i ,y i ,z i ) Aerodynamic force of lower flapping wing aircraft i F is:
wherein R is r2i Is a course coordinate system (x r ,y r ,z r ) To an inertial coordinate system (x i ,y i ,z i ) A transition matrix of the transition.
Thus in the inertial coordinate system (x i ,y i ,z i ) The dynamic model of the ornithopter is as follows:
wherein, represent derivative.For the position vector of the mass centre of the ornithopter +.>For the velocity vector of the mass centre of the ornithopter +.>Represents the angular velocity vector of the body, wherein omega x ,ω y ,ω z Respectively represent the machine body winding x b Angular velocity of axis, body around y b Shaft angular velocity and body wrap z b Shaft angular velocity. />The gravity vector, m, represents the mass of the ornithopter and g represents the gravitational acceleration. />Indicating external disturbance force->Representing the total disturbance moment of the ornithopter>Representing the moment of inertia of the ornithopter. />A transformation matrix from the euler angular velocity of the body to the rotation angular velocity of the body is represented.
In the hardware system 7, the attitude and position controllers adopt a cascade structure. As shown in fig. 4, the control method of the bird-like ornithopter driven by the three steering engines specifically comprises the following steps:
step one: the flutter amplitude of the wing is kept constant. The outer ring position controller will generate a corresponding outer ring desired force output signal based on the reference three-dimensional path information and the status information of the ornithopter itself and transmit it to the command generator. The status information of the flapping wing aircraft is obtained by an attitude sensor, an altitude sensor and a GPS sensor, and comprises a position signal P, a speed signal V and an acceleration signal A acc Euler angle signal q, body angular velocity signal omega and angular acceleration signal O acc 。
For the outer ring position controller, first, the reference three-dimensional path information is defined as P d Position tracking error e p ＝P d P, slip-form surface of the position ring s P ：
Wherein c P ＝diag[c P1 c P2 c P3 ]，c Pi >0,i＝1,2,3，diag[]Representing a diagonal matrix. Slip form surface s P For the exponential approach law, in order to reduce buffeting, a hyperbolic tangent function is selected for the sliding mode switching function to carry out smoothing treatment:
wherein ε P >0，k tP >0，k P >0。
Further get position controller u F The method comprises the following steps:
step two: the command generator generates a desired velocity dip from the outer ring desired force output signal, and then substitutes the outer ring desired force output signal and the desired velocity dip into a course coordinate system (x r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r In the expression F, the corresponding expected gesture signal and expected flutter frequency are solved through Newton's method.
Step three: the inner ring gesture controller generates a desired moment signal according to the desired gesture signal obtained in the second step and the gesture signal of the inner ring gesture controller b M u And transmitted to a command generator, which generates a desired torque signal based on the desired torque signal b M u And resolving to finally obtain wing flapping frequency, wing flapping balance position information and tail torsion angle, and transmitting the information as control information to three steering engine controllers to control steering engines to drive wings and tails.
For an inner loop attitude controller, define the desired attitude signal as q d The attitude tracking error is e q ＝q d Q, slip form surface s of attitude ring q The method comprises the following steps:
wherein c q ＝diag[c q1 c q2 c q3 ]，c qi >0, i=1, 2,3. Slip form surface s q For the exponential approach law, in order to reduce buffeting, a hyperbolic tangent function is selected for the sliding mode switching function to carry out smoothing treatment:
wherein ε>0，k tq >0，k q >0。
Further obtain the inner ring attitude controller u q The method comprises the following steps:
in the sinusoidal flapping movement process of the wing, the average flapping position of the wing is the wing balance position and is in parallel with the plane x of the fuselage b o b z b The included angle between the two is B. As shown in fig. 5 (a), when the wing is in equilibrium position in the fuselage plane x b o b z b In the upper part, B>0, the aerodynamic center of the wing equilibrium position is located in the plane x of the fuselage b o b z b Above, as shown in FIG. 5 (b), the flapping thrust F FlapThrust Is generated in the body coordinate system (x b ,y b ,z b ) Lower edge z b The pitch moment of the shaft in the clockwise direction reduces the pitch angle of the ornithopter and makes a diving motion. As shown in fig. 6 (a), when the wing is in equilibrium position in the fuselage plane x b o b z b In the lower part, B<0, the aerodynamic center of the wing equilibrium position is located in the plane x of the fuselage b o b z b Below, as shown in FIG. 6 (b), in the flapping thrust F FlapThrust Is generated in the body coordinate system (x b ,y b ,z b ) Lower edge z b The pitching moment of the shaft in the anticlockwise direction increases the pitch angle of the ornithopter and makes climbing motion. Controlling flapping angle theta of wing Flap Constant 60 °, wing equilibrium position and fuselage plane x b o b z b The variation range of the included angle B between the two is [ -40 DEG, 40 DEG]Under the drive of the steering engine, the angle range of the flapping track of a single wing on one side of the body is limited to be 140 degrees, so that the aerodynamic stability is ensured.
Claims (7)
1. A modeling method of a three steering engine driven bird-like ornithopter, wherein wings of the bird-like ornithopter are symmetrically distributed on two sides of a fuselage and are independently driven by two steering engines respectively; the fin of setting at the fuselage afterbody is by the independent drive of third steering wheel, its characterized in that: the method specifically comprises the following steps:
step one: calculating the speed coordinate system (x) of the ornithopter v ,y v ,z v ) Air lift experienced by the lower fuselageAnd resistance to
Wherein V is ∞ Representing speed in forward flight and aerodynamic liftIs perpendicular to the velocity V ∞ And point to y v Positive axis direction, air resistance->Direction and velocity V of (2) ∞ Is opposite in direction, ρ represents air density, S Wing Representing the area of the wing; c (C) L And C D Dimensionless coefficients of air lift and air resistance, respectively:
recording Euler angle vector of ornithopter asWhere y represents the roll angle, ψ represents the yaw angle,representing pitch angle, the resulting flight angle of attack a, ignoring sideslip angle β, is:
wherein θ is v Representing the speed and inclination angle of the flapping wing aircraft during the flight;
step two: calculating the speed coordinate system (x) of the ornithopter v ,y v ,z v ) The lower part is subjected to aerodynamic force v F air ：
Flapping wing aircraft in body coordinate system (x b ,y b ,z b ) The lower part is subjected to aerodynamic force b F air The method comprises the following steps:
wherein β=0, r v2b Is a velocity coordinate system (x v ,y v ,z v ) To the body coordinate system (x b ,y b ,z b ) A transformed transition matrix;
step three: in the body coordinate system (x b ,y b ,z b ) The flapping function θ (t) of the flapping wing vehicle is defined as follows:
θ(t)＝Θ Flap sin(2pft)+B (6)
wherein Θ is Flap The flutter amplitude of the wing is expressed, f represents flutter frequency, and B represents the balance position plane of the wing and the plane x of the fuselage b o b z b An included angle between the two;
dividing the tiny strips of the wing surface of the wing from inside to outside along the wing span direction of the wing, then calculating the flapping force of each tiny strip after dividing, and calculating the average flapping thrust F of one wing in one flapping period FlapThrust And average flapping lift force F FlapLift ：
Wherein v is flap Representing flapping speed of wing, C T,f And C L,f Respectively representing a flapping lift coefficient and a flapping thrust coefficient, wherein dA represents the area of a micro strip; equation (7) is further simplified to:
F FlapThrust ＝k T f 2
F FlapLift ＝k L f 2 (8)
wherein k is T And k L Respectively representing a thrust coefficient and a lift coefficient; average flapping thrust F FlapThrust And average flapping lift force F FlapLift Acting on the aerodynamic centre CP of the wing, the average flapping thrust F FlapThrust And x b The direction of the shaft is kept consistent; average flapping lift force F FlapLift Is perpendicular to the fuselage and is directed to y b An axial positive direction;
flapping wing aircraft in body coordinate system (x b ,y b ,z b ) The lower flapping wing has the power of b F W For average flapping thrust F on two wings FlapThrust And average flapping lift force F FlapLift Is a combination of:
the distance between the pneumatic center CP and the wing root of the wing is zeta, the distance between the pneumatic center CP and the gravity center of the wing is zeta, and the pneumatic center is coordinated with the wing root of the wing b P W The method comprises the following steps:
b P W ＝[ξ ζcosB 0] T (10)
further get the flapping wing air vehicleAerodynamic moment generated by double wings b M W The method comprises the following steps:
b M W ＝ b P W × b F W (11)
roll moment tau of ornithopter tail The method comprises the following steps:
τ tail ＝k γ sin(θ tail )||V ∞ || 2 S tail (12)
wherein k is γ Is the roll moment coefficient, θ tail Is the torsion angle of the tail wing, S tail Representing tail wing area;
further obtain the body coordinate system (x b ,y b ,z b ) Moment vector under b M is:
step four: the ornithopter obtained according to the formula (5) and the formula (9) is arranged in a body coordinate system (x b ,y b ,z b ) Lower aerodynamic force b F is:
b F＝ b F air + b F W (14)
further obtain the course coordinate system (x r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r F：
Wherein R is b2r Is the body coordinate system (x b ,y b ,z b ) Direction route coordinate System (x r ,y r ,z r ) Transfer matrix of conversion, R r2b ＝(R b2r ) -1 ， r F x 、 r F y 、 r F z Respectively, are the navigation path coordinate systems (x r ,y r ,z r ) Lower aerodynamic force r F is at x r Axis, y r Axis, z r Components in three directions of the axis;
step five: course coordinate system (x) when sideslip angle β=0 r ,y r ,z r ) Lower navigational bias angle psi v =ψ; obtaining an inertial coordinate system (x) according to equation (15) i ,y i ,z i ) Aerodynamic force of lower flapping wing aircraft i F is:
wherein R is r2i Is the course coordinate system (x r ,y r ,z r ) To an inertial coordinate system (x i ,y i ,z i ) Transfer matrix of conversion, R r2i ＝(R i2r ) -1 ；ψ v Representing yaw angle;
thus in the inertial coordinate system (x i ,y i ,z i ) The dynamic model of the ornithopter is as follows:
wherein, represent derivative;for the position vector of the mass centre of the ornithopter +.>For the velocity vector of the mass centre of the ornithopter +.>Represents the angular velocity vector of the body, wherein omega x ,ω y ,ω z Respectively represent the airframe winding x b Axis, y b Axis and z b Angular speed of the shaft; />The gravity vector, m represents the mass of the ornithopter, g represents the gravitational acceleration; />Indicating external disturbance force->Representing the total disturbance moment of the ornithopter,representing the moment of inertia of the ornithopter; />A transformation matrix from the euler angular velocity of the body to the rotation angular velocity of the body is represented.
2. The modeling method of the three steering engine driven bird-like ornithopter according to claim 1, wherein the modeling method comprises the following steps: course coordinate system (x) r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r F model: r F x direction and velocity V of (2) ∞ The projection directions of the flapping wing air vehicle are the same in the horizontal plane, and the speed of the flapping wing air vehicle in the horizontal plane is controlled; r F y direction and inertial coordinate system (x i ,y i ,z i ) Middle y i The direction of the shaft is consistent, and the shaft is used for controlling the speed of the ornithopter in a vertical plane; r F z is perpendicular to the velocity V ∞ The projection on the horizontal plane is used for controlling the lateral acceleration of the horizontal speed of the ornithopter, so that the course of the ornithopter is changed.
3. A control method of a three steering engine driven bird-like ornithopter is characterized by comprising the following steps of: the control method is controlled based on the model established in claim 1 or 2; the method specifically comprises the following steps:
step one: keeping the flutter amplitude of the wing constant; the outer ring position controller generates a corresponding outer ring expected force output signal based on the reference three-dimensional path information and the position information of the ornithopter, and transmits the corresponding outer ring expected force output signal to the instruction generator;
step two: the command generator generates a desired velocity dip from the outer ring desired force output signal, and then substitutes the outer ring desired force output signal and the desired velocity dip into a course coordinate system (x r ,y r ,z r ) Aerodynamic force of lower flapping wing aircraft r In the expression F, corresponding expected gesture signals and expected flutter frequencies are solved through a Newton method;
step three: the inner ring gesture controller generates a desired moment signal according to the desired gesture signal obtained in the second step and the gesture signal of the inner ring gesture controller b M u And transmitted to a command generator, which generates a desired torque signal based on the desired torque signal b M u And resolving to finally obtain wing flapping frequency, wing flapping balance position information and tail torsion angle, and transmitting the information as control information to three steering engine controllers to control steering engines to drive wings and tails.
4. A method of modeling a three steering engine driven bird-like ornithopter as claimed in claim 3, wherein: for the outer ring position controller, first, the reference three-dimensional path information is defined as P d Position tracking error e p ＝P d P, slip-form surface of the position ring s P ：
Wherein c P ＝diag[c P1 c P2 c P3 ]，c Pi >0,i＝1,2,3，diag[]Representing a diagonal matrix; slip form surface s P For the exponential approach law, in order to reduce buffeting, a hyperbolic tangent function is selected for the sliding mode switching function to carry out smoothing treatment:
wherein ε P >0，k tP >0，k P >0；
Further get position controller u F The method comprises the following steps:
5. a method of modeling a three steering engine driven bird-like ornithopter as claimed in claim 3, wherein: for an inner loop attitude controller, define the desired attitude signal as q d The attitude tracking error is e q ＝q d Q, slip form surface s of attitude ring q The method comprises the following steps:
wherein c q ＝diag[c q1 c q2 c q3 ]，c qi >0, i=1, 2,3; slip form surface s q For the exponential approach law, in order to reduce buffeting, a hyperbolic tangent function is selected for the sliding mode switching function to carry out smoothing treatment:
wherein ε>0，k tq >0，k q >0；
Further obtain the inner ring attitude controller u q The method comprises the following steps:
6. a method of modeling a three steering engine driven bird-like ornithopter as claimed in claim 3, wherein: in the sinusoidal flapping movement process of the wing, the average flapping position of the wing is the wing balance position and is in parallel with the plane x of the fuselage b o b z b The included angle between the two is B; let B>0, controlling the balance position of the wing to be in the plane x of the body b o b z b Above, i.e. with the aerodynamic centre of the wing in equilibrium position, in the plane x of the fuselage b o b z b Above, in the flapping thrust F FlapThrust Is generated in the body coordinate system (x b ,y b ,z b ) Lower edge z b The pitch moment of the shaft in the clockwise direction reduces the pitch angle of the ornithopter and makes a diving motion.
7. A method of modeling a three steering engine driven bird-like ornithopter as claimed in claim 3, wherein: let B<0, controlling the balance position of the wing to be in the plane x of the body b o b z b The aerodynamic centre below, i.e. at the equilibrium position of the wing, lies in the plane x of the fuselage b o b z b Below, at the flapping thrust F FlapThrust Is generated in the body coordinate system (x b ,y b ,z b ) Lower edge z b The pitching moment of the shaft in the anticlockwise direction increases the pitch angle of the ornithopter and makes climbing motion.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111543956.2A CN114115323B (en) | 2021-12-16 | 2021-12-16 | Modeling and control method of three-steering engine driven bird-like ornithopter |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111543956.2A CN114115323B (en) | 2021-12-16 | 2021-12-16 | Modeling and control method of three-steering engine driven bird-like ornithopter |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114115323A CN114115323A (en) | 2022-03-01 |
| CN114115323B true CN114115323B (en) | 2024-03-26 |
Family
ID=80366058
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111543956.2A Active CN114115323B (en) | 2021-12-16 | 2021-12-16 | Modeling and control method of three-steering engine driven bird-like ornithopter |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114115323B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115477006B (en) * | 2022-09-15 | 2023-05-19 | 哈尔滨工业大学 | Double-shaft tilting vector rotor craft and disturbance compensation control method thereof |
| CN118332707B (en) * | 2024-06-17 | 2024-08-09 | 中国空气动力研究与发展中心高速空气动力研究所 | Aircraft transverse direction flight control design method based on thrust control flight |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107203220A (en) * | 2017-05-27 | 2017-09-26 | 上海交通大学 | Flapping wing aircraft flight control method and system |
| CN108945430A (en) * | 2018-07-16 | 2018-12-07 | 武汉科技大学 | A kind of-bionic flapping-wing flying vehicle of active twist combination drive of fluttering-fold |
| WO2021047988A1 (en) * | 2019-09-13 | 2021-03-18 | Technische Universiteit Delft | Attitude control mechanism for a flapping wing aerial vehicle |
| CN112977818A (en) * | 2021-02-09 | 2021-06-18 | 南京航空航天大学 | Bionic winglet feather structure capable of changing flow around wing surface of leading edge of flapping wing aircraft |
-
2021
- 2021-12-16 CN CN202111543956.2A patent/CN114115323B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107203220A (en) * | 2017-05-27 | 2017-09-26 | 上海交通大学 | Flapping wing aircraft flight control method and system |
| CN108945430A (en) * | 2018-07-16 | 2018-12-07 | 武汉科技大学 | A kind of-bionic flapping-wing flying vehicle of active twist combination drive of fluttering-fold |
| WO2021047988A1 (en) * | 2019-09-13 | 2021-03-18 | Technische Universiteit Delft | Attitude control mechanism for a flapping wing aerial vehicle |
| CN112977818A (en) * | 2021-02-09 | 2021-06-18 | 南京航空航天大学 | Bionic winglet feather structure capable of changing flow around wing surface of leading edge of flapping wing aircraft |
Non-Patent Citations (1)
| Title |
|---|
| 扑翼微型飞行器飞行姿态模型研究;段洪君;史小平;;航空动力学报;20070815(第08期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114115323A (en) | 2022-03-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Darvishpoor et al. | Configurations, flight mechanisms, and applications of unmanned aerial systems: A review | |
| CN109614633B (en) | Nonlinear modeling and linearization balancing method for composite rotor craft | |
| Zufferey et al. | Design of the high-payload flapping wing robot e-flap | |
| Grant et al. | Flight dynamics of a morphing aircraft utilizing independent multiple-joint wing sweep | |
| Hochstenbach et al. | Design and control of an unmanned aerial vehicle for autonomous parcel delivery with transition from vertical take-off to forward flight–vertikul, a quadcopter tailsitter | |
| Ifju et al. | Flexible-wing-based micro air vehicles | |
| Jung et al. | Development and application of controller for transition flight of tail-sitter UAV | |
| CN114115323B (en) | Modeling and control method of three-steering engine driven bird-like ornithopter | |
| Bulka et al. | Automatic control for aerobatic maneuvering of agile fixed-wing UAVs | |
| Wenfu et al. | Flight control of a large-scale flapping-wing flying robotic bird: System development and flight experiment | |
| Zhou et al. | A unified control method for quadrotor tail-sitter uavs in all flight modes: Hover, transition, and level flight | |
| CN107985589B (en) | Take VTOL unmanned aerial vehicle of vector thrust duct engine | |
| CN113359472B (en) | Self-adaptive robust track tracking control method for four-rotor unmanned aerial vehicle | |
| Pan et al. | HIT-Hawk and HIT-Phoenix: Two kinds of flapping-wing flying robotic birds with wingspans beyond 2 meters | |
| Garcia et al. | Attitude stabilization with real-time experiments of a tail-sitter aircraft in horizontal flight | |
| Lustosa et al. | Longitudinal study of a tilt-body vehicle: modeling, control and stability analysis | |
| Knoebel et al. | Preliminary modeling, control, and trajectory design for miniature autonomous tailsitters | |
| Yang et al. | Conceptual design and flight test of two wingtip-docked multi-body aircraft | |
| CN115729264A (en) | Flexible self-adaptive winglet-based stability-variable stealth aircraft control method | |
| Chen | Research on AI application in the field of quadcopter UAVs | |
| CN114967724A (en) | Target surrounding anti-interference control method for quad-rotor unmanned aerial vehicle | |
| Kita et al. | Hovering control of a tail-sitter VTOL aerial robot | |
| CN113885358B (en) | Hybrid configuration fixed wing unmanned aerial vehicle maneuver simulation control law design method | |
| CN207078323U (en) | Microminiature can hover Fixed Wing AirVehicle | |
| CN116142497A (en) | Mars unmanned aerial vehicle and control method based on task manifold controller |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |