CN112650263A - Control method of combined unmanned aerial vehicle - Google Patents

Control method of combined unmanned aerial vehicle Download PDF

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CN112650263A
CN112650263A CN202011441516.1A CN202011441516A CN112650263A CN 112650263 A CN112650263 A CN 112650263A CN 202011441516 A CN202011441516 A CN 202011441516A CN 112650263 A CN112650263 A CN 112650263A
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unmanned aerial
aerial vehicle
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CN112650263B (en
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李福生
吴泽桂
张伟业
叶俊廷
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University of Electronic Science and Technology of China
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    • 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
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C27/00—Rotorcraft; Rotors peculiar thereto
    • B64C27/04—Helicopters
    • B64C27/08—Helicopters with two or more rotors
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C27/00—Rotorcraft; Rotors peculiar thereto
    • B64C27/52—Tilting of rotor bodily relative to fuselage
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64U—UNMANNED AERIAL VEHICLES [UAV]; EQUIPMENT THEREFOR
    • B64U10/00—Type of UAV
    • B64U10/40—Ornithopters
    • 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
    • G05D1/04—Control of altitude or depth
    • G05D1/042—Control of altitude or depth specially adapted for aircraft

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Abstract

The invention discloses a control method of a combined unmanned aerial vehicle, relates to the field of unmanned aerial vehicle control, and particularly relates to a multi-degree-of-freedom vector combined unmanned aerial vehicle. Aiming at the problems in the prior art, the unmanned aerial vehicle shows different properties in different combination modes, after combination, the unmanned aerial vehicle can hover at any angle, so that the load of the unmanned aerial vehicle can be increased through narrow spaces, and the single module can also work independently. Through the real-time modeling technology of the unmanned aerial vehicle, the unmanned aerial vehicle can be combined in the air. According to the unmanned aerial vehicle combination system, the unmanned aerial vehicle is split and combined in the air, the number and the combination mode of the combined unmanned aerial vehicles are changed, the purposes of improving the degree of freedom, improving the load and freely coping with narrow environments are achieved, and meanwhile when the number of combined modules is large, and after a power device of one module breaks down, the controller can control the whole combined stable flight through a control algorithm, so that the safety performance of the unmanned aerial vehicle is improved.

Description

Control method of combined unmanned aerial vehicle
Technical Field
The invention relates to the field of unmanned aerial vehicle control, in particular to a multi-degree-of-freedom vector combined unmanned aerial vehicle.
Background
In recent years, multi-rotor unmanned aerial vehicles are developing at a high speed, the application field is very wide, the multi-rotor unmanned aerial vehicles are often applied to load bearing, inspection, monitoring and the like, all rotors of the traditional multi-rotor unmanned aerial vehicles are generally on the same plane, and underactuation is caused. Compared with the design of fixed rotors, the unmanned aerial vehicle with dynamically changed rotor positions is also developed, for example, the unmanned aerial vehicle designed by Moju Zhao et al, researches a novel multi-rotor aircraft with two-dimensional multi-connecting rods, solves the challenge of passing through narrow spaces or gaps, establishes a model of a multi-rotor connecting rod module consisting of the two-dimensional multi-connecting rods, can be stably deformed in the air, and still is a huge challenge when passing through a small round hole.
The invention patent with publication number CN 108216629 a proposes a combined transportation unmanned aerial vehicle, but it is still a traditional multi-rotor unmanned aerial vehicle with rotors on the same plane, and can not hover at any angle. The utility model discloses a novel utility patent with publication number CN 205661655U proposes a modular combination formula unmanned aerial vehicle, and its essence is through a plurality of module mutual concatenations, but its single power module can't independent work.
The existing unmanned aerial vehicle has the following problems: 1, a single unmanned aerial vehicle is too large in size and cannot flexibly fly across in ruins and other scenes; 2, the degree of freedom is too low to hover at any angle; 3 the existing combined unmanned aerial vehicle has the problems that the degree of freedom is lower, a single module cannot fly independently, combination cannot be carried out in the air and the like.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a combined unmanned aerial vehicle design and a real-time modeling method thereof. Under the compound mode of difference, unmanned aerial vehicle demonstrates different properties, and after the combination, unmanned aerial vehicle can carry out the flight of hovering of arbitrary angle, helps through some narrow and small spaces, increases the unmanned aerial vehicle load, and single module also can independent work. Through the real-time modeling technology of the unmanned aerial vehicle, the unmanned aerial vehicle can be combined in the air.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: modular vector unmanned aerial vehicle, its characteristics are including a plurality of modularization dual rotor vector unmanned aerial vehicle, every module unmanned aerial vehicle is inhaled interface and module communication interface by two rotors that can vert and magnetism, the carbon fiber frame, the protective housing, the controller, data and power transmission line constitute. Unmanned aerial vehicle can have multiple compound mode, when two modules were made up, unmanned aerial vehicle controlled unmanned aerial vehicle through rotor angle of tilting's control and realized arbitrary pitch angle and hover. Unmanned aerial vehicle make up by three module, unmanned aerial vehicle carries out attitude control through both sides module, carries out the accelerated motion through middle module. The unmanned aerial vehicle is combined by four modules, and two combination modes are available; the combined rotor blades are combined on the same plane, pitching is realized through tilting rotor control, and the rotor blades can hover at any posture within the range of forty-five degrees of a roll angle; the space combination structure has the advantages that the two modules of the module face upwards, and the two modules face downwards to be combined, so that the all-attitude arbitrary hovering is realized. Unmanned aerial vehicle can also have multiple compound mode except complaining the compound mode on, can possess different performance characteristics. Real-time mathematical modeling of unmanned aerial vehicle, connect through magnetism communication interface, module unmanned aerial vehicle in the connection process can send the instruction to all communication interfaces on every side in real time, the unmanned aerial vehicle that receives the instruction then can return the answer signal, confirm the connection condition around self through the answer signal, unmanned aerial vehicle sends connection condition information on every side of self simultaneously returning the answer signal to this main control unit obtains the current combination condition of combination formula unmanned aerial vehicle in real time and models on next step.
The technical scheme of the invention is a control method of a combined unmanned aerial vehicle, wherein a single unmanned aerial vehicle in the method is a dual-rotor unmanned aerial vehicle, and the control method comprises the following steps:
step 1.1: using the central point of one of the unmanned aerial vehicles asEstablishing a coordinate system at an origin (assuming that a first frame W subjected to splicing is a mother aircraft), wherein a propeller in an aircraft is regarded as two points, connecting the two points, dividing the connecting line which is vertical to a Y axis into V types, dividing the connecting line which is vertical to an X axis into M types, and defining a position vector V of the V type (Y axis) at the positioniComprises the following steps:
Figure BDA0002822463730000021
wherein Vxi，VyiRespectively establishing X and Y coordinates of a coordinate system for the V-type unmanned aerial vehicle by taking the central point of W as an origin;
class M (X-axis) position vector MjComprises the following steps:
Figure BDA0002822463730000022
wherein M isxj，MyjRespectively establishing X and Y coordinates of a coordinate system for the V-type unmanned aerial vehicle by taking the central point of W as an origin; here, the total number of the rotors is N, and the total number of the V-type rotors is NVTotal number of M type rotors is NMI.e. N ═ NV+NM；
Obtaining the coordinate V of the two types of propellers with the center of the unmanned aerial vehicle as the origin of the coordinate axis at the moment according to the obtained position structure of the unmanned aerial vehicleiAnd Mj；
Step 1.2: aiming at the coordinates of the two types of propellers, obtaining X and Y coordinates C of the geometric center of the rigid body after all unmanned aerial vehicles are combined by using a geometric center vector formula:
Figure BDA0002822463730000023
then, the whole coordinate system is translated to a geometric center, the geometric center is defined as the center of the combined unmanned aerial vehicle body, and therefore the position coordinate V of the rotor wing of each unmanned aerial vehicle under the newly-established coordinate system can be obtainedi' and Mj′：
Figure BDA0002822463730000031
Figure BDA0002822463730000032
Considering that a plurality of unmanned aerial vehicles can realize many different functions after splicing, and the rotor inclination angle controlled by the steering engine among them also can have the condition of different, so use here to show two kinds of power: fvAnd FmRespectively representing the resultant force of the rotors of the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle in the direction vertical to the rotating plane; defining the coordinate system B of the rigid body after splicing to obtain the total moment M of the whole rigid bodyaComprises the following steps:
Figure BDA0002822463730000033
wherein alpha isiIs the rotation angle of the rotor wing in the ith V-type unmanned plane to the Y axis, betaiFor the rotation angle of the rotor wing in the ith M-type unmanned aerial vehicle to the X axis, FViThe resultant force on the ith unmanned aerial vehicle perpendicular to the plane of the rotor wing; vix' and Viy' is the X and Y axis coordinates of the ith V-type unmanned plane under the newly established coordinate system, and similarly, Mjx' and Mjy' respectively representing X-axis coordinates and Y-axis coordinates of the M-type unmanned aerial vehicle under a newly established coordinate system;
step 1.3: when the blades rotate, the blades are subjected to resistance to generate torque around an aerodynamic center; these moments act in the opposite direction to the rotor speed w; the rotor speeds of the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle are w respectivelyviAnd wmj(ii) a Defining a rotation matrix T from the moment of the rotor in the V-type unmanned plane to the world coordinate system WViAnd the rotation matrix from the rotor torque in the M-type unmanned aerial vehicle to the world coordinate system W is TMjQ is the torque of the reaction of the individual rotors to the body, QViAnd q isMjThe ith and the jth rotors in the V-type and M-type unmanned aerial vehicles respectivelyDefine their relationship to the speed of rotation of the rotor as:
qVi＝Ct·wvi 2qMi＝Ct·wmj 2，Ct＞0(7)
wherein C istIs a constant; calculating the reaction force torque:
Figure BDA0002822463730000041
wherein QViAnd QMjRespectively the reaction force torque of the ith rotor wing and the jth rotor wing in the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle to the airframe; passing these moments through a rotation matrix TVi，TMjTo the body coordinate system B, the total torque Q of the rotor reaction force is as followsS，QS1Representing the X-axis torque, QS2Representing the torque of the Y axis, QS3Represents the Z-axis torque:
Figure BDA0002822463730000042
in summary, the total moment M of the whole system is:
M＝Ma+Qs(10)
step 1.4: defining three coordinate axes in the world coordinate system W as X respectivelyW，YWAnd ZWAnd the origin of B is the geometric center C obtained in the above way; in the world coordinate system, Z-Y-X Euler angles are used to model the rotation process of the rigid body after splicing, wherein the corresponding relations are Z-Roll, Y-Yaw and X-Pitch, and in order to convert the coordinates under B to W, the Z representing Roll is supposed to be rotated firstWAxis, with its rotation angle denoted as φ, then representing Y of Yaw in the middle of the rotationWThe axis is rotated by a predetermined angle θ, and finally rotated by X representing PitchWAxis and rotation angle by ψ; the following rotation matrix C from B to W is obtainedW B：
Figure BDA0002822463730000043
In the entire rigid body system, consider the system at-ZWThe gravity in the direction, the following equation is established:
Figure BDA0002822463730000051
n denotes the number of rotors, m denotes the total mass, g denotes the gravitational force, axRepresents the acceleration in the X direction, ayRepresents acceleration in the Y direction, azRepresents the Z direction acceleration;
will rotate the matrix CW BSubstituting the above equation yields:
Figure BDA0002822463730000052
Figure BDA0002822463730000053
the system respectively represents the stress of the unmanned aerial vehicle in the x, y and z directions, the Euler equation is a relational expression of external moment and angular acceleration of the rigid body when describing the rotary motion of the rigid body on the basis of the theorem of angular momentum, and the total moment M of the whole system is brought into the Euler equation to obtain the following formula:
Figure BDA0002822463730000054
wherein
Figure BDA0002822463730000055
And
Figure BDA0002822463730000056
are respectively rigid body wound around ZW,YWAnd XWThe second derivative of the angle of rotation of the shaft; j. the design is a squarexx，JyyAnd JzzAre respectively provided withIs the moment of inertia of three coordinate axes of the rigid body under the coordinate system B,
Figure BDA0002822463730000057
and
Figure BDA0002822463730000058
are respectively rigid body wound around ZW,YWAnd XWThe first derivative of the shaft rotation angle; and controlling the combined unmanned aerial vehicle according to the results obtained by calculation of the formula (13) and the formula (14).
The invention has the beneficial effects that: a modular vector unmanned aerial vehicle, it is through carrying out the split combination in the air, changes the figure and the compound mode that make up unmanned aerial vehicle, reaches and improves the degree of freedom, improves the load, freely deals with the purpose of narrow environment, when the module of combination is more simultaneously, after certain module power device broke down, the controller can control the holistic stable flight of combination through control algorithm, has improved unmanned aerial vehicle's security performance.
Drawings
The invention is further described with reference to the figures and examples of the specification.
FIG. 1 is a schematic view of a combination of two vector dual rotor modules;
FIG. 2 is a schematic view of a three vector dual rotor module combination;
FIG. 3 is a schematic view of a first combination of four vector dual rotor modules;
figure 4 is a schematic view of a second combination of four vector dual rotor modules.
Detailed Description
The principles and modeling methods of the present invention are described below in conjunction with the drawings, the examples given are intended to illustrate the invention and are not intended to limit the scope of the invention.
As shown in fig. 1, the combined unmanned aerial vehicle is formed by combining two modules, is connected with a strong magnet in a tee port through a carbon fiber pipe, and realizes hovering at any pitch angle by controlling a rotor inclination angle through a steering engine;
as shown in fig. 2, the combined unmanned aerial vehicle is formed by combining three modules, the modules are connected with a strong magnet in a tee port through a carbon fiber pipe, power efficiency can be sacrificed by controlling the inclination angle of the module rotors on the left side and the right side and the rotating speed of a propeller to obtain hovering control at any roll angle, and an acceleration function is realized by controlling the inclination angle of the middle module rotor;
as shown in fig. 3, the combined unmanned aerial vehicle is formed by combining four modules, the modules are connected with a strong magnet in a tee port through a carbon fiber pipe, power efficiency can be sacrificed to obtain hovering control of any roll angle by controlling the inclination angles of the rotors of the modules on the left side and the right side and the rotating speed of the whole propeller, and power efficiency can be sacrificed to obtain hovering control of any pitch angle by controlling the inclination angles of the rotors of the two modules of the middle module and the rotating speed of the whole propeller;
as shown in fig. 4, the combined unmanned aerial vehicle is formed by combining four modules, and is connected with a strong magnet in a tee port through a carbon fiber tube, so that hovering in all postures at any angle can be realized;
example 1
The embodiment selects the combination mode as shown in fig. 3, and further describes the modeling process;
step 1.1: according to the communication nodes of each module, after current structural information is obtained, firstly, a coordinate system is established by taking the central point of one unmanned aerial vehicle as an original point (a first frame W which is spliced is taken as a mother aircraft), a propeller in one aircraft is taken as two points, after the two points are connected, the connecting line vertical to a Y axis is divided into V types, the connecting line vertical to an X axis is divided into M types, and the position vector V of the V type (Y axis) is specified hereiComprises the following steps:
Figure BDA0002822463730000071
wherein Vxi，VyiAnd respectively establishing X and Y coordinates of a coordinate system by taking the central point of the W as an origin for the V-type unmanned aerial vehicle.
Class M (X-axis) position vector MjComprises the following steps:
Figure BDA0002822463730000072
wherein M isxj，MyjAnd respectively establishing X and Y coordinates of a coordinate system by taking the central point of the W as an origin for the V-type unmanned aerial vehicle. Here, the total number of the rotors is N, and the total number of the V-type rotors is NVTotal number of M type rotors is NMI.e. N ═ NV+NM
According to the self structure obtained by the unmanned aerial vehicle in the last step, the coordinate V of the two types of propellers with the center of W as the origin of the coordinate axis of the unmanned aerial vehicle at the moment can be obtainediAnd Mj。
Step 1.2: aiming at the coordinates of the two types of propellers, obtaining X and Y coordinates C of the geometric center of the rigid body after all unmanned aerial vehicles are combined by using a geometric center vector formula:
Figure BDA0002822463730000073
then, the whole coordinate system is translated to a geometric center, the geometric center is defined as the center of the combined unmanned aerial vehicle body, and therefore the position coordinate V of the rotor wing of each unmanned aerial vehicle under the newly-established coordinate system can be obtainedi' and Mj′:
Figure BDA0002822463730000074
Figure BDA0002822463730000075
Considering that a plurality of unmanned aerial vehicles can realize a plurality of different functions after being spliced and the inclination angles of the rotors controlled by the steering engine in the unmanned aerial vehicles can be different, two types of forces are used for representing the forces, namely FvAnd FmThey represent respectively two classes of unmanned aerial vehicle in the above classification revolveThe resultant of the wings in a direction vertically upwards towards their plane of rotation. Defining the coordinate system B of the rigid body after splicing, and obtaining the total moment M of the whole rigid body by analyzing the stress of each component force of the rotor wing on the coordinate axis BaComprises the following steps:
Figure BDA0002822463730000081
wherein alpha isiIs the rotation angle of the rotor wing in the ith V-type unmanned plane to the Y axis, betaiFor the rotation angle of the rotor wing in the ith M-type unmanned aerial vehicle to the X axis, FViThe resultant force perpendicular to the rotor plane on the ith drone. Vix' and Viy' is the X and Y axis coordinates of the ith V-type unmanned plane under the newly established coordinate system, and similarly, Mjx' and Mjy' are X-axis coordinates and Y-axis coordinates of the M-type unmanned aerial vehicle under a newly established coordinate system respectively.
Step 1.3: as the blades rotate, they experience resistance, creating a torque around the aerodynamic center. These moments act in the opposite direction to w. The rotor speeds of the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle are respectively designated as wviAnd wmj. Here we define the rotation matrix of the torque of the rotor in a class V drone to the world coordinate system W as TViAnd the rotation matrix from the rotor torque in the M-type unmanned aerial vehicle to the world coordinate system W is TMjQ is the torque of the reaction of the individual rotors to the body, QViAnd q isMjThe action force of the ith and jth rotors to the fuselage in V-type and M-type unmanned aerial vehicles respectively can be simplified into the following relation with the rotating speed of the rotors:
qVi＝Ct·wvi 2qMi＝Ct·wmj 2，Ct＞0(21)
wherein C istIs a constant.
We denote Q in this way:
Figure BDA0002822463730000082
wherein QViAnd QMjBe the reaction force moment of the ith and jth rotor to the organism in V class and the M class unmanned aerial vehicle respectively. We can pass these moments through the rotation matrix TVi，TMjTo the body coordinate system B, the total torque Q of the rotor reaction force is as followsS：
Figure BDA0002822463730000091
In summary, the total moment M of the whole system is as follows:
M＝Ma+Qs(24)
step 1.4: we define three coordinate axes in the world coordinate system W as X respectivelyW，，YWAnd ZWThe origin of B is the geometric center C obtained as described above. In the world coordinate system, we use the Z-Y-X Euler angle to model the rotation process of the rigid body after splicing, wherein the corresponding relationship is Z-Roll, Y-Yaw, X-Pitch, and in order to convert the coordinates under B to W, we assume that Z representing Roll is rotated firstWAxis, with its rotation angle denoted as φ, then representing Y of Yaw in the middle of the rotationWThe axis is rotated by a predetermined angle θ, and finally rotated by X representing PitchWAxes and psi are used to represent rotation angles. By calculation, the following rotation matrix C from B to W can be obtainedW B：
Figure BDA0002822463730000092
In the entire rigid body system, consider the system at-ZWThe gravity action in the direction, the translational model of the rigid body is established by using Newton's second law, and the following equation can be established:
Figure BDA0002822463730000093
will rotate the matrix CW BBringing inThe above equation yields:
Figure BDA0002822463730000101
the Euler equation is a relational expression of external moment and angular acceleration of the rigid body when describing the rotational motion of the rigid body based on the theorem of angular momentum, and M is substituted into the Euler equation to obtain the following formula:
Figure BDA0002822463730000102
wherein
Figure BDA0002822463730000103
And
Figure BDA0002822463730000104
are respectively rigid body wound around ZW,YWAnd XWSecond derivative of the angle of rotation of the shaft, i.e. angular acceleration, Jxx，JyyAnd JzzRespectively the rotational inertia of three coordinate axes of the rigid body under a coordinate system B,
Figure BDA0002822463730000105
and
Figure BDA0002822463730000106
are respectively rigid body wound around ZW,YWAnd XWThe first derivative of the shaft rotation angle, i.e. the angular velocity. The above equations (13) and (14) are real-time mathematical models of the system.

Claims (1)

1. A method of controlling a combined drone, in which the single drone is a dual rotor drone, the method comprising:
step 1.1: establishing a coordinate system by taking a central point of one unmanned aerial vehicle as an original point, regarding a propeller in one unmanned aerial vehicle as two points, and dividing a connecting line perpendicular to a Y axis into two points after the two points are connectedClass V, divided into M classes perpendicular to the X-axis, where the position vector V of class V is specifiediComprises the following steps:
Figure FDA0002822463720000011
wherein Vxi，VyiRespectively establishing X and Y coordinates of a coordinate system for the V-type unmanned aerial vehicle by taking the central point of W as an origin;
class M position vector MjComprises the following steps:
Figure FDA0002822463720000012
wherein M isxj，MyjRespectively establishing X and Y coordinates of a coordinate system for the V-type unmanned aerial vehicle by taking the central point of W as an origin; here, the total number of the rotors is N, and the total number of the V-type rotors is NVTotal number of M type rotors is NMI.e. N ═ NV+NM；
Obtaining the coordinate V of the two types of propellers with the center of w as the origin of the coordinate axis according to the obtained position structure of the unmanned aerial vehicleiAnd Mj；
Step 1.2: aiming at the coordinates of the two types of propellers, obtaining X and Y coordinates C of the geometric center of the rigid body after all unmanned aerial vehicles are combined by using a geometric center vector formula:
Figure FDA0002822463720000013
then, the whole coordinate system is translated to a geometric center, the geometric center is defined as the center of the combined unmanned aerial vehicle body, and therefore the position coordinate V of the rotor wing of each unmanned aerial vehicle under the newly-established coordinate system can be obtainedi' and Mj′：
Figure FDA0002822463720000014
Figure FDA0002822463720000015
Considering that a plurality of unmanned aerial vehicles can realize many different functions after splicing, and the rotor inclination angle controlled by the steering engine among them also can have the condition of different, so use here to show two kinds of power: fvAnd FmRespectively representing the resultant force of the rotors of the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle in the direction vertical to the rotating plane; defining the coordinate system B of the rigid body after splicing to obtain the total moment M of the whole rigid bodyaComprises the following steps:
Figure FDA0002822463720000021
wherein alpha isiIs the rotation angle of the rotor wing in the ith V-type unmanned plane to the Y axis, betaiFor the rotation angle of the rotor wing in the ith M-type unmanned aerial vehicle to the X axis, FViThe resultant force on the ith unmanned aerial vehicle perpendicular to the plane of the rotor wing; vix' and Viy' is the X and Y axis coordinates of the ith V-type unmanned plane under the newly established coordinate system, and similarly, Mjx' and Mjy' respectively representing X-axis coordinates and Y-axis coordinates of the M-type unmanned aerial vehicle under a newly established coordinate system;
step 1.3: when the blades rotate, the blades are subjected to resistance to generate torque around an aerodynamic center; these moments act in the opposite direction to the rotor speed w; the rotor speeds of the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle are w respectivelyviAnd wmj(ii) a Defining a rotation matrix T from the moment of the rotor in the V-type unmanned plane to the world coordinate system WViAnd the rotation matrix from the rotor torque in the M-type unmanned aerial vehicle to the world coordinate system W is TMjQ is the torque of the reaction of the individual rotors to the body, QViAnd q isMjThe acting force of the ith rotor and the jth rotor in the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle to the fuselage is defined as follows:
qVi＝Ct·wvi 2 qMi＝Ct·wmj 2，Ct＞0 (7)
wherein C istIs a constant; calculating the reaction force torque:
Figure FDA0002822463720000022
wherein QViAnd QMjRespectively the reaction force torque of the ith rotor wing and the jth rotor wing in the V-type unmanned aerial vehicle and the M-type unmanned aerial vehicle to the airframe; passing these moments through a rotation matrix TVi，TMjTo the body coordinate system B, the total torque Q of the rotor reaction force is as followsS，QS1Representing the X-axis torque, QS2Representing the torque of the Y axis, QS3Represents the Z-axis torque:
Figure FDA0002822463720000031
in summary, the total moment M of the whole system is:
M＝Ma+Qs (10)
step 1.4: defining three coordinate axes in the world coordinate system W as X respectivelyW，YWAnd ZWAnd the origin of B is the geometric center C obtained in the above way; in the world coordinate system, Z-Y-X Euler angles are used to model the rotation process of the rigid body after splicing, wherein the corresponding relations are Z-Roll, Y-Yaw and X-Pitch, and in order to convert the coordinates under B to W, the Z representing Roll is supposed to be rotated firstwAxis, with its rotation angle denoted as φ, then representing Y of Yaw in the middle of the rotationwThe axis is rotated by a predetermined angle θ, and finally rotated by X representing PitchwAxis and rotation angle by ψ; the following rotation matrix C from B to W is obtainedW B：
Figure FDA0002822463720000032
In the entire rigid body system, consider the system at-ZwThe gravity in the direction, the following equation is established:
Figure FDA0002822463720000033
n denotes the number of rotors, m denotes the total mass, g denotes the gravitational force, axRepresents the acceleration in the X direction, ayRepresents acceleration in the Y direction, azRepresents the Z direction acceleration;
will rotate the matrix CW BSubstituting the above equation yields:
Figure FDA0002822463720000041
Figure FDA0002822463720000042
the system respectively represents the stress of the unmanned aerial vehicle in the x, y and z directions, the Euler equation is a relational expression of external moment and angular acceleration of the rigid body when describing the rotary motion of the rigid body on the basis of the theorem of angular momentum, and the total moment M of the whole system is brought into the Euler equation to obtain the following formula:
Figure FDA0002822463720000043
wherein
Figure FDA0002822463720000044
And
Figure FDA0002822463720000045
are respectively rigid body wound around Zw，YwAnd XwThe second derivative of the angle of rotation of the shaft; j. the design is a squarezz，JyyAnd JzzRespectively the rotational inertia of three coordinate axes of the rigid body under a coordinate system B,
Figure FDA0002822463720000046
and
Figure FDA0002822463720000047
are respectively rigid body wound around Zw，YWAnd XwThe first derivative of the shaft rotation angle; and controlling the combined unmanned aerial vehicle according to the results obtained by calculation of the formula (13) and the formula (14).
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