CN112882493A - Cluster cooperative deployment method based on distributed optimal energy MPC - Google Patents
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Abstract
The invention discloses a cluster cooperative deployment method based on distributed optimal energy MPC, which is characterized in that a plurality of unmanned aerial vehicles are communicated in an ad hoc network, and each unmanned aerial vehicle independently generates a control instruction to realize cooperative deployment of an unmanned aerial vehicle cluster. The cluster cooperative deployment method based on the distributed optimal energy MPC is based on a distributed model predictive control method, an optimal control equation is established, a suboptimal analytic solution is obtained by solving a Hamilton equation, the calculated amount in the optimization process is greatly reduced, the generation of a real-time track is realized, and the cluster cooperative deployment method has the advantages of no need of central server control, large number of cluster unmanned aerial vehicles, high unmanned aerial vehicle density and the like.
Description
Technical Field
The invention relates to a cluster cooperative deployment method, in particular to a cluster cooperative deployment method based on distributed optimal energy MPC, and belongs to the field of unmanned aerial vehicle control.
Background
The scheme of the multi-unmanned aerial vehicle for cooperatively executing the task is widely used for various tasks, and the multi-unmanned aerial vehicle has higher task execution efficiency in cooperation compared with the single unmanned aerial vehicle for executing the task.
The conventional coordination scheme is usually started to be executed after the unmanned aerial vehicle approaches the target or the moving speed of the targeted task target is slow, however, when the task faces a wide environment, especially for an air-sea task environment, the range of the unmanned aerial vehicle executing the task reaches thousands of kilometers, the distance between the unmanned aerial vehicle and the task target is long, and when the task target has high mobility, when the conventional coordination scheme is used, the flight trajectory of the unmanned aerial vehicle in the process of approaching the task target is poor, a large amount of fuel is wasted, a situation that the unmanned aerial vehicle does not approach the task target yet and starts to execute the coordination task mode may occur, fuel is exhausted, and subsequent tasks cannot be performed.
Traditional collaborative scheme, adopt central server to generate all unmanned aerial vehicle's control command mostly, central server carries out wireless communication with unmanned aerial vehicle in real time, obtain the target location that each unmanned aerial vehicle's position and unmanned aerial vehicle detected, generate each unmanned aerial vehicle's control command according to positional information, transmit control command to each unmanned aerial vehicle through wireless communication's mode again, thereby control all unmanned aerial vehicle's flight state, however, when the target distance server is far away, communication between central server and the unmanned aerial vehicle can receive the influence, lead to data transmission stability to descend, and then lead to the control command error that central server generated, and control frequency descends, seriously influence the execution effect of collaborative task.
In addition, in the conventional control method, data are transmitted back to the server by the unmanned aerial vehicle, and then the server generates a control command to transmit back to the unmanned aerial vehicle, so that a large time delay is generated, and when a target moves rapidly, the unmanned aerial vehicle cannot accurately contact the target.
In addition, considering the target resource demand, sometimes need the multimachine to contact with the target simultaneously, realize the saturation interaction, traditional unmanned aerial vehicle cooperative scheme is provided by central server, owing to there is great control error, for guaranteeing unmanned aerial vehicle safety, unmanned aerial vehicle distance each other is far away, causes the intensive degree of unmanned aerial vehicle lower, is difficult to realize the saturation interaction.
Therefore, a cluster cooperative deployment method which is independent of a central server, large in task adaptation range and high in task target mobility is urgently needed to be designed.
Disclosure of Invention
In order to overcome the problems, the inventor of the invention carries out intensive research and designs a cluster cooperative deployment method based on a distributed optimal energy MPC, wherein through the self-networking communication of a plurality of unmanned aerial vehicles, each unmanned aerial vehicle independently generates a control instruction to realize the cooperative deployment of an unmanned aerial vehicle cluster.
The method comprises the following steps:
s1, carrying out self-networking communication on a plurality of unmanned aerial vehicles;
s2, the unmanned aerial vehicle generates respective predicted tracks and transmits the respective predicted tracks and state information to the adjacent unmanned aerial vehicle;
s3, each unmanned aerial vehicle generates an optimal track of the unmanned aerial vehicle at the next moment according to the predicted track of the adjacent unmanned aerial vehicle;
and S4, generating a control command of the next moment by each unmanned aerial vehicle according to the optimal track, and repeating the steps S2 and S3 to realize the continuous autonomous control of each unmanned aerial vehicle.
In step S1, the unmanned aerial vehicle ad hoc network communication means that the unmanned aerial vehicles communicate with each other by using Zigbee technology networking
In step S2, the predicted trajectory is a trajectory planned by the drone based on the detected target position information and the state information of the drone itself
In step S3, an optimal trajectory is obtained by solving a distributed energy optimal control model expressed by the form of an objective function:
where the index i indicates the different drones, t indicates the time,
t0representing the initial time of the prediction time domain, tfRepresenting a terminal time of a prediction time domain;
ui(t) represents the control acceleration of the drone, which is the control quantity of the flight state of the drone, whose two components on the horizontal plane are represented by [ u [ u ] ]xi(t),uyi(t)]', superscript' denotes transpose;
φ(xi,tf) And a terminal cost function representing a prediction time domain, wherein the function value represents that the unmanned aerial vehicle is enabled to reach a desired state at the prediction terminal.
Further, the terminal cost φ (x)i,tf) The specific form of (b) may be expressed as: phi (x)i,tf)＝wvcφvc(xi,tf)+wvaφva(xi,tf)+waφa(xi,tf) (IV)
Wherein, wvcWeight, w, representing cluster speed controlvaWeight, w, representing velocity consistencyaWeights representing a multimachine aggregation;
φvc(xi,tf) Is a cluster speed control term, phiva(xi,tf) Is a multiple machine speed uniform term, phia(xi,tf) Is a multi-machine aggregation item。
According to the invention, the cluster speed control term phivc(xi,tf) Expressed as:
[vxd,vyd]' indicates the desired flight direction, i.e. the direction of flight towards the target,
multiple machine speed uniformity term phiva(xi,tf) Expressed as:
[vxavg,vyavg]' denotes the average speed of a plurality of drones.
Is a multi-machine aggregation term phia(xi,tf) Expressed as:
l is a parameter related to distance.
Preferably, the drone speed satisfies the constraint:
multiple machine speed uniformity term phiva(xi,tf) The following constraints are satisfied:
wherein the content of the first and second substances,
representing the maximum acceleration that the drone can reach.
According to the invention, said solving for the distributed energy optimal control model is carried out in the following way,
constructing a Hamiltonian by a distributed energy optimal control model:
wherein u isi(t) is a control quantity [ u ]xi(t),uyi(t)]′，vi(t) is the velocity [ v ]xi(t),vyi(t)]′，
And
is a co-modal variable that is,
the method is obtained by utilizing a minimum value principle:
the optimal conditions are as follows:
the state equation is as follows:
the collaborative equation:
the cross-section conditions are as follows:
boundary conditions:
and (3) simultaneously establishing an optimal condition equation, a state equation and a synergetic equation to obtain an integral coefficient vector:
wherein [ a ]xi,ayi]′，[bxi,byi]′，[cxi,cyi]' and [ dxi,dyi]' is the integral coefficient to be solved;
solving the integral coefficient vector by using a numerical solver according to the cross section condition and the boundary condition to obtain [ a ]xi,ayi]′，[bxi,byi]′，[cxi,cyi]' and [ dxi,dyi]' these four integral coefficients, to obtain the control acceleration u of the drone itself at the next momentiAnd (t), the track calculated by controlling the acceleration is the optimal track.
In step S4, each drone generates a control command at the next time according to the control acceleration of the drone itself at the next time obtained in step S3, and the steps S2 and S3 are repeated, so that continuous autonomous control of each drone can be completed, and cooperative deployment is realized.
The invention has the advantages that:
(1) according to the cluster cooperative deployment method based on the distributed optimal energy MPC, provided by the invention, a Zigbee ad hoc network communication network is adopted as a communication medium between multiple machines and between the machines and a ground station, and each unmanned aerial vehicle is a mobile base station, so that the capacity of a multi-machine system can be effectively improved;
(2) according to the cluster cooperative deployment method based on the distributed optimal energy MPC, which is provided by the invention, an optimal control equation is established based on a distributed model predictive control method, a suboptimal analytic solution is obtained by solving a Hamilton equation, the calculated amount in the optimization process is greatly reduced, and the generation of a real-time track is realized;
(3) according to the cluster cooperative deployment method based on the distributed optimal energy MPC, the control of a central server is not needed, the flight trajectory is short, and the density of unmanned aerial vehicles is high.
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FIG. 1 is a schematic flow chart of a cluster cooperative deployment method based on distributed optimal energy MPC according to a preferred embodiment of the present invention;
fig. 2 shows the effect of the simulation experiment in example 1.
Detailed Description
The invention is explained in more detail below with reference to the figures and examples. The features and advantages of the present invention will become more apparent from the description.
The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration. Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
The invention provides a cluster cooperative deployment method based on distributed optimal energy MPC, which is characterized in that a plurality of unmanned aerial vehicles are communicated in an ad hoc network, and each unmanned aerial vehicle independently generates a control instruction to realize cooperative deployment of an unmanned aerial vehicle cluster.
By means of autonomous generation of control instructions by the unmanned aerial vehicles, namely generation of the control instructions based on the distributed mode, a mode that the central server generates the control instructions of the unmanned aerial vehicles in a traditional cooperative deployment method is abandoned, and the defects of high delay, poor stability and the like of the central server cooperative control method are overcome.
Specifically, the cluster cooperative deployment method based on the distributed optimal energy MPC includes the following steps:
s1, carrying out self-networking communication on a plurality of unmanned aerial vehicles;
s2, the unmanned aerial vehicle generates respective predicted tracks and transmits the respective predicted tracks and state information to the adjacent unmanned aerial vehicle;
s3, each unmanned aerial vehicle generates an optimal track of the unmanned aerial vehicle at the next moment according to the predicted track of the adjacent unmanned aerial vehicle;
and S4, generating a control command of the next moment by each unmanned aerial vehicle according to the optimal track, and repeating the steps S2 and S3 to realize the continuous autonomous control of each unmanned aerial vehicle.
In step S1, the unmanned aerial vehicle ad hoc network communication means that the unmanned aerial vehicles communicate with each other by using Zigbee technology networking.
The Zigbee technology is a wireless communication technology applied to short distance and low speed, has the characteristics of low cost, low power consumption and low transmission rate, supports various network topological structures such as star, tree and mesh, and is very suitable for the application occasions of multi-unmanned aerial vehicle cooperative tasks. In addition, the theoretical capacity of the Zigbee network is 65000 nodes, and a cluster consisting of hundreds of unmanned aerial vehicles can be completely loaded, and the multi-machine communication range can be expanded to thousands of meters through the self-networking communication of Zigbee.
Through the ad hoc network communication, the adjacent unmanned aerial vehicles can exchange the state information of each other and the target position information detected by the unmanned aerial vehicles quickly and accurately.
The state information includes position information, speed information and acceleration information of the unmanned aerial vehicle.
In step S2, the predicted trajectory refers to a trajectory planned by the drone according to the detected target position information and the state information of the drone itself, and a specific trajectory planning method may adopt any known standard method, such as a proportional guidance method, which is not particularly limited in the present invention.
When a certain unmanned aerial vehicle does not detect the target position information, the unmanned aerial vehicle can acquire the target position information detected by the adjacent unmanned aerial vehicle through the communication network, so that the predicted track is planned by combining the state information of the unmanned aerial vehicle.
Because the calculation capability of the airborne computer of the unmanned aerial vehicle is weak, the calculation amount of the conventional cooperative control algorithm is large, and the unmanned aerial vehicle is difficult to apply to the unmanned aerial vehicle.
In step S3, an optimal trajectory is obtained by solving the distributed energy optimal control model.
Specifically, the distributed energy optimal control model may be represented by the form of an objective function:
where subscript i denotes different drones, t denotes time, t0Representing the initial time of the prediction time domain, tfRepresenting a terminal time of a prediction time domain;
ui(t) represents the control acceleration of the drone, which is the control quantity of the flight state of the drone, whose two components on the horizontal plane are represented by [ u [ u ] ]xi(t),uyi(t)]', superscript' denotes transpose;
φ(xi,tf) A terminal cost function representing a prediction time domain, wherein the function value represents that the unmanned aerial vehicle is enabled to reach a desired state at the prediction terminal;
further, the air conditioner is provided with a fan,
According to the invention, [ u ] in formula (I)xi(t),uyi(t)]' can be obtained from a double integral system dynamics model:
wherein，[pxi(t),pyi(t)]′，[vxi(t),vyi(t)]' separately representing the position and velocity of drone i, in the present invention, for a more concise representation, the position and velocity of drone i are noted as state xi(t) then there are
xi(t)＝[pxi(t),pyi(t),vxi(t),vyi(t)]' (III)
According to the invention, the terminal cost phi (x) in equation (one)i,tf) The specific form of (b) may be expressed as:
φ(xi,tf)＝wvcφvc(xi,tf)+wvaφva(xi,tf)+waφa(xi,tf) (IV)
Wherein, wvcWeight, w, representing cluster speed controlvaWeight, w, representing velocity consistencyaRepresenting the weight of the multimachine aggregation.
According to the present invention, in order to more conveniently adjust the attention of the controller to speed control, speed consistency and multi-machine aggregation, preferably, the three parameters can be expressed as:
wherein k isd，kvIs the velocity gain, kpIs a position gain, more preferably, kd，kvAnd kpThe values are as follows:
| variables of | (symbol) | Value of |
| Position gain | kp | 1.5 |
| Velocity gain 1 | kv | 1.0 |
| Velocity gain 2 | kd | 3.0 |
Further, phi in the formula (IV)vc(xi,tf) Is the cluster speed control term:
[vxd,vyd]' denotes the desired flight direction, i.e. the direction of flight towards the target, and the drone speed satisfies the constraint:
Phi in the formula (IV)va(xi,tf) The multi-unmanned aerial vehicle is a multi-aircraft speed consistent item, and the multi-unmanned aerial vehicle is prompted to form a consistent speed through the multi-aircraft speed consistent item, and the speed is cooperatively flown to a target, which can be expressed as:
in the formula (VII) [ vxavg,vyavg]' represents the average speed of a plurality of drones, obtained by:
wherein a represents a set of drones, a ═ 1,2, …, N };
h represents the communication range of the unmanned aerial vehicle;
Ni(t) represents a set of adjacent drones to drone i, in the present invention, all other drones within the communication range of a drone are considered to be drones adjacent to this drone, a different drone in the set is represented by j, [ s ]xij(t),syij(t)]' representing the relative position vectors of drone i and drone j, can be obtained by:
further, phi in the formula (IV)va(xi,tf) The following constraints are also satisfied:
wherein the content of the first and second substances,
representing the maximum acceleration that the drone can reach.
Phi in the formula (IV)a(xi,tf) Is a multi-machine aggregation item, through which a plurality of unmanned aerial vehicles are promoted to aggregate into a group, avoiding separation, can be expressed as:
the scalar L is a parameter related to distance and used for controlling the distribution density of the multiple unmanned aerial vehicles, generally speaking, the value of L is 5L-10L, wherein L is the wheel base of the rotor unmanned aerial vehicle, and when the volume of a task target is large or the positioning accuracy of the target is low, the value of L is large so as to reduce the distribution density of the unmanned aerial vehicles and enlarge the interception range of the unmanned aerial vehicles; and on the contrary, L selects a larger value to increase the distribution density of the unmanned aerial vehicle and improve the contact probability of the unmanned aerial vehicle and the target.
In step S3, the solving of the distributed energy optimal control model is preferably performed by:
constructing a Hamiltonian by a distributed energy optimal control model:
wherein u isi(t) is a control quantity [ u ]xi(t),uyi(t)]′，vi(t) is the velocity [ v ]xi(t),vyi(t)]′，
And
is a covariate, and is convenient for representation, and makes
The method is obtained by utilizing a minimum value principle:
the optimal conditions are as follows:
the state equation is as follows:
the collaborative equation:
the cross-section conditions are as follows:
boundary conditions:
wherein the initial boundary condition is
Further, the optimal condition equation, the state equation and the collaborative equation are simultaneously combined to obtain an integral coefficient vector:
wherein [ a ]xi,ayi]′，[bxi,byi]′，[cxi,cyi]' and [ dxi,dyi]' is the integral coefficient to be solved.
Further, according to the cross section condition and the boundary condition, the integral coefficient vector is solved by using a numerical solver, and then [ a ] can be quickly obtainedxi,ayi]′，[bxi,byi]′，[cxi,cyi]' and [ dxi,dyi]The four integral coefficients are substituted into the formula (fourteen) to obtain each parameter in the formula (one), so as to obtain the control acceleration u of the unmanned aerial vehicle at the next momentiAnd (t), the track calculated by controlling the acceleration is the optimal track.
In step S4, each drone generates a control command at the next time according to the control acceleration of the drone itself at the next time obtained in step S3, and the steps S2 and S3 are repeated, so that continuous autonomous control of each drone can be completed, and cooperative deployment is realized.
The autonomous control means that the unmanned aerial vehicle autonomously controls the flight state of the unmanned aerial vehicle.
In a good priorityIn the selected implementation mode, the control acceleration u corresponding to the optimal track at the next moment is obtained by each unmanned aerial vehicleiAnd (t) after the step (d), before the control command is generated, performing collision check on the optimal track.
Specifically, each unmanned aerial vehicle sends the generated optimal track to the adjacent unmanned aerial vehicle, receives the optimal track of the adjacent unmanned aerial vehicle, and checks whether the tracks are intersected.
If the unmanned aerial vehicle does not intersect with the adjacent unmanned aerial vehicle, the unmanned aerial vehicle and the adjacent unmanned aerial vehicle do not collide with each other, and a control instruction at the next moment is generated according to the optimal track;
if the unmanned aerial vehicle and the adjacent unmanned aerial vehicle are intersected, the unmanned aerial vehicle is collided with the adjacent unmanned aerial vehicle, and the step S3 needs to be repeated to obtain the optimal track again; further, in the process of repeating step S3, a collision constraint is added to the distributed energy optimal control model to avoid collision again with the optimal trajectory reacquired by the adjacent drone.
Specifically, in the formula (IV), p [ s ]xij(t),syij(t)]' increasing collision restraint:
wherein R represents the radius of the drone.
Because the probability of the intersection of the optimal tracks is low, whether the collision occurs is judged by checking the generated optimal tracks instead of directly increasing collision constraint in the distributed energy optimal control model, so that the operation amount is greatly reduced, the onboard computer of the unmanned aerial vehicle can rapidly complete planning, the control frequency is improved, the control precision of the unmanned aerial vehicle is improved, and the high-density and target saturated interaction of the unmanned aerial vehicle becomes possible.
Examples
Example 1
And carrying out simulation experiments, wherein 6 unmanned aerial vehicles are set for collaborative deployment in the experiments, the maximum speed of the unmanned aerial vehicles is 1m/s, the initial positions of targets are [2.5,2.0], and the unmanned aerial vehicles are initially distributed around the targets to carry out cluster optimal collaborative target aggregation and tracking.
And each unmanned aerial vehicle adopts a proportion guidance law to predict the track and sends the predicted track to the adjacent unmanned aerial vehicle.
After each unmanned aerial vehicle obtains the predicted track of the adjacent unmanned aerial vehicle, the optimal track is obtained through solving by a distributed energy optimal control model, wherein the distributed energy optimal control model is expressed as:
wherein the terminal cost phi (x)i,tf) Expressed as:
φ(xi,tf)＝wvcφvc(xi,tf)+wvaφva(xi,tf)+waφa(xi,tf) (IV)
Further, phi in the formula (IV)vc(xi,tf) Is the cluster speed control term:
phi in the formula (IV)va(xi,tf) Is a multi-machine speed consistent item:
phi in the formula (IV)a(xi,tf) Is a multi-machine cluster term:
wherein L value is 8L, and L is rotor unmanned aerial vehicle's wheel base.
Solving a distributed energy optimal control model in the following way:
constructing a Hamiltonian by a distributed energy optimal control model:
the method is obtained by utilizing a minimum value principle:
the optimal conditions are as follows:
the state equation is as follows:
the collaborative equation:
the cross-section conditions are as follows:
boundary conditions:
wherein the initial boundary condition is
And (3) simultaneously establishing an optimal condition equation, a state equation and a synergetic equation to obtain an integral coefficient vector:
and solving the integral coefficient vector by using a numerical solver according to the cross condition and the boundary condition to obtain each parameter in the formula (I), so as to obtain the control acceleration corresponding to the optimal track of the unmanned aerial vehicle at the next moment.
Generating the optimal track of each unmanned aerial vehicle according to the control acceleration, exchanging the optimal track between adjacent unmanned aerial vehicles, checking whether the tracks are crossed or not, if the tracks are crossed, increasing collision constraint in the distributed energy optimal control model:
and the control acceleration corresponding to the optimal track of the unmanned aerial vehicle at the next moment is obtained again.
The flight state of the drone is controlled using the obtained control acceleration, the result of which is shown in fig. 2, where denotes the mission target, whose trajectory is moving to the upper right, different line segments denote the trajectories of different drones, which gather from the surroundings and then chase the target.
As can be seen from the flight tracks of the unmanned aerial vehicles on the graph, in the process from the starting of the unmanned aerial vehicles to the contact with the task targets, the flight tracks of the unmanned aerial vehicles are shorter without the participation of a central server, the distances between the unmanned aerial vehicles are well coordinated, the fuel consumption of the unmanned aerial vehicles is reduced, and the task execution efficiency is improved.
In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "rear", and the like indicate orientations or positional relationships based on operational states of the present invention, and are only used for convenience of description and simplification of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise specifically stated or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; the connection may be direct or indirect via an intermediate medium, and may be a communication between the two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The present invention has been described above in connection with preferred embodiments, but these embodiments are merely exemplary and merely illustrative. On the basis of the above, the invention can be subjected to various substitutions and modifications, and the substitutions and the modifications are all within the protection scope of the invention.
Claims (10)
1. A cluster cooperative deployment method based on distributed optimal energy MPC is characterized in that a plurality of unmanned aerial vehicles are communicated in an ad hoc network, and each unmanned aerial vehicle independently generates a control instruction to realize cooperative deployment of an unmanned aerial vehicle cluster.
2. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 1,
the method comprises the following steps:
s1, carrying out self-networking communication on a plurality of unmanned aerial vehicles;
s2, the unmanned aerial vehicle generates respective predicted tracks and transmits the respective predicted tracks and state information to the adjacent unmanned aerial vehicle;
s3, each unmanned aerial vehicle generates an optimal track of the unmanned aerial vehicle at the next moment according to the predicted track of the adjacent unmanned aerial vehicle;
and S4, generating a control command of the next moment by each unmanned aerial vehicle according to the optimal track, and repeating the steps S2 and S3 to realize the continuous autonomous control of each unmanned aerial vehicle.
3. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 1,
in step S1, the unmanned aerial vehicle ad hoc network communication means that the unmanned aerial vehicles communicate with each other by using Zigbee technology networking.
4. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 1,
in step S2, the predicted trajectory is a trajectory planned by the drone based on the detected target position information and the state information of the drone itself.
5. The cluster cooperative deployment method based on the distributed optimal energy MPC as claimed in one of claims 1 to 4,
in step S3, an optimal trajectory is obtained by solving a distributed energy optimal control model expressed by the form of an objective function:
where subscript i denotes different drones, t denotes time, t0Representing the initial time of the prediction time domain, tfRepresenting a terminal time of a prediction time domain;
ui(t) represents the control acceleration of the drone, which is the control quantity of the flight state of the drone, whose two components on the horizontal plane are represented by [ u [ u ] ]xi(t)，uyi(t)]', superscript' denotes transpose;
φ(xi，tf) Representing the terminal cost function of the prediction time domain.
6. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 5,
terminal cost phi (x)i，tf) The specific form of (b) may be expressed as:
φ(xi，tf)＝wvcφvc(xi，tf)+wvaφva(xi，tf)+waφa(xi，tf) (IV)
Wherein, wvcWeight, w, representing cluster speed controlvaIndicates a speed of oneWeight of sexual origin, waWeights representing a multimachine aggregation;
φvc(xi，tf) Is a cluster speed control term, phiva(xi，tf) Is a multiple machine speed uniform term, phia(xi，tf) Are multi-machine aggregated items.
7. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 6,
cluster speed control term phivc(xi，tf) Expressed as:
[vxd，vyd]' indicates the desired flight direction, i.e. the direction of flight towards the target,
multiple machine speed uniformity term phiva(xi，tf) Expressed as:
[vxavg，vyavg]' denotes the average speed of a plurality of drones,
multiple machine aggregation term phia(xi，tf) Expressed as:
l is a parameter related to distance.
8. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 7,
the unmanned aerial vehicle speed satisfies the constraint:
multiple machine speed uniformity term phiva(xi，tf) The following constraints are satisfied:
wherein the content of the first and second substances,
representing the maximum acceleration that the drone can reach.
9. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 5,
the solving for the distributed energy optimal control model is performed in the following manner,
constructing a Hamiltonian by a distributed energy optimal control model:
wherein u isi(t) is a control quantity [ u ]xi(t)，uyi(t)]′，vi(t) is the velocity [ v ]xi(t)，vyi(t)]′，
And
is a co-modal variable that is,
the method is obtained by utilizing a minimum value principle:
the optimal conditions are as follows:
the state equation is as follows:
the collaborative equation:
the cross-section conditions are as follows:
boundary conditions:
and (3) simultaneously establishing an optimal condition equation, a state equation and a synergetic equation to obtain an integral coefficient vector:
wherein [ a ]xi，ayi]′，[bxi，byi]′，[cxi，Cyi]' and [ dxi，dyi]' is the integral coefficient to be solved;
solving the integral coefficient vector by using a numerical solver according to the cross section condition and the boundary condition to obtain [ a ]xi，ayi]′，[bxi，byi]′，[cxi，cyi]' and [ dxi，dyi]The four integral coefficients are substituted into the formula (fourteen) to obtain each parameter in the formula (one), so as to obtain the next integral coefficient of the unmanned aerial vehicleControl acceleration u of timeiAnd (t), the track calculated by controlling the acceleration is the optimal track.
10. The method for cluster cooperative deployment based on distributed optimal energy MPC as claimed in claim 2,
in step S4, each drone generates a control command at the next time according to the control acceleration of the drone itself at the next time obtained in step S3, and the steps S2 and S3 are repeated, so that continuous autonomous control of each drone can be completed, and cooperative deployment is realized.
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