CN111506117A - Four-rotor space circular formation decoupling control method based on limit ring - Google Patents

Four-rotor space circular formation decoupling control method based on limit ring Download PDF

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CN111506117A
CN111506117A CN202010501096.5A CN202010501096A CN111506117A CN 111506117 A CN111506117 A CN 111506117A CN 202010501096 A CN202010501096 A CN 202010501096A CN 111506117 A CN111506117 A CN 111506117A
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徐伟
蔡晨晓
万铧
瞿余成
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
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    • 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
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
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    • 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
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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
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    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
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Abstract

The invention discloses a limit ring-based four-rotor space circular formation decoupling control method, which comprises the following steps of: establishing a four-rotor mathematical model; constructing a perception topological structure and a formation of a four-rotor formation system; a decoupling controller based on a limit ring is designed, four-rotor space circular formation control is decoupled into height control, circular convergence spiral control and individual interval adjustment control, and a distributed controller consisting of a height controller, a circular convergence controller, an interval layout controller and a collision avoidance controller is designed. The decoupling control method for the spatial circular formation only utilizes the center of a target circle and the position information of the adjacent four rotors, not only can form expected spatial circular formation distribution within limited time, but also has very strong fault tolerance rate and expansibility.

Description

Four-rotor space circular formation decoupling control method based on limit ring
Technical Field
The invention belongs to the field of four-rotor formation control, and particularly relates to a limit-ring-based decoupling control method for four-rotor spatial circular formation.
Background
The four-rotor formation has great potential in various practical applications, and has superiority in the aspects of high efficiency, robustness, covering capacity and the like compared with a single-rotor formation. Circular formation is one of the common formation patterns in formation control, and for example, in security monitoring and detection tasks, a group of detection circles need to be formed around a task area in order to collect information. When distributed control is adopted, only part of relative information can be acquired among four rotor teams, and the control mode is required to have strong fault tolerance rate and expansibility, so that mutual cooperation becomes a great difficulty.
In recent years, due to the characteristic that the oscillator gradually tends to a limit ring along with the time, extensive research is carried out in the field of multi-intelligent agents, and a decoupling design method based on the limit ring is adopted in the literature (Wang C, Xie G, L image-cycle-based compensated design of cyclic Control with communication of information and agents in a plane [ J ]. IEEE Transactions on Automatic Control,2017,62(12):6560 and 6567), so that a group of mass points in a Control plane forms a plane circular formation.
Disclosure of Invention
The invention aims to provide a decoupling control method for four-rotor spatial circular formation based on a limit ring, which can avoid collision, quickly complete the four-rotor spatial circular formation in limited time and meet the requirements of the four-rotor spatial circular formation on fault tolerance and expansibility.
The technical solution for realizing the purpose of the invention is as follows: a four-rotor space circular formation decoupling control method based on a limit ring comprises the following steps:
step 1, establishing a four-rotor mathematical model, including a torque equation, a dynamic model and an attitude angle resolving equation;
step 2, constructing a perception topological structure and a formation of a four-rotor formation system, and designing a single integral model of a four-rotor spatial circular formation controller;
step 3, designing a height controller, and controlling the four-rotor formation to fly at an expected height by adopting a PID (proportion integration differentiation) controller based on deviation control;
step 4, designing a circular convergence controller, and controlling four-rotor formation to carry out circular convergence circling in the horizontal direction by adopting an oscillator with a stable limit ring;
step 5, designing a spacing layout controller, and controlling the spacing between the four rotor individuals by adopting a finite time control law to form set circular relative position distribution;
step 6, designing a collision avoidance controller, and controlling four-rotor formation to avoid collision by adopting an artificial potential field method;
step 7, designing a space circular formation controller, wherein the space circular formation controller is formed by combining a distributed controller formed by the controllers in the steps 3-5 and the collision avoidance controller in the step 6; obtaining a target speed relative to a target circle center through a space circular formation controller, converting the target speed into a target acceleration under a geodetic coordinate system by using an acceleration conversion formula of a machine body coordinate system, and performing posture inverse solution to obtain a target Euler angle including a roll angle of four rotors
Figure BDA0002524837490000021
And a pitch angle theta.
Compared with the prior art, the invention has the following remarkable advantages: (1) the invention expands the round formation control problem in a plane into a round formation control problem in a three-dimensional space. (2) The invention designs a limited time control law, accelerates the process of forming circular relative position distribution, enables the circular relative position distribution to be completed within limited time, and is suitable for actual flying formation tasks. (3) The collision avoidance controller is designed, and the safety of the four-rotor formation in the task space is ensured on the premise of considering the actual size of the four rotors. The four-rotor formation control mode has strong fault tolerance rate and expansibility.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a general flow chart of the control method of the present invention.
Fig. 2 is a schematic view of an X-type quad-rotor.
Figure 3 is a top view of a quad rotor space system numbering.
Fig. 4 is a top view of topology information that can be sensed by each quad-rotor itself.
Figure 5 is a top view depicting the spatial trajectory of the quadrotors and the desired formation.
Fig. 6 is a top view of the minimum safety and collision avoidance distances between two quadrotors.
Fig. 7 is a control block diagram of a quad-rotor space circular formation controller.
Fig. 8 is a simulation diagram formed by asymptotic distribution of relative positions of circles without collision avoidance.
Fig. 9 is a simulation diagram showing the collision avoidance and the gradual distribution of the relative positions of circles.
FIG. 10 is a simulation of collision avoidance, circular relative position distribution finite time.
FIG. 11 is a graph of actual flight data records formed by asymptotically approximating a circular relative position distribution.
FIG. 12 is a graph of actual flight data records formed over a limited time period of a circular relative position distribution.
Detailed Description
With reference to fig. 1, the decoupling control method for spatial circular formation of four rotors based on limit rings of the present invention includes the following steps:
step 1, establishing a four-rotor mathematical model: the method comprises a torque equation, a dynamic model and an attitude angle resolving equation, and the target position acceleration is converted into target Euler angles phi and theta for attitude control.
Step 1.1, a four-rotor torque equation is established, and the torque tau of the four rotors in the directions of the x axis, the y axis and the z axis is obtainedx、τyAnd τzThe expression of (a) is as follows:
Figure BDA0002524837490000031
wherein, CTIs the lift coefficient of the rotor; l is the distance from the center of mass of the four rotors to the rotating shaft of the rotors; omegai(i is 1,2,3,4) is the rotating speed of the No. i motor; cDIs the rotor drag coefficient.
Step 1.2, neglecting air resistance, and establishing a four-rotor dynamic model as follows:
Figure BDA0002524837490000032
in the formula, xe、ye、zeThe positions of the four rotors in the geodetic coordinate system,
Figure BDA0002524837490000033
acceleration in a geodetic coordinate system;
Figure BDA0002524837490000034
the total tension of the four propellers; m is the total mass of a single four-rotor wing;
Figure BDA0002524837490000035
theta and psi are roll angle, pitch angle and yaw angle of the four rotors;
Figure BDA0002524837490000036
the roll angle, the pitch angle and the yaw angle,
Figure BDA0002524837490000037
angular accelerations of roll angle, pitch angle and yaw angle, g is gravity acceleration; i isx、Iy、IzThe rotary inertia of the four rotors around the x, y and z axes.
Step 1.3, establishing an attitude angle resolving equation and converting the acceleration under a geodetic coordinate system
Figure BDA0002524837490000038
And
Figure BDA0002524837490000039
is converted into acceleration under a body coordinate system
Figure BDA00025248374900000310
And
Figure BDA00025248374900000311
as shown in the following formula:
Figure BDA00025248374900000312
then, a solving formula of the target Euler angle under the body coordinate system can be obtained according to the formulas 2 and 3:
Figure BDA0002524837490000041
psi is the measured yaw angle, which will then be controlled by controlling the euler angles of the four rotors
Figure BDA0002524837490000042
And theta, obtaining stable attitude control of the four rotors, and further obtaining space circular formation position control of the four rotors under a geodetic coordinate system.
Step 2, constructing a perception topological structure and a formation of a four-rotor formation system, including the definitions of system numbers, collision avoidance parameters and the like, and designing a single integral model of a four-rotor spatial circular formation controller:
step 2.1, defining the relative position of each four rotors i relative to the center of a target circle
Figure BDA0002524837490000049
The equations 5 and 6 are expressed by rectangular coordinates and cylindrical coordinates, respectively:
Figure BDA0002524837490000043
Figure BDA0002524837490000044
among other things, the invention contemplates a set of systems consisting of N quadrotors, each of which may be designated by the number I, where I ∈ InN, with the four rotors i in position pi＝[xei,yei,zei]TThe circle center position of the circular formation is p0＝[x0,y0,z0]TOn the vertical projection horizontal plane of the four-rotor space system,
Figure BDA0002524837490000045
distance of the i center of the quadrotors from the target center, αi∈ [0,2 π) is the azimuth of each quad-rotor to the target point.
Step 2.2, defining the number of the four rotors adjacent to the four rotors i as follows:
Figure BDA0002524837490000046
wherein each four rotors has an azimuth α relative to the center of the target circleiThe number order is determined, and for the same azimuth, the numbers are sorted in increments according to the distance from the target point.
Step 2.3, describing the information of the perception topological structure of the four-rotor system as follows:
Figure BDA0002524837490000047
wherein, each four rotors can only obtain the horizontal position information of the four rotors relative to the target circle center and the adjacent serial number, and the perception topology of the four rotor system can be described as
Figure BDA0002524837490000048
Wherein γ ═ InThe term {1, 2., N } denotes a set of four rotors, and { (1,2), (2,3), }, (N-1, N), (N, 1) } denotes a set of adjacent relations. On the vertical projection horizontal plane of the four-rotor space,
Figure BDA0002524837490000051
the relative distance from the center of quad i to the center of quad i + 1. And define
Figure BDA0002524837490000052
The angular distance from the four rotors i to i +1 is an angle formed by the fact that a straight line extending to the four rotors i from the target circle center rotates anticlockwise to the four rotors i + 1; in the same way canObtaining the relative distance from the four rotors i-1 to the four rotors i
Figure BDA0002524837490000053
And angular distance
Figure BDA0002524837490000054
Step 2.4, describing the formation of the four-rotor space circular formation, which is described by the height h, the radius r and the circular relative position distribution d, wherein the expected circular relative position distribution d is expressed as:
d＝[d1,d2,...,dN]T，
Figure BDA0002524837490000055
(9)
wherein d isiRepresenting the desired horizontal angular distance from i to i +1, while each quad-rotor i uses only the information diAnd di-1。
And 2.5, self-setting collision avoidance parameters between the four rotors according to the actual volumes and experiences of the four rotors, namely the minimum safety distance and the collision avoidance distance. In particular, each quadrotor needs to avoid collision with the adjacent quadrotors in space, and the minimum safe distance between the adjacent quadrotors is defined as R1，R1And l is the distance from the center of mass of the four rotors to the rotating shaft. Defining the collision avoidance distance as R2，R2＞R1When R is1＜||pa-pb||＜R2In this case, collision avoidance control is performed.
Step 2.6, the invention models the space circular formation controller into the following single integral model:
Figure BDA0002524837490000056
wherein u isxi、uyi、uziIn order for the control input to be designed,
Figure BDA0002524837490000057
i.e. four rotors facing the eyeThe centre of the circle is xe、ye、zeDesired speed in the axial direction.
Given a spatially circular formation described in terms of height h, radius r and graphical distribution d, a distributed controller is designed
Figure BDA0002524837490000058
Under the condition that the four rotors are sorted according to the space distribution reverse time needle, the solution of the formula 10 tends to be an equilibrium point
Figure BDA0002524837490000059
Namely, the following equation is satisfied:
Figure BDA00025248374900000510
wherein the content of the first and second substances,
Figure BDA00025248374900000511
the desired height of the four rotors i is indicated,
Figure BDA00025248374900000512
representing the desired distance of the center of the quad i rotor from the target center,
Figure BDA00025248374900000513
the desired azimuth angle of the quad-rotor i relative to the target center.
Step 3, designing a height controller, and controlling the four-rotor formation to fly at an expected height by adopting a PID (proportion integration differentiation) controller based on deviation control:
Figure BDA0002524837490000061
wherein, KP、KI、KDProportional, integral and differential time constants, eziThe altitude control controller is capable of controlling the quadrotors to fly at a set spatial circular formation altitude for deviations of the actual altitude of each quadrotor from the desired altitude.
And 4, designing a circular convergence controller, and enabling each four rotors to carry out circular convergence circling in the horizontal direction through circular convergence control.
The circular convergence controller adopts an oscillator with a stable limit ring, and has the characteristic that the track near the limit cycle finally tends to the limit ring along with the time, so that the circular convergence requirement designed by the invention can be well met. The invention will use a second order nonlinear oscillator and the limit ring has the desired circle radius with the target point as the center. Designed limit ring oscillator
Figure BDA0002524837490000062
The following were used:
Figure BDA0002524837490000063
wherein lambda is more than 0, gamma is more than 0 and is a constant,
Figure BDA0002524837490000064
R2a two-dimensional space is represented in which,
Figure BDA0002524837490000065
the relative position of the four rotors i with respect to the center of the target circle,
Figure BDA0002524837490000066
the relative position coordinates of the four rotor wings i about the center of a target circle; it should be noted that circular convergence control
Figure BDA0002524837490000067
Using only the relative position information between quadrotors i and the target circle center for dealing with the problem of circular convergence hovering, i.e. each quadrotor surrounding the target p0Rotating counterclockwise with a radius r.
And 5, designing a spacing layout controller, and controlling the adjustment spacing among the four rotor individuals by adopting a finite time control law to form set circular relative position distribution.
To form the desired circular distribution, fourRotor i also needs to coordinate control with the adjacent quadrotors using relative position information. Thus, when designing the distributed control of the controller, the individual pitch adjustment needs to focus on the angular distance between two of the quadrotors
Figure BDA0002524837490000068
The designed circular relative position distribution control law is as follows:
Figure BDA0002524837490000069
where α is the controller coefficient,
Figure BDA00025248374900000610
r represents a one-dimensional space, when 0 < α < 1, the four-rotor circular relative position distribution is formed in a limited time, when α is 1, the process of forming the four-rotor circular relative position distribution is gradual, and then, a designed interval layout controller
Figure BDA00025248374900000611
Comprises the following steps:
Figure BDA00025248374900000612
wherein, c1≥c2The number > 0 is a constant number,
Figure BDA0002524837490000071
the pitch layout controller can be used to handle individual pitch adjustments, i.e. the number of quadrotors required to form the desired circular relative position distribution d.
And 6, designing a collision avoidance controller, and controlling four-rotor formation to avoid collision by adopting an artificial potential field method.
The invention needs to consider the actual size of the four rotors and the collision between each four rotor and the vertical cylinder of the adjacent four rotors in the space. Therefore, the collision avoidance is guaranteed by adopting an artificial potential field method, and when the horizontal distance between the four adjacent rotors is smaller than a certain distance, the potential field acting force enables the four adjacent rotors to move in opposite directions. Defining the potential field function between adjacent quadrotors as:
Figure BDA0002524837490000072
wherein R is2＞R1> 0, as introduced in section II, R2Indicates the distance to collision, R1Represents the minimum safe distance, P is the minimum safe distance and the collision avoidance distance when the distance between two quadrotors is between the minimum safe distance and the collision avoidance distanceij(pi,pj) Is a non-zero value. For the topology structure of the whole multi-four rotor system, the collision avoidance between each four rotors and the adjacent four rotors is ensured, so that the collision avoidance of the whole multi-four rotor system can be ensured, and the P is further describedij(pi,pj) Only i-1 and i +1 need to be considered for j in (1). Then Pij(pi,pj) To piThe partial derivative is calculated to obtain the following formula:
Figure BDA0002524837490000073
wherein p isiPosition of four rotors i, pjThe position of the quad rotor j;
next, a function P is definediThe following formula:
Pi＝Pi,i-1+Pi,i+1,i∈In(18)
wherein, PiThe larger the value of (b), the closer the distance between the ith quadrirotor and one or two adjacent quadrirotors is to the minimum safety distance, so that the gradient descent method is adopted to ensure that P isiAchieving a minimum ensures avoidance of collisions. The invention designs the collision avoidance controller as follows:
Figure BDA0002524837490000074
wherein the content of the first and second substances,
Figure BDA0002524837490000075
the control input of the collision avoidance controller is the speed signals of the x and y axes.
Step 7, designing a decoupling controller based on a limit ring, decoupling the four-rotor space circular formation control into three aspects of height, circular convergence circling and individual distance adjustment, and designing a distributed controller which integrates the steps 3-6, namely a height-controlled decoupling controller
Figure BDA0002524837490000081
Circular convergence control
Figure BDA0002524837490000082
And pitch layout control
Figure BDA0002524837490000083
Formed distributed controller, in combination with collision avoidance controller
Figure BDA0002524837490000084
The controller for forming the space circular formation whole body is as follows:
Figure BDA0002524837490000085
β is the coefficient of collision avoidance controller for adjusting the sensitivity of collision avoidance control
Figure BDA0002524837490000086
Namely, the target speed of the quadrotors relative to the center of the target circle, and the motion control amount on the horizontal plane needs to be converted into the target acceleration under the geodetic coordinate system according to the following formula 21.
Figure BDA0002524837490000087
Wherein the content of the first and second substances,
Figure BDA0002524837490000088
is uxi、uyiThe first derivation of (a) is performed,
Figure BDA0002524837490000089
and the measured yaw angle psi is then carried into a formula 4 for attitude calculation, and further an Euler angle is obtained.
For the purpose of illustrating the technical solutions and technical objects of the present invention, the present invention will be further described with reference to the accompanying drawings and specific embodiments.
Examples
This embodiment uses a 240mm wheelbase X-type quad-rotor based Pixhawk flight control, with a profile and rotor steering as shown in fig. 2. The main parameters of the four rotors used in the experiment are shown in table 1.
TABLE 1 quadrotor parameters and their meanings
Figure BDA00025248374900000810
FIG. 3 is a numbered plan view of a quad-rotor space system, each quad-rotor defined by an azimuth angle α relative to the center of the target circleiThe number order is determined, and for the same azimuth, the numbers are sorted in increments according to the distance from the target point.
FIG. 4 is a top view of each four-rotor wing self-perceivable topological structure information, and the invention considers that each four-rotor wing can only obtain four-rotor wing horizontal position information relative to a target circle center and adjacent numbers, and can describe the four-rotor wing system perceivable topology as
Figure BDA0002524837490000091
Wherein γ ═ InThe term {1, 2., N } denotes a set of four rotors, and { (1,2), (2,3), }, (N-1, N), (N, 1) } denotes a set of adjacent relations.
Fig. 5 is a top view depicting the spatial trajectory of the quadrotors and the desired formation: the four rotors take off from the initial position, control and fly to the set height, simultaneously circle and converge towards the circle, and adjust the relative position distribution of the four rotors on the circle, finally form the desired formation and continuously circle.
Fig. 6 is a top view of the minimum safety and collision avoidance distances between two quadrotors. The invention takes into account the actual volume of the four rotors, each four rotor and the adjacent four rotors being in spaceTo avoid collision, the minimum safe distance between adjacent quadrotors is defined as R1I.e. the minimum case distance between quadrotors a and b to avoid collision (satisfying the center distance | | p)a-pb||＞R1). Defining the collision avoidance distance as R2When R is1＜||pa-pb||＜R2In this case, collision avoidance control is performed.
Fig. 7 is a control block diagram of a quad-rotor space circular formation controller. Designing a decoupling control method based on a limit ring: and the four-rotor-wing spatial circular formation control is decoupled into three aspects of height, circular convergence circling and individual distance adjustment. A distributed controller is provided that is comprised of a height controller, a circular convergence controller, a pitch layout controller, and a collision avoidance controller. The height control can enable the four rotors to be controlled at a set flying height, the circular convergence control enables the four rotors to perform circular convergence and circling in the horizontal direction, and the distance layout control enables the four rotors to perform distance adjustment, so that set circular relative position distribution can be formed in limited time. Meanwhile, the actual size of the four rotors is also required to be considered, and collision avoidance control is performed.
The embodiment performs simulation experiments in MAT L AB and realizes the spatial circular formation control of 3 quadrotors in the environment of a VICON system as a position sensor in a geodetic coordinate system.
In the spatial circular formation control, the following parameters are set as shown in table 2:
TABLE 2 spatial circular formation parameters and their meanings
Figure BDA0002524837490000092
In order to embody the effectiveness of the four-rotor space circular formation controller, the effect of avoiding collision of the controllers and the effect formed in the limited time of circular relative position distribution, a simulation experiment is carried out.
The four-rotor space circular formation controller can pass parameters lambda, gamma and c1、c2Adjustment, in which λ γ can change the circleThe speed of rotation can be varied while x converges. Selecting parameters lambda as 1, gamma as 0.0000025, c by regulating parameters for multiple times1＝c2＝2，t＝7s，KP＝8，TI＝+∞，TDWhen the parameters of the circular formation controller formed by the collision avoidance and the gradual distribution of the circular relative positions are set to be 0.525, β is set to be 0, α is set to be 1, the simulation effect graph is shown in fig. 8, and it can be found that the relative distance of each four rotors is lower than R once1. Holding parameters lambda, gamma, c1、c2The size is unchanged at R1And R2The collision avoidance control is carried out, the parameters of the controller formed by the gradual approach of the collision avoidance and the circular formation relative position distribution are β -200, α -1, the simulation effect graph is shown in fig. 9, and the relative distance of each four rotors is not lower than R1Further, the formation controller parameters for the formation of circles within a limited time for avoiding collision and distribution of relative positions of circles are β -200 and α -0.1, as shown in fig. 10, it can be found that a desired distribution of circles is formed within a limited time.
And then performing physical verification, wherein each four rotary wings are lifted to a set height from an initial position, and simultaneously performing circular formation and circling in the horizontal direction. Two sets of simulation experiment parameters with collision avoidance, gradual formation of circular relative position distribution and limited time formation of circular relative position distribution are selected for flight experiment, and an actual flight data recording diagram is obtained as shown in fig. 11 and 12.
The actual flight track and the simulation track have higher fitting degree, so the effectiveness of the four-rotor space circular formation controller can be verified, and meanwhile, the characteristics of the collision avoidance controller and the effect formed by the improved circular relative position distribution in limited time can be seen.
From the above, in the embodiment, the limit-ring-based decoupling control method for the spatial circular formation of the four rotors is simulated and tested, and a mathematical model is established for the four rotors firstly; secondly, constructing a perception topological structure and a formation of a four-rotor formation system; designing a decoupling control controller based on a limit ring, and providing a distributed controller consisting of a height controller, a circular convergence controller, a spacing layout controller and a collision avoidance controller; and finally, the practicability of the algorithm is verified through simulation and experiments. The decoupling control method for spatial circular formation only utilizes the center of a target circle and the position information of the adjacent four rotors, not only can form expected spatial circular formation distribution within limited time, but also has very strong fault tolerance rate and expansibility, and is very suitable for spatial circular formation of the four rotors.

Claims (8)

1. A four-rotor space circular formation decoupling control method based on a limit ring is characterized by comprising the following steps:
step 1, establishing a four-rotor mathematical model, including a torque equation, a dynamic model and an attitude angle resolving equation;
step 2, constructing a perception topological structure and a formation of a four-rotor formation system, and designing a single integral model of a four-rotor spatial circular formation controller;
step 3, designing a height controller, and controlling the four-rotor formation to fly at an expected height by adopting a PID (proportion integration differentiation) controller based on deviation control;
step 4, designing a circular convergence controller, and controlling four-rotor formation to carry out circular convergence circling in the horizontal direction by adopting an oscillator with a stable limit ring;
step 5, designing a spacing layout controller, and controlling the spacing between the four rotor individuals by adopting a finite time control law to form set circular relative position distribution;
step 6, designing a collision avoidance controller, and controlling four-rotor formation to avoid collision by adopting an artificial potential field method;
step 7, designing a space circular formation controller, wherein the space circular formation controller is formed by combining a distributed controller formed by the controllers in the steps 3-5 and the collision avoidance controller in the step 6; obtaining a target speed relative to a target circle center through a space circular formation controller, converting the target speed into a target acceleration under a geodetic coordinate system by using an acceleration conversion formula of a machine body coordinate system, and performing posture inverse solution to obtain a target Euler angle including a roll angle of four rotors
Figure FDA0002524837480000011
And a pitch angle theta.
2. The limit-ring-based quadrotor space circular formation decoupling control method according to claim 1, wherein the establishment of the quadrotor mathematical model in step 1 specifically comprises the following steps:
step 1.1, establishing a four-rotor torque equation as follows:
Figure FDA0002524837480000012
wherein, taux、τyAnd τzFor four-rotor torque about the x, y and z axes, CTIs the lift coefficient of the rotor; l is the distance from the center of mass of the four rotors to the rotating shaft of the rotors; omegaiThe rotation speed of the motor No. i is 1,2,3 and 4; cDIs the rotor drag coefficient;
step 1.2, establishing a four-rotor dynamic model as follows:
Figure FDA0002524837480000021
in the formula, xe、ye、zeThe positions of the four rotors in the geodetic coordinate system are shown;
Figure FDA0002524837480000022
acceleration in the geodetic coordinate system, Fsum＝CT(ω1 2+ω2 2+ω3 2+ω4 2) The total tension of the four propellers; m is the total mass of a single four-rotor wing;
Figure FDA0002524837480000023
theta and psi are roll angle, pitch angle and yaw angle of the four rotors;
Figure FDA0002524837480000024
the roll angle, the pitch angle and the yaw angle,
Figure FDA0002524837480000025
angular accelerations of roll angle, pitch angle and yaw angle, g is gravity acceleration; i isx、Iy、IzThe rotary inertia of the four rotors around the x, y and z axes;
step 1.3, establishing an attitude angle resolving equation, and firstly, enabling the acceleration under a geodetic coordinate system to be accelerated
Figure FDA0002524837480000026
And
Figure FDA0002524837480000027
is converted into acceleration under a body coordinate system
Figure FDA0002524837480000028
And
Figure FDA0002524837480000029
Figure FDA00025248374800000210
then, a solving formula of the target Euler angle under the body coordinate system can be obtained according to the formulas 2 and 3:
Figure FDA00025248374800000211
where ψ is the measured yaw angle.
3. The decoupling control method for spatial circular formation of quadrotors based on limit rings according to claim 1, wherein the step 2 of constructing a sensing topology and formation of a quadrotor formation system specifically comprises the following steps:
step 2.1, defining the relative position of the four rotors i relative to the center of a target circle
Figure FDA00025248374800000212
Comprises the following steps:
Figure FDA00025248374800000213
Figure FDA00025248374800000214
wherein, I ∈ InN denotes that the circular formation is composed of N quadrotors, i denotes a quadrotor number, and the position of the quadrotor i is pi＝[xei,yei,zei]TThe circle center position of the circular formation is p0＝[x0,y0,z0]T，
Figure FDA00025248374800000215
The relative position coordinates of the four rotors i about the center of a target circle are calculated, on the vertical projection horizontal plane of the four-rotor space system,
Figure FDA0002524837480000031
distance of the i center of the quadrotors from the target center, αi∈ [0,2 π) is the azimuth of quad-rotor i with respect to the target point;
step 2.2, defining the number of the four rotors adjacent to the four rotors i as follows:
Figure FDA0002524837480000032
wherein each four rotors has an azimuth α relative to the center of the target circleiThe number sequence is determined according to the increasing sequence of the number, and for the same azimuth angle, the number is gradually increased and sorted according to the distance from the target point;
step 2.3, describing the information of the perception topological structure of the four-rotor system as follows:
Figure FDA0002524837480000033
on the vertical projection horizontal plane of the four-rotor space,
Figure FDA0002524837480000034
the relative distance from the center of the four rotors i to the center of the four rotors i +1,
Figure FDA0002524837480000035
the relative distance from the center of the four rotors i-1 to the center of the four rotors i;
step 2.4, the formation of the four-rotor spatial circular formation is described by the height h, the radius r and the circular relative position distribution d, and the expected circular relative position distribution d is expressed as:
Figure FDA0002524837480000036
wherein d isiRepresenting the desired horizontal angular distance from i to i +1, while each quad-rotor i uses only the information diAnd di-1；
Step 2.5, self-setting collision avoidance parameters among the four rotors according to the actual volumes of the four rotors, namely the minimum safe distance R1And a collision avoidance distance R2，R1、R2Satisfies the following conditions: 2l < R1＜R2L is the distance from the center of mass of the four rotors to the rotating shaft;
step 2.6, modeling the space circular formation controller into a single integral model as follows:
Figure FDA0002524837480000037
wherein u isxi、uyi、uziIn order for the control input to be designed,
Figure FDA0002524837480000038
i.e. the four rotors are at x relative to the target circle centere、ye、zeDesired speed in axial directionAnd (4) degree.
4. The limit ring-based quadrotor space circular formation decoupling control method according to claim 1, wherein the deviation control-based PID controller in step 3
Figure FDA0002524837480000039
Comprises the following steps:
Figure FDA0002524837480000041
wherein I represents the four-rotor number, I ∈ InN denotes a circular formation consisting of N quadrotors, KP、KI、KDProportional, integral and differential time constants, eziThe actual height of each quad-rotor deviates from the desired height.
5. The limit ring based quadrotor space circular formation decoupling control method according to claim 1, wherein the limit ring oscillator of step 4
Figure FDA0002524837480000042
The following were used:
Figure FDA0002524837480000043
wherein lambda is more than 0, gamma is more than 0 and is a constant, r is the radius of the space circular formation,
Figure FDA0002524837480000044
R2a two-dimensional space is represented in which,
Figure FDA0002524837480000045
the relative position of the four rotors i with respect to the center of the target circle,
Figure FDA0002524837480000046
the relative position coordinates of the four rotors i about the center of a target circle.
6. The limit ring-based quadrotor space circular formation decoupling control method according to claim 1, wherein the controller of circular relative position distribution in step 5
Figure FDA0002524837480000047
Comprises the following steps:
Figure FDA0002524837480000048
wherein the content of the first and second substances,
Figure FDA0002524837480000049
the angular distance from the four rotors i to i +1 is an angle formed by the fact that a straight line extending to the four rotors i from the target circle center rotates anticlockwise to the four rotors i + 1;
Figure FDA00025248374800000410
the angular distance from quad i-1 to i, α is the controller coefficient,
Figure FDA00025248374800000411
r represents a one-dimensional space, when the value is more than 0 and less than α and less than 1, the four-rotor circular relative position distribution can be formed in a limited time, and when the value is α equal to 1, the process of forming the four-rotor circular relative position distribution is gradual;
pitch layout controller design-after-design
Figure FDA00025248374800000412
Comprises the following steps:
Figure FDA00025248374800000413
wherein, c1≥c2The number > 0 is a constant number,
Figure FDA00025248374800000414
the pitch layout controller can be used to handle the goal of individual pitch adjustments, i.e., the number of quadrotors needed to form the desired circular relative position distribution d.
7. The decoupling control method for limit ring based quadrotor space circular formation according to claim 1, wherein the collision avoidance controller is designed in step 6 by first defining a potential field function P between adjacent quadrotorsij(pi,pj) Comprises the following steps:
Figure FDA0002524837480000051
wherein p isiPosition of four rotors i, pjThe position of the quad rotor j;
then Pij(pi,pj) To piThe partial derivative is calculated to obtain the following formula:
Figure FDA0002524837480000052
next, a function P is definediThe following formula:
Pi＝Pi,i-1+Pi,i+1,i∈In(17)
using a gradient descent method to make PiObtaining the minimum value ensures avoidance of collisions:
Figure FDA0002524837480000053
wherein the content of the first and second substances,
Figure FDA0002524837480000054
R2representing a two-dimensional space, the control input of the collision avoidance controller is the x-and y-axis velocity signals.
8. The decoupling control method of limit ring based quadrotor spatial circular formation according to claim 1, wherein the spatial circular formation controller of step 7 is:
Figure FDA0002524837480000055
β is the coefficient of collision avoidance controller for adjusting the sensitivity of collision avoidance and the control quantity
Figure FDA0002524837480000056
Namely, the target speed of the four rotors relative to the center of a target circle, and the motion control quantity on the horizontal plane is converted into the target acceleration under the geodetic coordinate system according to the following formula:
Figure FDA0002524837480000057
wherein the content of the first and second substances,
Figure FDA0002524837480000058
is uxi、uyiThe first derivation of (a) is performed,
Figure FDA0002524837480000059
and carrying out attitude calculation by the measured yaw angle psi in the formula 4 to obtain an Euler angle.
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CN107688554A (en) * 2017-09-01 2018-02-13 南京理工大学 Frequency domain identification method based on adaptive Fourier decomposition
CN109324636A (en) * 2018-10-24 2019-02-12 中北大学 Formation control method is cooperateed with based on second order consistency and more quadrotor master-slave modes of active disturbance rejection

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