CN112859913A - Multi-quad-rotor unmanned aerial vehicle attitude consistency optimal control method considering output constraint - Google Patents
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Abstract
The utility model provides a multi-quad-rotor unmanned aerial vehicle attitude consistency optimal control method and system considering output constraints. Firstly, carrying out mathematical modeling on the attitude dynamic characteristics of the quad-rotor unmanned aerial vehicle; then, converting the system attitude control problem with output constraint into an optimal control problem under the unconstrained condition by adopting system conversion based on a barrier function; aiming at the transformed stateless constraint system, a single-network self-adaptive dynamic programming method is adopted to solve a distributed Hamilton-Jacobian-Bellman equation so as to obtain a distributed optimal attitude control law; the output of the attitude system of the multi-quad rotor unmanned aerial vehicle can effectively track the attitude signal of the leader and keep in the required safety range.
Description
Technical Field
The utility model belongs to the technical field of four rotor unmanned aerial vehicle control, especially, relate to a many four rotor unmanned aerial vehicle gesture unanimous optimal control method who considers 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 quad-rotor unmanned aerial vehicle is more and more popular in civil and military fields due to the characteristics of light weight, small size, strong maneuverability, strong adaptability and the like. Compare in the independent task of carrying out of single four rotor unmanned aerial vehicle, many four rotor unmanned aerial vehicle's cooperation has bigger advantage. For example, under the background that the high-rise fire extinguishing problem is obvious, the fire detection is carried out by utilizing a plurality of four-rotor unmanned aerial vehicles, and the fire-fighting robot is undoubtedly an effective solution for high-rise building fire fighting. However, in the high-rise building fire scene environment, due to the complexity of the building structure, the posture of the quad-rotor unmanned aerial vehicle is limited by the environment, and the quad-rotor unmanned aerial vehicle cannot swing by a large margin. Therefore, the method has very important practical significance in considering the attitude consistency control of the quadrotor unmanned aerial vehicle with a limited attitude angle.
The inventor finds that in recent years, the attitude control of a quad-rotor unmanned aerial vehicle with output constraint is widely concerned and obtains a plurality of important research results; however, most of the achievements do not consider the problem of optimal control, and meanwhile, because the output of the attitude system of the quad-rotor unmanned aerial vehicle needs to be met in a certain safety range, it is very difficult to design an effective optimal controller for the quad-rotor unmanned aerial vehicle.
Disclosure of Invention
The present disclosure provides an optimal control method for attitude consistency of a multi-quad-rotor unmanned aerial vehicle considering output constraints in order to solve the above problems.
According to a first aspect of the disclosed embodiments, there is provided a method for controlling attitude consistency of a multi-quad rotor unmanned aerial vehicle in consideration of output constraints, including:
modeling the attitude physical characteristics of a single quad-rotor unmanned aerial vehicle;
converting an equation model obtained by modeling into a state equation with constraints according to the physical characteristics of a single quad-rotor unmanned aerial vehicle;
determining a communication topological structure of the multi-quad-rotor unmanned aerial vehicle, and converting a state equation with output constraint into an unconstrained state equation based on a barrier function;
determining a cooperative consistency error and a performance index function thereof aiming at an unconstrained state equation;
determining a distributed Hamilton-Jacobian-Bellman equation, and adopting a single network adaptive dynamic programming method to approximately solve the Hamilton-Jacobian-Bellman equation so as to obtain a distributed optimal attitude control law.
Further, the physical attitude characteristics of the single quad-rotor unmanned aerial vehicle are modeled, the model is a quad-rotor unmanned aerial vehicle attitude dynamics model based on euler angle description, and the model is specifically represented as follows:
wherein ,Θi＝[φi,θi,ψi]TRepresenting the Euler angle in the coordinate system of the body, and phii，θi，ψiRespectively representing a rolling angle, a pitch angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle; omegai＝[ωix,ωiy,ωiz]TRepresenting the angular velocity vector, ωix，ωiy，ωizRespectively representing a rolling angular velocity, a pitch angular velocity and a yaw angular velocity; i isi＝diag(Iix,Iiy,Iiz) Representing a positive definite inertia matrix; mi＝[uiφ,uiθ,uiψ]TRepresenting the rotation torque input by the attitude angle of the quad-rotor unmanned aerial vehicle; t isiRepresenting a transformation matrix, the transformation matrix being:
further, the equation model obtained by modeling is converted into a state equation with constraints, and the state equation is expressed as follows:
yi＝[xi1,xi3,xi5]T
wherein ,
g(xi)＝diag[1/Iix,1/Iiy,1/Iiz]；
ui＝[uiφuiθuiψ]T；xi＝[xi1,xi2,xi3,xi4,xi5,xi6]T
here, xi1＝φi，xi2＝ωix，xi3＝θi，xi4＝ωiy，xi5＝ψi，xi6＝ωizAnd need to satisfy
Further, the determining the communication topology of the multi-quad-rotor unmanned aerial vehicle comprises the following steps:
describing a communication connection relation between the unmanned aerial vehicles in the formation by using a directed graph G ═ { V, E, A }; where V ═ 0, 1., N-1} represents the set of nodes in graph G,
representing a set of directed edges in the diagram, A ═ aij]∈Rn×nA weight matrix representing the directed graph G;
if a wing plane i can receive information from a wing plane j, then aij1(i ≠ j), otherwise, aij0; defining neighbor nodes of node i as NiWhere { j ∈ V | (i, j) ∈ E, i ≠ j }, and the in-degree matrix D is D ═ diag { D ≠ j }1,...dN}, wherein 
Suppose aiiWhen the value is 0, the directed graph is strictly connected; the connection between a wing plane i and a leader is represented by a diagonal matrix B ═ diag { B }1,...,bNIf a bureaucratic i is able to receive information from the leader, then b i1, otherwise bi＝0。
Further, the converting the state equation with the output constraint into the unconstrained state equation comprises the following steps:
predefining a state conversion mapping relation;
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 as follows:
wherein ,
further, for the unconstrained equation of state, determining the cooperative consistency error and the performance indicator function are as follows:
defining a cooperative consistency error as
wherein ,sdThe trajectory is desired for the leader that needs to be tracked.
Defining a performance indicator function as
wherein ,
further, the determining a distributed hamilton-jacobi-bellman equation comprises:
respectively determining a Hamiltonian function, an optimal performance index function and a distributed optimal cooperative control law function;
and substituting the distributed optimal cooperative control law function into the Hamiltonian to obtain a Hamiltonian-Jacobi-Bellman equation.
Further, the approximate solution of the hamilton-jacobi-bellman equation by using the single network adaptive dynamic programming method includes:
constructing an evaluation network to approach an optimal performance index function on line based on the approximation capability of a neural network to a 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 posture-consistent control system of a multi-quad-rotor unmanned aerial vehicle considering output constraints, which includes a processor unit, wherein the processor unit executes the steps of the posture-consistent optimal control method of a multi-quad-rotor unmanned aerial vehicle considering output constraints.
Compared with the prior art, the beneficial effect of this disclosure is:
(1) according to the scheme, a state conversion technology is introduced to generate an equivalent unconstrained nonlinear system, and the output limited optimal control problem of the original posture system of the quad-rotor unmanned aerial vehicle is converted into the traditional unconstrained optimal control problem; aiming at the converted unconstrained equivalent system, the optimal controller is obtained by adopting a self-adaptive dynamic programming method, so that the attitude angle of the unmanned aerial vehicle is kept within a safety range, and the control performance of the unmanned aerial vehicle is optimal.
(2) According to the scheme disclosed by the disclosure, the performance index function is approximated by using the single network structure, the optimal cooperative control law is obtained, the single evaluation network is used in a multi-quad rotor attitude system instead of a typical execution-evaluation dual-network structure, the significance is higher, and the memory requirement and the calculation burden can be reduced.
Advantages of 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 embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.
Fig. 1 is a structural model diagram of a quad-rotor drone according to a first embodiment of the disclosure;
fig. 2 is a communication topology diagram of a multi-quad-rotor drone according to a first embodiment of the disclosure;
FIG. 3 is a graph illustrating the effects of roll angle tracking according to one embodiment of the present disclosure;
fig. 4 is a diagram illustrating a pitch tracking effect according to a first embodiment of the disclosure;
fig. 5 is a diagram illustrating the effect of tracking the yaw angle according to the first embodiment of the disclosure.
Detailed Description
The present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the 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 example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict. The first embodiment is as follows:
the purpose of this embodiment is to provide a many four rotor unmanned aerial vehicle gesture uniformity optimal control method of considering output constraint.
A multi-quad rotor unmanned aerial vehicle attitude consistency optimization control method considering output constraints comprises the following steps:
s1: modeling the attitude physical characteristics of a single quad-rotor unmanned aerial vehicle;
the quad-rotor unmanned aerial vehicle studied in this embodiment has a coaxial structure with 4 rotors. The structure is shown in figure 1, 4 rotors are arranged at the tail ends of connecting rods in pairs to provide power for various flight missions. The method comprises the following steps of establishing a four-rotor unmanned aerial vehicle attitude dynamics model based on Euler angle description:
wherein ,Θi＝[φi,θi,ψi]TRepresenting the Euler angle in the coordinate system of the body, and phii，θi，ψiRespectively representing a rolling angle, a pitch angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle; omegai＝[wix,wiy,wiz]TDenotes the angular velocity vector, wix，wiy，wizRespectively indicating rollsAngular velocity, pitch angular velocity and yaw angular velocity; i isi＝diag(Iix,Iiy,Iiz) Representing a positive definite inertia matrix. Mi＝[uiφ,uiθ,uiψ]TThe rotation torque that represents four rotor unmanned aerial vehicle attitude angle input.
Transformation matrix
Then, the four-rotor unmanned aerial vehicle model can be further represented as
Wherein the attitude angle phii，θi，ψiNeed to satisfy
The control target of the embodiment is that the output of the multi-quad-rotor unmanned aerial vehicle attitude system can track a given signal in an optimal mode, and meanwhile, the performance index function is minimum, so that all signals of the system are consistent and finally bounded.
And S2, converting the equation model obtained by modeling into a state equation according to the physical characteristics of the single four-rotor unmanned aerial vehicle as follows:
let xi1＝φi，xi2＝ωix，xi3＝θi，xi4＝ωiy，xi5＝ψi，xi6＝ωiz. Thus, the state space of the quad-rotor drone attitude system is represented as
yi＝[xi1,xi3,xi5]T
wherein ,yiIs output by the system and needs to be satisfied
Writing a four-rotor unmanned aerial vehicle attitude dynamics model into the following compact structure
yi＝[xi1,xi3,xi5]T
wherein ,
g(xi)＝diag[1/Iix,1/Iiy,1/Iiz]；
ui＝[uiφuiθuiψ]T；xi＝[xi1,xi2,xi3,xi4,xi5,xi6]T
s3, determining the communication topology of the multi-quad-rotor unmanned aerial vehicle as follows:
describing a communication connection relation between the unmanned aerial vehicles in the formation by using a directed graph G ═ { V, E, A };
where V ═ 0, 1., N-1} represents the set of nodes in graph G,
representing a set of directed edges in the diagram, A ═ aij]∈Rn×nA weight matrix representing the directed graph G;
if a wing plane i can receive information from a wing plane j, then aij1(i ≠ j), otherwise, aij0; defining neighbor nodes of node i as NiWhere { j ∈ V | (i, j) ∈ E, i ≠ j }, and the in-degree matrix D is D ═ diag { D ≠ j }1,...dN}, wherein 
Suppose aiiWhen the value is 0, the directed graph is strictly connected; the connection between a wing plane i and a leader is represented by a diagonal matrix B ═ diag { B }1,...,bNIf a bureaucratic i is able to receive information from the leader, then b i1, otherwise bi＝0。
S4, converting the state equation with the output constraint into an unconstrained state equation based on the barrier function as follows:
to deal with the output limitation problem, barrier function conversion techniques are introduced. One state transition mapping is defined as follows:
wherein ,
then the system dynamics after conversion without output constraints are
wherein ,si＝[si1,si2,si3,si4,si5,si6]T，
S5, for the unconstrained equation of state, the co-ordination consistency error and performance indicator function is defined as follows:
defining a cooperative consistency error as
wherein ,sdThe trajectory is desired for the leader that needs to be tracked.
Defining a performance indicator function as
wherein ,
s6, deducing a distributed Hamilton-Jacobian-Bellman equation as follows:
the Hamiltonian can be defined as
The optimal performance indicator function can be expressed in the form
Where U (Ω) is a set of allowed controls.
According to the principle of optimality of Bellman, composed of
The distributed optimal cooperative control law can be obtained as follows:
substituting the optimal cooperative control law into a Hamiltonian, wherein the corresponding distributed Hamiltonian-Jacobi-Bellman equation is
It is noted that the Hamilton-Jacobian-Bellman equation is difficult to obtain an analytic solution, and in order to overcome the problem, a single-network ADP method is adopted for approximate solution.
S7, adopting a single network self-adaptive dynamic programming method to approximately solve the Hamilton-Jacobi-Bellman equation, thereby obtaining the distributed optimal attitude control law as follows:
based on the approximation capability of the neural network to the nonlinear function, the online approximation optimal performance index function of the evaluation network is constructed as
wherein ,wci∈RlRepresenting the ideal weight vector, σi(δi)∈RlRepresents the excitation function, and l is the number of hidden layer neurons. Epsilonci(δi) Representing the approximation error of the neural network. Approximated by
Representing an ideal weight vector wciAn estimate of (d).
The actual distributed optimal attitude control law uiIs composed of
The update law of the design evaluation network weights is as follows
wherein ,λiThe learning rate is a proper normal number.
To confirm the effectiveness of this example, a simulation experiment was performed as follows:
in the simulation experiment, the control target is tracking the attitude angle phi of the leader0＝0.1sin(t)，θ0＝0.1sin(t)，ψ 00. According to the actual system, the physical parameters of the system in the model adopted in the embodiment are selected as Iix＝0.0081Nms-2，Iiy＝0.0142Nms-2，Iiz＝0.0081Nms-2. The attitude angle limited parameter is selected as
Attitude initial value of each quad-rotor unmanned aerial vehicle
s1＝[0.1,-0.5,0.1,-0.5,0.1,-0.5]T，s2＝[0.2,0.5,0.2,0.5,0.2,0.5]T，s3＝[0.2,0.5,0.2,0.5,0.2,0.5]T，s4＝[0.25,1,0.25,1,0.25,1]T。
The scheme provides a distributed self-adaptive optimal attitude control scheme aiming at formation of four-rotor unmanned aerial vehicles in a leader-leader cooperative mode, so that the attitude angle of each leader tends to be consistent with that of the leader, and meanwhile, the attitude angle of each unmanned aerial vehicle meets certain constraint conditions.
And (4) analyzing results:
selecting Lyapunov functions
As can be seen from fig. 3, 4 and 5, the roll angle, pitch angle and yaw angle of each wing plane can be kept consistent with the wing plane, the tracking effect is good, and the amplitude of the output signal is kept within a range of ± 0.15 safety.
The embodiment realizes the consistency control of the multi-quad-rotor unmanned aerial vehicle attitude system under the directed communication network based on the single-network self-adaptive dynamic planning method, and considers the problem of limited system output. And (3) converting the attitude system of the quad-rotor unmanned aerial vehicle with limited output into an unconstrained equivalent system by a barrier function system conversion technology. Aiming at an unconstrained equivalent system, a self-adaptive dynamic programming method is adopted to solve a Hamilton-Jacobi-Bellman equation, so that an optimal control strategy considering output limitation is obtained. The proposal not only leads the attitude angle of the wing plane to be consistent with the leader in an optimal way, but also leads the output of the attitude system to be kept in a certain limited range.
The scheme disclosed by the disclosure provides a novel system conversion method based on barrier functions, which is different from the barrier Lyapunov method in the prior art, can convert an output-limited system into an equivalent system without output limitation, provides convenience for processing other control problems through system equivalent conversion, has feasibility in theory, and is easier to realize in practice.
Example two:
the purpose of this embodiment is to provide a many four rotor unmanned aerial vehicle consistent in attitude optimal control system who considers output constraint.
A multi-quad-rotor unmanned aerial vehicle attitude consistency optimization control system considering output constraints comprises a processor unit, wherein the processor executes the steps of the multi-quad-rotor unmanned aerial vehicle attitude consistency optimization control method considering the output constraints.
The multi-quad-rotor unmanned aerial vehicle attitude consistency optimization control method and system considering the output constraint can be realized, and have a wide application prospect.
The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.
Claims (10)
1. The utility model provides a many four rotor unmanned aerial vehicle gesture unanimous optimal control method of considering output constraint which characterized in that includes:
modeling the attitude physical characteristics of a single quad-rotor unmanned aerial vehicle;
converting an equation model obtained by modeling into a state equation with constraints according to the physical characteristics of a single quad-rotor unmanned aerial vehicle;
determining a communication topological structure of the multi-quad-rotor unmanned aerial vehicle, and converting a state equation with output constraint into an unconstrained state equation based on a barrier function;
determining a cooperative consistency error and a performance index function thereof aiming at an unconstrained state equation;
determining a distributed Hamilton-Jacobian-Bellman equation, and adopting a single network adaptive dynamic programming method to approximately solve the Hamilton-Jacobian-Bellman equation so as to obtain a distributed optimal attitude control law.
2. The attitude-consistent optimal control method for multiple quad-rotor unmanned aerial vehicles considering output constraints as claimed in claim 1, wherein the physical characteristics of the attitude of the single quad-rotor unmanned aerial vehicle are modeled, and the modeled model is a quad-rotor unmanned aerial vehicle attitude dynamics model based on Euler angle description, and the model is specifically represented as follows:
wherein ,Θi＝[φi,θi,ψi]TRepresenting the Euler angle in the coordinate system of the body, and phii，θi，ψiRespectively representing a rolling angle, a pitch angle and a yaw angle in the attitude of the quad-rotor unmanned aerial vehicle; omegai＝[ωix,ωiy,ωiz]TRepresenting the angular velocity vector, ωix，ωiy，ωizRespectively representing a rolling angular velocity, a pitch angular velocity and a yaw angular velocity; i isi＝diag(Iix,Iiy,Iiz) Representing a positive definite inertia matrix; mi＝[uiφ,uiθ,uiψ]TRepresenting the rotation torque input by the attitude angle of the quad-rotor unmanned aerial vehicle; t isiRepresenting a transformation matrix, the transformation matrix being:
3. the attitude-consistent optimal control method for the multi-quad-rotor unmanned aerial vehicle considering the output constraints as claimed in claim 1, wherein the equation model obtained by modeling is converted into a state equation with constraints, and the state equation is expressed as follows:
yi＝[xi1,xi3,xi5]T
wherein ,
g(xi)＝diag[1/Iix,1/Iiy,1/Iiz]；
ui＝[uiφuiθuiψ]T；xi＝[xi1,xi2,xi3,xi4,xi5,xi6]T
here, xi1＝φi，xi2＝ωix，xi3＝θi，xi4＝ωiy，xi5＝ψi，xi6＝ωizAnd need to satisfy
4. The attitude-consistent optimal control method for multiple quad-rotor drones considering output constraints as claimed in claim 1, wherein the determining the communication topology of the multiple quad-rotor drones comprises the following steps:
describing a communication connection relation between the unmanned aerial vehicles in the formation by using a directed graph G ═ { V, E, A }; where V ═ 0, 1., N-1} represents the set of nodes in graph G,
representing a set of directed edges in the diagram, A ═ aij]∈Rn×nA weight matrix representing the directed graph G;
if a wing plane i can receive information from a wing plane j, then aij1(i ≠ j), otherwise, aij0; defining neighbor nodes of node i as NiWhere { j ∈ V | (i, j) ∈ E, i ≠ j }, and the in-degree matrix D is D ═ diag { D ≠ j }1,...dN}, wherein 
Suppose aiiWhen the value is 0, the directed graph is strictly connected; the connection between a wing plane i and a leader is represented by a diagonal matrix B ═ diag { B }1,...,bNIf a bureaucratic i is able to receive information from the leader, then bi1, otherwise bi＝0。
5. The attitude-consistent optimal control method for multi-quad rotor unmanned aerial vehicles considering output constraints as claimed in claim 1, wherein the step of converting the state equation with the output constraints into an unconstrained state equation comprises the steps of:
predefining a state conversion mapping relation;
and converting the state equation with the output constraint into an unconstrained state equation by using the mapping relation.
6. The attitude-consistent optimal control method for multiple quad-rotor unmanned aerial vehicles considering output constraints as claimed in claim 1, wherein the state transformation mapping relation is:
wherein ,
7. the attitude-consistent optimal control method for multi-quad-rotor unmanned aerial vehicle considering output constraints as claimed in claim 1, wherein the determining of the cooperative consistency error and the performance index function for the unconstrained equation of state is as follows:
defining a cooperative consistency error as
wherein ,sdA track is expected for a leader needing to be tracked;
defining a performance indicator function as
wherein ,
8. the attitude-consistent optimal control method for multiple-quad-rotor unmanned aerial vehicles considering output constraints as claimed in claim 1, wherein the determining distributed hamilton-jacobi-bellman equations comprises:
respectively determining a Hamiltonian function, an optimal performance index function and a distributed optimal cooperative control law function;
and substituting the distributed optimal cooperative control law function into the Hamiltonian to obtain a Hamiltonian-Jacobi-Bellman equation.
9. The attitude-consistent optimal control method for multiple-quad-rotor unmanned aerial vehicle considering output constraints as claimed in claim 1, wherein the approximate solution of Hamilton-Jacobian-Bellman equation by using a single network adaptive dynamic programming method comprises:
constructing an evaluation network to approach an optimal performance index function on line based on the approximation capability of a neural network to a nonlinear function;
and obtaining an actual distributed optimal attitude control law based on the online approximation optimal performance index function.
10. A multi-quad-rotor drone attitude-coherent optimal control system considering output constraints, comprising a processor unit, characterized in that said processor performs the steps of a multi-quad-rotor drone attitude-coherent optimal control method considering output constraints according to any one of claims 1 to 7.
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Cited By (3)
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| CN113885548A (en) * | 2021-10-28 | 2022-01-04 | 南京邮电大学 | Many four rotor unmanned aerial vehicle output restraint state unanimous game controller |
| CN114415734A (en) * | 2022-03-31 | 2022-04-29 | 天津大学 | Four-rotor unmanned aerial vehicle formation reconfiguration control system based on ADP and obstacle avoidance mechanism |
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