CN112859913B - Multi-quad-rotor unmanned helicopter attitude consistency optimal control method considering output constraint - Google Patents

Multi-quad-rotor unmanned helicopter attitude consistency optimal control method considering output constraint Download PDF

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CN112859913B
CN112859913B CN202110043323.9A CN202110043323A CN112859913B CN 112859913 B CN112859913 B CN 112859913B CN 202110043323 A CN202110043323 A CN 202110043323A CN 112859913 B CN112859913 B CN 112859913B
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attitude
rotor unmanned
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李鸿一
郭子杰
鲁仁全
周琪
陶杰
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Guangdong University of Technology
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Abstract

The invention provides a method and a system for optimally controlling the posture consistency of a multi-quad-rotor unmanned helicopter in consideration of output constraint. Firstly, carrying out mathematical modeling on the attitude dynamic characteristics of the quadrotor unmanned aerial vehicle; then, adopting system conversion based on an obstacle function to convert the system attitude control problem with output constraint into an optimal control problem under an unconstrained condition; aiming at the converted stateless constraint system, a single-network self-adaptive dynamic programming method is adopted to solve a distributed Hamiltonian-Jacobian-Belman equation, so as to obtain a distributed optimal attitude control law; the output of the multi-four-rotor unmanned aerial vehicle attitude system can effectively track the attitude signal of the collar machine and is kept in a required safety range.

Description

Multi-quad-rotor unmanned helicopter attitude consistency optimal control method considering output constraint
Technical Field
The disclosure belongs to the technical field of four-rotor unmanned aerial vehicle control, and particularly relates to a multi-four-rotor unmanned aerial vehicle gesture consistency optimal control method considering output constraint.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The four-rotor unmanned aerial vehicle is more and more popular in the civil and military fields due to the characteristics of light weight, small volume, strong maneuverability, strong adaptability and the like. Compared with a single-frame four-rotor unmanned aerial vehicle which independently executes tasks, the cooperation of a plurality of four-rotor unmanned aerial vehicles has a greater advantage. For example, under the background that the problem of high-rise fire extinguishment is prominent, the multi-frame four-rotor unmanned aerial vehicle is utilized to detect the fire, and the multi-rotor unmanned aerial vehicle is certainly an effective solution for high-rise building fire control. However, in a high-rise building fire scene environment, the posture of the quadrotor unmanned aerial vehicle is limited by the environment due to the complexity of the building structure, and cannot swing greatly. Therefore, the four-rotor unmanned aerial vehicle attitude consistency control considering the limitation of the attitude angle has very important practical significance.
The inventor finds that in recent years, four-rotor unmanned aerial vehicle attitude control with output constraint is widely focused, and a plurality of important research results are obtained; however, most of the results do not consider the optimal control problem, and meanwhile, as the output of the attitude system of the four-rotor unmanned aerial vehicle needs to be satisfied within a certain safety range, it is very difficult to design an effective optimal controller for the four-rotor unmanned aerial vehicle.
Disclosure of Invention
In order to solve the problems, the present disclosure provides a method for optimally controlling the attitude consistency of a multi-quad-rotor unmanned helicopter in consideration of output constraints.
According to a first aspect of the embodiments of the present disclosure, there is provided a method for optimally controlling posture consistency of a multi-quad-rotor unmanned helicopter in consideration of output constraints, including:
modeling the attitude physical characteristics of a single quadrotor unmanned aerial vehicle;
according to the physical characteristics of a single quadrotor unmanned aerial vehicle, converting an equation model obtained by modeling into a state equation with constraint;
determining a communication topological structure of the multi-quad-rotor unmanned helicopter, and converting a state equation with output constraint into an unconstrained state equation based on an obstacle function;
determining a cooperative consistency error and a performance index function of the cooperative consistency error aiming at an unconstrained state equation;
and determining a distributed Hamiltonian-Jacobian-Belman equation, and approximately solving the Hamiltonian-Jacobian-Belman equation by adopting a single-network self-adaptive dynamic programming method, so as to obtain a distributed optimal attitude control law.
Further, the modeling is performed on the attitude physical characteristics of the single quadrotor unmanned aerial vehicle, the built model is a quadrotor unmanned aerial vehicle attitude dynamics model based on Euler angle description, and the model is specifically expressed as follows:
Figure BDA0002896161850000021
Figure BDA0002896161850000022
wherein ,Θi ＝[φ i ,θ i ,ψ i ] T Represent Euler angles in the body coordinate system, and phi i ，θ i ，ψ i Respectively representing a roll angle, a pitch angle and a yaw angle in the posture of the quadrotor unmanned aerial vehicle; omega shape i ＝[ω ix ,ω iy ,ω iz ] T Represents the angular velocity vector, ω ix ，ω iy ，ω iz Respectively representing the rolling angle speed, the pitch angle speed and the yaw angle speed; i i ＝diag(I ix ,I iy ,I iz ) Representing a positive definite inertia matrix; m is M i ＝[u iφ ,u iθ ,u iψ ] T The method comprises the steps of representing the rotation torque input by the attitude angle of the quadrotor unmanned aerial vehicle; t (T) i Representing a transformation matrix, the transformation matrix being:
Figure BDA0002896161850000023
further, the equation model obtained by modeling is converted into a state equation with constraint, and the state equation is expressed as follows:
Figure BDA0002896161850000024
y i ＝[x i1 ,x i3 ,x i5 ] T
wherein ,
Figure BDA0002896161850000025
g(x i )＝diag[1/I ix ,1/I iy ,1/I iz ]；
u i ＝[u iφ u iθ u iψ ] T ；x i ＝[x i1 ,x i2 ,x i3 ,x i4 ,x i5 ,x i6 ] T
here, x i1 ＝φ i ，x i2 ＝ω ix ，x i3 ＝θ i ，x i4 ＝ω iy ，x i5 ＝ψ i ，x i6 ＝ω iz And needs to meet
Figure BDA0002896161850000031
Figure BDA0002896161850000032
Further, the determining the communication topology structure of the multi-quad-rotor unmanned helicopter comprises the following steps:
describing a communication connection relationship between unmanned aerial vehicles in formation by using a directed graph G= { V, E, A }; where v= {0, 1..n-1 } represents the set of nodes in graph G,
Figure BDA0002896161850000039
represents a set of directed edges in the graph, a= [ a ] ij ]∈R n×n A weight matrix representing a directed graph G;
if the plane i can receive information from plane j, then a ij =1 (i+.j), otherwise, a ij =0; defining the neighbor node of node i as N i = { j E v| (i, j) E, i+.j }, the ingress matrix D is d=diag { D } 1 ,...d N}, wherein
Figure BDA0002896161850000033
Suppose a ii =0, directed graph is a strict join; the connection between the assistant i and the collar is represented as a diagonal matrix b=diag { B 1 ,...,b N If the bureau i is able to receive information from the leader, b i =1, otherwise b i ＝0。
Further, the converting the state equation with the output constraint into the unconstrained state equation comprises the following steps:
a state conversion mapping relation is predefined;
and converting the state equation with the output constraint into an unconstrained state equation by using the mapping relation.
Further, the state transition mapping relationship is:
Figure BDA0002896161850000034
Figure BDA0002896161850000035
Figure BDA0002896161850000036
wherein ,
Figure BDA0002896161850000037
/>
further, the determining the cooperative consistency error and the performance index function for the unconstrained state equation is as follows:
defining a collaborative consistency error as
Figure BDA0002896161850000038
wherein ,sd The track is expected for the collar machine to be tracked.
Defining the performance index function as
Figure BDA0002896161850000041
wherein ,
Figure BDA0002896161850000042
further, the determining the distributed hamilton-jacobian-bellman equation includes:
respectively determining a Hamiltonian function, an optimal performance index function and a distributed optimal cooperative control law function;
substituting the distributed optimal cooperative control law function into the Hamiltonian function to obtain a Hamiltonian-Jacobian-Belman equation.
Further, the method for approximately solving the hamilton-jacobian-bellman equation by adopting the single-network adaptive dynamic programming method comprises the following steps:
constructing an evaluation network on-line approximation optimal performance index function based on approximation capability of the neural network to the nonlinear function;
and obtaining an actual distributed optimal attitude control law based on the online approximation optimal performance index function.
According to a second aspect of the embodiments of the present disclosure, there is provided a multi-quad-rotor unmanned helicopter attitude consistency control system taking into account output constraints, which includes a processor unit, where the processor performs the steps of the above-mentioned multi-quad-rotor unmanned helicopter attitude consistency optimal control method taking into account output constraints.
Compared with the prior art, the beneficial effects of the present disclosure are:
(1) The scheme introduces a state conversion technology to generate an equivalent unconstrained nonlinear system, and converts the problem of limited optimal control of the output of the original four-rotor unmanned aerial vehicle attitude system into the problem of traditional unconstrained optimal control; aiming at the converted unconstrained equivalent system, the self-adaptive dynamic programming method is adopted to obtain the optimal controller, so that the attitude angle of the unmanned aerial vehicle is ensured to be kept within a safe range, and the control performance of the unmanned aerial vehicle is optimized.
(2) According to the scheme, the single-network structure is used for approximating the performance index function, so that the optimal cooperative control law is obtained, the single-evaluation network is used in the multi-four-rotor gesture system instead of the typical execution-evaluation double-network structure, so that the significance is more important, and the memory requirement and the calculation burden can be reduced.
Additional aspects of the disclosure will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the disclosure.
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The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate and explain the exemplary embodiments of the disclosure and together with the description serve to explain the disclosure, and do not constitute an undue limitation on the disclosure.
Fig. 1 is a structural model diagram of a quad-rotor unmanned helicopter according to a first embodiment of the present disclosure;
fig. 2 is a communication topology diagram of a multi-quad-rotor unmanned helicopter according to a first embodiment of the present disclosure;
FIG. 3 is a graph of roll angle tracking effects according to a first embodiment of the present disclosure;
FIG. 4 is a graph of pitch tracking effects as described in embodiment one of the present disclosure;
fig. 5 is a diagram showing a yaw angle tracking effect according to the first embodiment of the present disclosure.
Detailed Description
The disclosure is further described below with reference to the drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments in accordance with the present disclosure. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Embodiments of the present disclosure and features of embodiments may be combined with each other without conflict. Embodiment one:
the aim of the embodiment is to provide an optimal control method for the attitude consistency of the multi-quad-rotor unmanned helicopter considering output constraint.
A multi-quad-rotor unmanned helicopter attitude consistency optimal control method considering output constraint comprises the following steps:
s1: modeling the attitude physical characteristics of a single quadrotor unmanned aerial vehicle;
the four-rotor unmanned aerial vehicle studied in this embodiment has a coaxial structure of 4 rotors. The structure is shown in fig. 1, and 4 rotors are installed at the tail ends of the connecting rods in pairs to provide power for various flight tasks. The four-rotor unmanned aerial vehicle attitude dynamics model based on Euler angle description is established as follows:
Figure BDA0002896161850000061
Figure BDA0002896161850000062
wherein ,Θi ＝[φ i ,θ i ,ψ i ] T Represent Euler angles in the body coordinate system, and phi i ，θ i ，ψ i Respectively representing a roll angle, a pitch angle and a yaw angle in the posture of the quadrotor unmanned aerial vehicle; omega shape i ＝[w ix ,w iy ,w iz ] T Represents the angular velocity vector, w ix ，w iy ，w iz Respectively representing the rolling angle speed, the pitch angle speed and the yaw angle speed; i i ＝diag(I ix ,I iy ,I iz ) Representing positive definiteAn inertial matrix. M is M i ＝[u iφ ,u iθ ,u iψ ] T And the rotation torque input by the attitude angle of the four-rotor unmanned aerial vehicle is represented.
Conversion matrix
Figure BDA0002896161850000063
Then, the quad-rotor unmanned helicopter model may be further represented as
Figure BDA0002896161850000064
Figure BDA0002896161850000065
Figure BDA0002896161850000066
/>
Figure BDA0002896161850000067
Figure BDA0002896161850000068
Figure BDA0002896161850000069
Wherein the attitude angle phi i ，θ i ，ψ i Needs to meet the requirements of
Figure BDA00028961618500000610
Figure BDA00028961618500000611
The control objective of the embodiment is that the output of the four-rotor unmanned aerial vehicle attitude system can track given signals in an optimal mode, and meanwhile, the performance index function is minimum, so that all signals of the system are consistent and finally bounded.
S2, according to the physical characteristics of the single quadrotor unmanned aerial vehicle, converting an equation model obtained by modeling into a state equation as follows:
let x i1 ＝φ i ，x i2 ＝ω ix ，x i3 ＝θ i ，x i4 ＝ω iy ，x i5 ＝ψ i ，x i6 ＝ω iz . Thus, the state space of the four-rotor unmanned aerial vehicle attitude system is represented as
Figure BDA0002896161850000071
Figure BDA0002896161850000072
Figure BDA0002896161850000073
Figure BDA0002896161850000074
Figure BDA0002896161850000075
Figure BDA0002896161850000076
y i ＝[x i1 ,x i3 ,x i5 ] T
wherein ,yi Is output by the system and needs to be satisfied
Figure BDA0002896161850000077
Writing four-rotor unmanned aerial vehicle attitude dynamics model into the following compact structure
Figure BDA0002896161850000078
y i ＝[x i1 ,x i3 ,x i5 ] T
wherein ,
Figure BDA0002896161850000079
g(x i )＝diag[1/I ix ,1/I iy ,1/I iz ]；
u i ＝[u iφ u iθ u iψ ] T ；x i ＝[x i1 ,x i2 ,x i3 ,x i4 ,x i5 ,x i6 ] T
and S3, determining the communication topological structure of the multi-quad-rotor unmanned aerial vehicle as follows:
describing a communication connection relationship between unmanned aerial vehicles in formation by using a directed graph G= { V, E, A };
where v= {0, 1..n-1 } represents the set of nodes in graph G,
Figure BDA00028961618500000710
represents a set of directed edges in the graph, a= [ a ] ij ]∈R n×n A weight matrix representing a directed graph G;
if the plane i can receive information from plane j, then a ij =1 (i+.j), otherwise, a ij =0; defining the neighbor node of node i as N i = { j E v| (i, j) E, i+.j }, the ingress matrix D is d=diag { D } 1 ,...d N}, wherein
Figure BDA0002896161850000081
Suppose a ii =0, directed graph is severeConnecting grids; the connection between the assistant i and the collar is represented as a diagonal matrix b=diag { B 1 ,...,b N If the bureau i is able to receive information from the leader, b i =1, otherwise b i ＝0。
S4, converting a state equation with output constraint into an unconstrained state equation based on the barrier function, wherein the state equation is as follows:
to address the problem of output limitation, barrier function conversion techniques are introduced. A state transition map is defined as follows:
Figure BDA0002896161850000082
Figure BDA0002896161850000083
Figure BDA0002896161850000084
wherein ,
Figure BDA0002896161850000085
then the system dynamics without output constraints after conversion is
Figure BDA0002896161850000086
wherein ,si ＝[s i1 ,s i2 ,s i3 ,s i4 ,s i5 ,s i6 ] T ，
Figure BDA0002896161850000087
Figure BDA0002896161850000088
S5, aiming at an unconstrained state equation, defining a cooperative consistency error and a performance index function as follows:
defining a collaborative consistency error as
Figure BDA0002896161850000089
wherein ,sd The track is expected for the collar machine to be tracked.
Defining the performance index function as
Figure BDA00028961618500000810
wherein ,
Figure BDA00028961618500000811
s6, deducing a distributed Hamiltonian-Jacobian-Belman equation as follows:
the Hamiltonian may be defined as
Figure BDA0002896161850000091
/>
The optimal performance index function may be expressed as follows
Figure BDA0002896161850000092
Where U (Ω) is the set of allowed controls.
According to the optimality principle of Bellman, by
Figure BDA0002896161850000093
The distributed optimal cooperative control law can be obtained as follows:
Figure BDA0002896161850000094
substituting the optimal cooperative control law into Hamiltonian function, and adopting the corresponding distributed Hamiltonian-Jacobian-Bellman equation as
Figure BDA0002896161850000095
Note that the hamilton-jacobian-bellman equation is difficult to obtain its analytical solution, and to overcome this problem, a single network ADP method is used to approximate the solution.
S7, approximately solving a Hamiltonian-Jacobian-Bellman equation by adopting a single-network self-adaptive dynamic programming method, so as to obtain a distributed optimal attitude control law as follows:
based on the approximation capability of the neural network to the nonlinear function, constructing an evaluation network to approximate the optimal performance index function on line as follows
Figure BDA0002896161850000096
wherein ,wci ∈R l Representing ideal weight vector, sigma i (δ i )∈R l Representing the excitation function, l is the number of hidden layer neurons. Epsilon ci (δ i ) Representing the approximation error of the neural network. The approximation is
Figure BDA0002896161850000097
Figure BDA0002896161850000098
Representing an ideal weight vector w ci Is used for the estimation of the estimated value of (a).
The actual distributed optimal attitude control law u i Is that
Figure BDA0002896161850000101
The design evaluation network weight update law is as follows
Figure BDA0002896161850000102
wherein ,λi Representing the learning rate is a suitable positive constant.
Figure BDA0002896161850000103
Figure BDA0002896161850000104
In order to confirm the effectiveness of this example, simulation experiments were performed as follows:
in the simulation experiment, the control target is to track the attitude angle phi of the collar machine 0 ＝0.1sin(t)，θ 0 ＝0.1sin(t)，ψ 0 =0. According to the actual system, the system physical parameter in the model adopted in the example is selected as I ix ＝0.0081Nms -2 ，I iy ＝0.0142Nms -2 ，I iz ＝0.0081Nms -2 . The attitude angle limited parameter is selected as
Figure BDA0002896161850000105
Figure BDA0002896161850000106
Gesture initial value of each four-rotor unmanned aerial vehicle
s 1 ＝[0.1,-0.5,0.1,-0.5,0.1,-0.5] T ，s 2 ＝[0.2,0.5,0.2,0.5,0.2,0.5] T ，s 3 ＝[0.2,0.5,0.2,0.5,0.2,0.5] T ，s 4 ＝[0.25,1,0.25,1,0.25,1] T 。
Aiming at four-rotor unmanned aerial vehicle formation of a class of tractor-plane coordination mode, the scheme provides a distributed self-adaptive optimal attitude control scheme, so that the attitude angles of all planes tend to be consistent with the tractor, and meanwhile, the attitude angles of all unmanned aerial vehicles meet certain constraint conditions.
Analysis of results:
selecting a Liapunov function
Figure BDA0002896161850000107
Time derivative is obtained for it, thus obtaining +.>
Figure BDA0002896161850000108
Then the neural network weight error is +.>
Figure BDA0002896161850000109
And a synergistic consistency error delta i Is consistent and ultimately bounded, i.e., the neural network weights can converge to ideal values, and the attitude angles of all the wings can be consistent with the attitude angle of the leader.
As can be seen from fig. 3, 4 and 5, the roll angle, pitch angle and yaw angle of each of the wing can be kept consistent with those of the tractor, the tracking effect is good, and the amplitude of the output signal is kept within a safe range of + -0.15.
The embodiment realizes the consistency control of the multi-four-rotor unmanned aerial vehicle attitude system under the directional communication network based on the single-network self-adaptive dynamic programming method, and considers the problem of limited system output. And converting the four-rotor unmanned aerial vehicle attitude system with limited output into an unconstrained equivalent system through an obstacle function system conversion technology. Aiming at an unconstrained equivalent system, a self-adaptive dynamic programming method is adopted to solve the Hamiltonian-Jacobian-Bellman equation, so that an optimal control strategy considering output limitation is obtained. The proposal not only enables the attitude angle of the plane to be consistent with the collar plane in an optimal way, but also enables the output of the attitude system to be kept within a certain limited range.
The scheme of the disclosure provides a new system conversion method based on an obstacle function, which is different from the obstacle Lyapunov method in the prior art, can convert an output limited system into an equivalent system without output limitation, and provides convenience for processing other control problems through system equivalent conversion, thereby not only being feasible in theory, but also being easier to realize in practice.
Embodiment two:
the aim of the embodiment is to provide an optimal control system for the posture consistency of the multi-quad-rotor unmanned helicopter taking output constraint into consideration.
The system for optimally controlling the posture consistency of the multi-quad-rotor unmanned aerial vehicle by considering the output constraint comprises a processor unit, wherein the processor executes the steps of the method for optimally controlling the posture consistency of the multi-quad-rotor unmanned aerial vehicle by considering the output constraint.
The multi-quad-rotor unmanned helicopter attitude consistency optimization control method and system considering output constraint provided by the embodiment can be realized, and have wide application prospects.
The foregoing description of the preferred embodiments of the present disclosure is provided only and not intended to limit the disclosure so that various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
While the specific embodiments of the present disclosure have been described above with reference to the drawings, it should be understood that the present disclosure is not limited to the embodiments, and that various modifications and changes can be made by one skilled in the art without inventive effort on the basis of the technical solutions of the present disclosure while remaining within the scope of the present disclosure.

Claims (9)

1. The utility model provides a four rotor unmanned aerial vehicle gesture unanimous optimal control method of many considering output constraint which characterized in that includes:
modeling the attitude physical characteristics of a single quadrotor unmanned aerial vehicle;
according to the physical characteristics of a single quadrotor unmanned aerial vehicle, converting an equation model obtained by modeling into a state equation with output constraint;
determining a communication topological structure of the multi-quad-rotor unmanned helicopter, and converting a state equation with output constraint into an unconstrained state equation based on an obstacle function;
determining a cooperative consistency error and a performance index function of the cooperative consistency error aiming at an unconstrained state equation;
determining a distributed hamilton-jacobian-bellman equation, and adopting a single-network self-adaptive dynamic programming method to approximately solve the hamilton-jacobian-bellman equation so as to obtain a distributed optimal attitude control law;
the state transition mapping relation is as follows:
Figure FDA0004211105750000011
Figure FDA0004211105750000012
Figure FDA0004211105750000013
wherein ,
Figure FDA0004211105750000014
the state equation without output constraint after conversion is:
Figure FDA0004211105750000015
wherein ,si ＝[s i1 ,s i2 ,s i3 ,s i4 ,s i5 ,s i6 ] T ，
Figure FDA0004211105750000016
Figure FDA0004211105750000017
2. The optimal control method for the posture consistency of the multi-rotor unmanned aerial vehicle taking output constraint into consideration according to claim 1, wherein the modeling is performed on the posture physical characteristics of a single four-rotor unmanned aerial vehicle, the built model is a four-rotor unmanned aerial vehicle posture dynamics model based on Euler angle description, and the model is specifically expressed as follows:
Figure FDA0004211105750000021
Figure FDA0004211105750000022
wherein ,Θi ＝[φ i ,θ i ,ψ i ] T Represent Euler angles in the body coordinate system, and phi i ，θ i ，ψ i Respectively representing a roll angle, a pitch angle and a yaw angle in the posture of the quadrotor unmanned aerial vehicle; omega shape i ＝[ω ix ,ω iy ,ω iz ] T Represents the angular velocity vector, ω ix ，ω iy ，ω iz Respectively representing the rolling angle speed, the pitch angle speed and the yaw angle speed; i i ＝diag(I ix ,I iy ,I iz ) Representing a positive definite inertia matrix; m is M i ＝[u iφ ,u iθ ,u iψ ] T The method comprises the steps of representing the rotation torque input by the attitude angle of the quadrotor unmanned aerial vehicle; t (T) i Representing a transformation matrix, the transformation matrix being:
Figure FDA0004211105750000023
3. the optimal control method for the attitude consistency of the multi-quad-rotor unmanned helicopter taking output constraints into consideration according to claim 1, wherein the equation model obtained by modeling is converted into a state equation with the output constraints, and the state equation is expressed as follows:
Figure FDA0004211105750000024
y i ＝[x i1 ,x i3 ,x i5 ] T
wherein ,
Figure FDA0004211105750000025
g(x i )＝diag[1/I ix ,1/I iy ,1/I iz ]；
u i ＝[u iφ u iθ u iψ ] T ；x i ＝[x i1 ,x i2 ,x i3 ,x i4 ,x i5 ,x i6 ] T
here, x i1 ＝φ i ，x i2 ＝ω ix ，x i3 ＝θ i ，x i4 ＝ω iy ，x i5 ＝ψ i ，x i6 ＝ω iz And needs to meet
Figure FDA0004211105750000026
Figure FDA0004211105750000027
4. The method for optimally controlling the attitude consistency of the multi-quad-rotor unmanned helicopter taking output constraints into consideration according to claim 1, wherein the determining the communication topology of the multi-quad-rotor unmanned helicopter comprises the following steps:
describing a communication connection relationship between unmanned aerial vehicles in formation by using a directed graph G= { V, E, A }; where v= {0, 1..n-1 } represents the set of nodes in graph G,
Figure FDA0004211105750000033
represents a set of directed edges in the graph, a= [ a ] ij ]∈R n×n A weight matrix representing a directed graph G;
if the plane i can receive information from plane j, then a ij =1 (i+.j), otherwise, a ij =0; defining the neighbor node of node i as N i = { j E v| (i, j) E, i+.j }, the ingress matrix D is d=diag { D } 1 ,...d N}, wherein
Figure FDA0004211105750000031
Suppose a ii =0, directed graph is a strict join; the connection between the assistant i and the collar is represented as a diagonal matrix b=diag { B 1 ,...,b N If the bureau i can receive information from the leader, b i =1, otherwise b i ＝0。
5. The optimal control method for the attitude consistency of the multi-quad-rotor unmanned helicopter taking output constraints into consideration according to claim 1, wherein the step of converting the state equation with the output constraints into the unconstrained state equation comprises the following steps:
a state conversion mapping relation is predefined;
and converting the state equation with the output constraint into an unconstrained state equation by using the mapping relation.
6. The optimal control method for the attitude consistency of the multi-quad-rotor unmanned helicopter taking output constraints into consideration according to claim 1, wherein the determining of the collaborative consistency error and the performance index function for the unconstrained state equation is as follows:
defining a collaborative consistency error as
Figure FDA0004211105750000032
wherein ,sd The expected track of the collar machine is required to be tracked;
defining the performance index function as
Figure FDA0004211105750000041
/>
wherein ,
Figure FDA0004211105750000042
7. the optimal control method for the attitude consistency of a multi-quad-rotor unmanned helicopter taking into account output constraints according to claim 1, wherein said determining a distributed hamilton-jacobian-bellman equation comprises:
respectively determining a Hamiltonian function, an optimal performance index function and a distributed optimal cooperative control law function;
substituting the distributed optimal cooperative control law function into the Hamiltonian function to obtain a Hamiltonian-Jacobian-Belman equation.
8. The optimal control method for the attitude consistency of the multi-quad-rotor unmanned helicopter taking output constraints into consideration according to claim 1, wherein the method for approximately solving the hamilton-jacobian-bellman equation by adopting a single-network adaptive dynamic programming method comprises the following steps:
constructing an evaluation network on-line approximation optimal performance index function based on approximation capability of the neural network to the nonlinear function;
and obtaining an actual distributed optimal attitude control law based on the online approximation optimal performance index function.
9. A multi-quad-rotor unmanned helicopter attitude consistency optimal control system taking output constraints into consideration, comprising a processor unit, wherein the processor performs the steps of a multi-quad-rotor unmanned helicopter attitude consistency optimal control method taking output constraints into consideration as claimed in any of claims 1-6.
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