CN111443728B - Chaos wolf optimization-based unmanned aerial vehicle formation control method - Google Patents

Chaos wolf optimization-based unmanned aerial vehicle formation control method Download PDF

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CN111443728B
CN111443728B CN202010216392.0A CN202010216392A CN111443728B CN 111443728 B CN111443728 B CN 111443728B CN 202010216392 A CN202010216392 A CN 202010216392A CN 111443728 B CN111443728 B CN 111443728B
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CN111443728A (en
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吴坤
张田
蔡志浩
赵江
王英勋
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Beihang University
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    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
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Abstract

The invention provides an unmanned aerial vehicle formation control method based on chaos grey wolf optimization, which establishes a distributed MPC framework for unmanned aerial vehicle formation control, wherein each unmanned aerial vehicle only shares information with neighbors, and communication requirements and calculation complexity are reduced; the chaos optimization algorithm and the gray wolf optimization algorithm are combined, and the algorithm performance is improved. And combining the algorithm with the distributed MPC to solve FHCP, thereby realizing unmanned aerial vehicle formation control.

Description

Chaos wolf optimization-based unmanned aerial vehicle formation control method
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle cooperative control, and particularly relates to an unmanned aerial vehicle formation control method based on chaos grey wolf optimization.
Background
Unmanned Aerial Vehicles (UAVs) have a variety of applications in military and civilian fields, such as reconnaissance, surveillance, precision agriculture, cargo transportation, and forest fire protection. At present, the war shows more and more "unmanned" trend, and the development momentum of unmanned aerial vehicle technique is also better and better, compares with single unmanned aerial vehicle, and many unmanned aerial vehicle formations possess "self-healing" ability, environmental fitness height, task execution reinforce. The multi-unmanned aerial vehicle system has better performance in complex tasks, for example, in the aspect of investigation, unmanned aerial vehicle formation is beneficial to building a three-dimensional battlefield model; in air battles, the cooperative battles can be carried out, the killing range is enlarged, and the hit rate is improved. Unmanned aerial vehicle formation can many unmanned aerial vehicle system survey, the ability of location and perception to help going on of tasks such as aerial refueling and self-organization. In order to realize autonomous flight of unmanned aerial vehicle formation and execution of complex tasks, the problem of unmanned aerial vehicle formation control needs to be solved.
Formation flight can be generally divided into stages of aggregation, formation keeping and reconstruction, and includes consideration of disturbance conflict in the process. Common methods for unmanned aerial vehicle formation control include: the navigation Follower method (Leader-Follower), the behavior-based method, the virtual structure method, the consistency-based method and the like have advantages and disadvantages, and can be selected according to task needs and environments. The pilot follower method is a common method in formation control, one airplane is designated as a pilot, other airplanes are followers, and when the pilot flies according to a reference track, the airplane serving as the follower follows the pilot unmanned aerial vehicle according to a certain strategy. The behavior-based method is characterized in that defined basic behaviors (such as obstacle avoidance, following and the like) of several unmanned aerial vehicles are weighted, so that a formation control method is obtained, and each individual in the system can cooperate with other individuals to complete tasks according to own decisions.
Model Predictive Control (MPC) was applied in early exploration in some industrial sectors to solve the constrained dynamic optimization problem of multivariable Control that needs on-line solution. However, based on the consideration of control cost and control parameters, the early stage did not pay enough attention, and as far as 2000, Mayne and Rawlingst and the like utilize Lyapunov (Lyapunov) stability theory, adopt optimal control to solve the problems, realize the linear or nonlinear control constraint and stability guarantee of model predictive control, so that the model predictive control theory has great progress and becomes one of advanced control technologies after PID control. However, due to the limitation of model predictive control, the calculation amount of the online solution constraint optimization problem is large, and the application space is limited by the calculation time and the equipment requirement. In practice, it is difficult to solve some large-scale constraint optimization problems by using centralized model predictive control, and a Distributed Model Predictive Control (DMPC) may be used to reduce the complexity of the calculation. Compared with a traditional MPC, the distributed MPC has stronger capability of processing a multi-input multi-output system with state and control constraint, converts the original control problem into the problem of controlling a group of subsystems of the original system, constructs a plurality of distributed prediction platforms with information interaction, realizes optimization tasks together, reduces the calculated amount to a great extent, improves the robustness of the system and can better solve the control problem. Therefore, for unmanned plane formation control, a distributed MPC method can be adopted.
The Grey Wolf Optimization algorithm (GWO) is a population intelligent algorithm, and its inspiration comes from the social behavior of Grey Wolf, the social ranking system and hunting mechanism of Grey Wolf. The Chaos Optimization Algorithm (COA) is a global Optimization Algorithm inspired by the Chaos phenomenon that exhibits uncertain and unpredictable behavior.
Disclosure of Invention
In order to improve the global Optimization capability and convergence speed of GWO, a chaos Optimization strategy is adopted in a parameter setting and Optimization mechanism of GWO, a chaos Grey Wolf Optimization algorithm (CGWO) is provided in combination with an MPC to solve a Finite time domain Optimization Control Problem (FHOCP) and solve an unmanned aerial vehicle formation Control Problem. Specifically, the invention establishes a distributed MPC framework controlled by unmanned aerial vehicle formation, wherein each UAV only shares information with neighbors, thereby reducing communication requirements and computational complexity; the chaos optimization algorithm and the gray wolf optimization algorithm are combined, algorithm performance is improved, the chaos optimization algorithm and the gray wolf optimization algorithm are used for solving FHOCP, and therefore unmanned aerial vehicle formation control is achieved. The specific technical scheme of the invention is as follows:
an unmanned aerial vehicle formation control method based on chaos grey wolf optimization is characterized by comprising the following steps:
s1: establishing an unmanned aerial vehicle formation model:
if N unmanned aerial vehicle do the flight of level, be in the same two-dimensional plane promptly, every unmanned aerial vehicle can be regarded as a particle, every unmanned aerial vehicle's motion model is:
Figure BDA0002424595230000021
wherein p isi＝[pix,piy]TIs the position of drone i, pixIs the coordinate of unmanned plane i on the x-axis, piyIs the coordinate of drone i on the y-axis,
Figure BDA0002424595230000022
is pixThe first derivative of (a), representing the speed of drone i in the direction of the x-axis,
Figure BDA0002424595230000031
is piyIs a first derivative of (a), representing the velocity of the drone i in the direction of the y-axis, viAnd thetaiIs the flight speed and heading angle of drone i,
Figure BDA0002424595230000032
is thetaiThe first derivative of (a) is,
Figure BDA0002424595230000033
is viFirst derivative of, omegaiAnd aiRepresenting the angular velocity and acceleration of drone i;
s2: establishing an unmanned aerial vehicle kinetic equation under the condition of communication limitation:
for the nonlinear model predictive control problem, the unmanned plane kinetic equation is expressed as:
Figure BDA0002424595230000034
wherein the content of the first and second substances,
Figure BDA0002424595230000035
is the system state trajectory, n is the number of state quantities,
Figure BDA0002424595230000036
is the first derivative of z (t),
Figure BDA0002424595230000037
is the system control trajectory, m is the number of control quantities, t0Is the initial time, z0Is the initial state trajectory of the system;
for the problem of distributed model predictive control, the decoupling time-invariant nonlinear dynamics of an unmanned aerial vehicle i belonging to V is equivalent to that:
Figure BDA0002424595230000038
the above system vector is represented as: z is (z)1,z2,...,zN)，u＝(u1,u2,...,uN)，f(z,u)＝(f1(z1,u1),f2(z2,u2),...,fN(zN,uN))，
Figure BDA0002424595230000039
Is zi(t), V is a set of N drones;
under the limited condition of communication, it can only be integrated with unmanned aerial vehicle i
Figure BDA00024245952300000310
In (3) neighbor drone communication, in the set
Figure BDA00024245952300000311
The number of unmanned aerial vehicles in is NiFor the unmanned aerial vehicles which are not neighbors in the formation, the unmanned aerial vehicle i can only indirectly receive corresponding information through the neighbors,
Figure BDA00024245952300000312
represents a set of drones that are not neighbors of drone i;
in distributed model predictive control, drone j is a neighboring drone to drone i,
Figure BDA00024245952300000313
neighborhood of drone iThe control trajectory and the state trajectory of the host drone are represented as: u. of-i(t)＝{uj(t) } and z-i(t)＝{zj(t) }, the kinetic equation is:
Figure BDA00024245952300000314
drone k is a non-neighbor drone to drone i,
Figure BDA00024245952300000315
is a set of neighboring drones of drone j, the control trajectory and state trajectory of the non-neighboring drones of drone i being denoted u～i(t)＝{uk(t) } and z～i(t)＝{zk(t) }, the kinetic equation is:
Figure BDA0002424595230000041
wherein the content of the first and second substances,
Figure BDA0002424595230000042
is z-i(t) first derivative;
Figure BDA0002424595230000043
is z～i(t) first derivative;
s3: initializing parameters of the chaotic grayish optimization algorithm:
let the total number of wolf clusters be NgThe search space is D dimension, the maximum iteration number is tmax；
S4: designing a chaos gray wolf optimization algorithm:
s4-1: a gray wolf optimization algorithm;
let the position vector of the ig wolf be
Figure BDA0002424595230000044
ig∈{1,2,...,Ng}，
Figure BDA0002424595230000045
Representing the position of the wolf in D-dimensional space, the hunting process of the igth wolf is represented as:
Dig＝|Cig·Xp(tg)-Xig(tg)| (6)
Xig(tg+1)＝Xp(tg)-Aig·Dig (7)
wherein, tgFor the current number of iterations, Xig(tg) For the position vector of the ig wolf in the current iteration, Xig(tg+1) is the position vector of the ith wolf in the next iteration, DigIs a distance vector, Xp(tg) A position vector representing a prey, also representing an optimal solution, a coefficient vector AigAnd CigObtained by the following expression:
Aig＝2a·r1-a (8)
Cig＝2·r2 (9)
wherein r is1And r2Is [0,1 ] in D-dimensional space]Random vector of (a) 2-2tg/tmax，tmaxIs the maximum iteration number;
the wolf pack leader is considered to know the position of the prey more, the first three optimal solutions are wolf α, β and δ, which are the leaders of the wolf pack, are closer to the position of the prey, the position vector of the leaders wolf is taken as the position vector of the prey (6),
(7) in the middle, the process of hunting by other wolves following the captain is represented as:
Figure BDA0002424595230000046
Figure BDA0002424595230000051
wherein, Xα(tg),Xβ(tg) And Xδ(tg) Is of wolf alpha, beta and deltaPosition vector, X(1)(tg+1),X(2)(tg+1) and X(3)(tg+1) is the position vector of the next iteration calculated when the position of the prey is based on the three head wolfs, Aα,Aβ,AδAnd Cα,Cβ,CδThe coefficients of the positions of the prey are wolf alpha, beta and delta respectively;
s4-2: a chaotic grayish wolf optimization algorithm;
during initialization, chaotic mapping is used for generating 2 XN ordered by fitness valuegSelecting an odd number term as an initial solution, and simultaneously generating a by a chaotic operator;
including the optimal solution for each individual in the search mechanism:
Figure BDA0002424595230000052
wherein the content of the first and second substances,
Figure BDA0002424595230000053
represents the individual optimal solution of the igth wolf,
Figure BDA0002424595230000054
is composed of
Figure BDA0002424595230000055
The position vector of the next iteration is calculated,
Figure BDA0002424595230000056
is composed of
Figure BDA0002424595230000057
Position vector of current iteration, AbAnd CbIs composed of
Figure BDA0002424595230000058
Corresponding coefficient vectors, in order to emphasize the roles of the three head wolfs in the search mechanism, the location update process is:
Figure BDA0002424595230000059
wherein, omega represents the non-leading wolf in the wolf group, f (·) is the fitness function of the individual, Xα(tg+1),Xβ(tg+1) and Xδ(tg+1) are the position vectors of wolf α, β and δ, respectively, at the next iteration; (ii) a
Then, introducing a chaos optimization strategy in a search mechanism, and integrating a greedy strategy of a differential evolution method into a chaos search strategy;
s4-2-1: limiting the search range to [ Xmin,Xmax]Is mixing Xig(tg+1) to range (0,1), the mapping formula being:
Figure BDA00024245952300000510
s4-2-2: the number of iterations is CmaxA series of chaotic variables
Figure BDA00024245952300000511
q＝1,2,...,CmaxIterative computation is carried out by chaotic mapping, and then a chaotic sequence can be obtained by inverse mapping:
Figure BDA0002424595230000061
s4-2-3: selecting an optimal solution from the chaotic solution sequence based on the fitness,
Figure BDA0002424595230000062
the solution with the optimal fitness in the chaotic solution sequence of the next iteration is the ig wolf:
Figure BDA0002424595230000063
s4-2-4: defining greedy threshold as xiGTo obtain a new position update equation:
Figure BDA0002424595230000064
Wherein r is3Is [0,1 ]]A random number in between;
s5: establishing a distributed model predictive control framework based on chaos grey wolf optimization:
s5-1: designing a cost function;
the distributed cost function of the ith unmanned aerial vehicle is as follows:
Fi(zi(t),ui(t))＝wi1Fi1(zi(t),ui(t))+wi2Fi2(zi(t),ui(t))+wi3Fi3(zi(t),ui(t))
(18)
wherein, wi1,wi2And wi3Is a constant value of the weight, and,
Fi1(zi(t),ui(t)) represents the formation distance constraint:
Figure BDA0002424595230000065
wherein the content of the first and second substances,
Figure BDA0002424595230000066
is the set of adjacent unmanned aerial vehicles in the formation of unmanned aerial vehicles, and for each unmanned aerial vehicle i in the formation, if any, the adjacent unmanned aerial vehicles
Figure BDA0002424595230000067
Then define
Figure BDA0002424595230000068
And is
Figure BDA0002424595230000069
pij(t)＝pi(t)-pj(t) represents the distance between drone i and drone j, pi(t) andpj(t) are the positions of drone i and drone j respectively,
Figure BDA00024245952300000610
is the desired distance between drone i and drone j;
Fi2(zi(t),ui(t)) represents the angle constraint in the formation:
Figure BDA00024245952300000611
wherein the content of the first and second substances,
Figure BDA0002424595230000071
is the angle constraint between drone i and drone j,
Figure BDA0002424595230000072
is the desired angle constraint between drone i and drone j;
Fi3(zi(t),ui(t)) represents the tracking of the reference trajectory by the convoy:
Figure BDA0002424595230000073
wherein the content of the first and second substances,
Figure BDA0002424595230000074
is the location of the center of the formation,
Figure BDA0002424595230000075
is the expected location of the formation center;
considering the estimated control trajectory and the estimated state trajectory, the distributed cost function of each drone i is:
Figure BDA0002424595230000076
wherein the content of the first and second substances,
Figure BDA0002424595230000077
is the predicted location of the drone i,
Figure BDA0002424595230000078
is the estimated location of drone j,
Figure BDA0002424595230000079
is the estimated position of drone k;
Figure BDA00024245952300000710
is the desired distance between drone i and drone j,
Figure BDA00024245952300000711
is the desired distance between drone i and drone k,
Figure BDA00024245952300000712
is the desired distance between the center and the reference track;
Figure BDA00024245952300000713
is a desired angle constraint between drone i and drone j,
Figure BDA00024245952300000714
is a predicted angle constraint between drone i and drone j;
s5-2: designing a distributed model predictive control framework based on chaos grayish wolf optimization;
in model predictive control, the prediction horizon is TpE (0, infinity), control interval deltaT∈(0，Tp]With a rolling time-domain control time tc＝t0+δTc, c is belonged to {0,1, 2. }, and at each control time tcThe problem of solving the model predictive control is the problem of finite time domain optimization control;
tcand then, the different states and control tracks of the unmanned aerial vehicle i are as follows:
Figure BDA00024245952300000715
and
Figure BDA00024245952300000716
are the predicted control trajectory and the predicted state trajectory,
Figure BDA00024245952300000717
and
Figure BDA00024245952300000718
are an optimal control trajectory and an optimal state trajectory,
Figure BDA0002424595230000081
and
Figure BDA0002424595230000082
is an estimated control trajectory and an estimated state trajectory; accordingly, the method can be used for solving the problems that,
Figure BDA0002424595230000083
and
Figure BDA0002424595230000084
is that
Figure BDA0002424595230000085
The estimated control trajectory and the estimated state trajectory of the drone,
Figure BDA0002424595230000086
and
Figure BDA0002424595230000087
is that
Figure BDA0002424595230000088
Estimating a control track and an estimated state track of the medium unmanned aerial vehicle;
at each control time tcFirst with the previous prediction period [ t ]c-1,tc-1+Tp]Initializing the control input of the unmanned aerial vehicle in the formation by the optimal control track; then, each drone is connected from its neighborReceiving information and generating an estimated control track; the estimated state trajectory is calculated based on two parts, one part is the control trajectory of the neighboring unmanned aerial vehicle in the previous prediction period, and the other part is the control trajectory of the non-neighboring unmanned aerial vehicle in the previous two prediction periods, because the information from the non-neighboring unmanned aerial vehicle is indirectly transmitted from the neighboring unmanned aerial vehicle; based on the estimated state and the estimated control track from the neighbor, each unmanned aerial vehicle in the formation calculates the distributed cost function of the unmanned aerial vehicle, and finds the current prediction period [ t [ [ t ]c,tc+Tp]The predicted control trajectory of (2); finally, an optimal control sequence is obtained through chaos grey wolf optimization, and a first control interval [ t ] is usedc,tc+1]Updating the state of each unmanned aerial vehicle by the optimal control track;
s6: outputting a result of the unmanned aerial vehicle formation control method:
and giving out an expected formation form and a reference track, finally realizing that the unmanned aerial vehicle keeps the expected formation form, and carrying out formation flying by the formation center according to the reference track.
The invention has the beneficial effects that:
1. compared with centralized MPC control, the distributed MPC reduces the communication requirement between the unmanned aerial vehicles in the formation, and the unmanned aerial vehicles do not need to receive the information of all other unmanned aerial vehicles and only need to communicate with the 'neighbor' unmanned aerial vehicle, thereby reducing the calculation complexity.
2. The chaos grey wolf optimization algorithm combines the chaos optimization algorithm into the parameter setting and searching mechanism of the original grey wolf algorithm, and improves the overall optimization performance and convergence speed of the algorithm. The unmanned aerial vehicle formation control problem can be effectively solved in combination with distributed MPC.
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In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
fig. 1 is a schematic diagram of communication limitation in formation of unmanned aerial vehicles;
fig. 2 is a communication topology diagram of an unmanned aerial vehicle according to an embodiment of the present invention;
FIG. 3 is a design scheme of the CGWO of the present invention;
FIG. 4 is a diagram illustrating a formation constraint according to an embodiment of the present invention;
FIG. 5 is a flow chart of the present invention for solving UAV formation control using CGWO in combination with distributed MPC;
FIG. 6 illustrates the generation of an estimated control trajectory in accordance with an embodiment of the present invention;
fig. 7 is a diagram of unmanned aerial vehicle formation trajectories according to an embodiment of the present invention;
fig. 8 is a state diagram of formation of drones according to an embodiment of the present invention;
fig. 9 is a distance diagram of a formation center of unmanned aerial vehicles and a reference trajectory according to an embodiment of the present invention;
fig. 10 is a distance map between drones according to an embodiment of the present invention;
fig. 11 is an angle constraint diagram of formation of unmanned aerial vehicles according to an embodiment of the present invention;
FIG. 12 is a graph comparing cost functions for embodiments of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
The invention solves the problem of unmanned aerial vehicle formation control, and provides a distributed model prediction framework based on chaos wolf optimization for unmanned aerial vehicle formation control. Compared with centralized model predictive control, the distributed model predictive control has the advantages that the requirement on the communication capacity in unmanned aerial vehicle formation is reduced, and the complexity of calculation is reduced. The chaos optimization algorithm is used for improving the parameter setting and optimization mechanism of the original gray wolf optimization algorithm, and the algorithm performance is improved. The designed chaos wolf optimization algorithm is used for solving FHOCP in the distributed MPC, so that the problem of unmanned aerial vehicle formation control is solved.
In order to facilitate understanding of the above technical solutions of the present invention, the above technical solutions of the present invention are described in detail below by specific examples, and validity of the formation control method proposed by the present invention is verified. The chaos grey wolf optimization-based unmanned aerial vehicle formation control method specifically comprises the following steps:
s1: and establishing an unmanned aerial vehicle formation model.
Assuming that three unmanned aerial vehicles fly at a fixed height, namely, the three unmanned aerial vehicles are positioned in the same two-dimensional plane, each unmanned aerial vehicle can be regarded as a particle, the model of each unmanned aerial vehicle in formation is as formula (1), the initial state of each unmanned aerial vehicle is as shown in table 1, and the acceleration limit of each unmanned aerial vehicle is [ -10m/s ]2,+10m/s2]The angular velocity is limited to [ -0.15rad/s, +0.15rad/s]。
Table 1 initial position of drone in example of invention
Figure BDA0002424595230000101
S2: and establishing an unmanned aerial vehicle kinetic equation under the condition of communication limitation.
The dynamics of the three drones in the example for the case of a distributed MPC can be expressed in the form of equation (3). The schematic diagram of the communication limitation in the formation of unmanned aerial vehicles is shown in fig. 1, the communication topology of three unmanned aerial vehicles is shown in fig. 2, the UAV1 and the UAV3 cannot communicate directly, the neighbor of the UAV1 is UAV2, the neighbor of the UAV2 is UAV1 and UAV3, and the neighbor of the UAV3 is UAV2, that is, the schematic diagram is shown in fig. 2
Figure BDA0002424595230000102
S3: initializing parameters of the chaotic grayling optimization algorithm.
Let the total number of wolf clusters be N g20, the search space is D2-dimensional, and the maximum number of iterations is tmax＝30。
S4: and designing a chaos gray wolf optimization algorithm.
Wolfs α, β, and δ are the leaders of the wolf pack, and the leaders are considered to have better understanding of the positions (optimal solutions) of the prey than other wolfs, so the leaders are the three wolfs with the highest fitness in the wolf pack, and the other wolfs update their own positions following the leaders, enclosing the prey, i.e., approaching the optimal solution. The design mechanism of CGWO is shown in fig. 3, which combines COA with the parameter setting and searching mechanism of GWO.
The wolf pack population, search space, and maximum number of iterations are first initialized. The initial value has great influence on the convergence speed of the algorithm, the searching capability of the algorithm at the initial time can be increased by utilizing the ergodicity of the chaotic variable, the algorithm is subjected to chaotic initialization, and chaotic mapping is selected to generate 2NgAnd (3) setting an initial solution, wherein some chaotic maps are shown in table 2, and other chaotic maps can be selected for generating the initial solution. And calculating and sequencing the individual costs of the generated initial solution, and selecting odd items as initial values to avoid the algorithm from falling into the local optimal solution.
Table 2 chaos mapping example
Figure BDA0002424595230000111
In conventional GWO, the distance between the wolf and the prey and the coefficient vector AiAnd CiIt is related. When the value of a decreases from 2 to 0, AiThe variation range is reduced because AiIs limited to [ -2a,2a [ ]]。|AiIf < 1, the wolf group is close to the prey, | AiWhen the value is greater than 1, the wolf colony is far away from the prey, so that the linear reduction of a from 2 to 0 is unfavorable for the searching capability of the algorithm, therefore, a can be generated by a chaotic operator, and the optimization capability of the algorithm is enhanced.
Initialization a, Ai,CiAnd solving three solutions with the highest fitness, namely the positions of the three leaders according to the formulas (6) to (10). In the conventional GWO algorithm, the current optimal solution is the average of the first three optimal solutions in the population, andthe historical optimal solution for an individual is irrelevant. The concept of individual optimal solution is introduced into CGWO, so that the global optimization capability of the algorithm is enhanced. The formula (12) contains the information of the individual optimal solution, and is used for guiding the individual in the wolf group to search. The formula (13) emphasizes the leadership function and the individual optimal positions of the three leaderships, and the individual positions are updated by determining the weight coefficients according to the fitness values.
And then, introducing a chaotic optimization strategy in a search mechanism to enhance the global optimizing capability. The obtained individual position is mapped between (0,1) by the mapping function of equation (14). Performing C with the selected iterative functionmaxSolving a series of chaotic variables in 5 iterations
Figure BDA0002424595230000114
q is 1, 2., 5, and then the chaotic sequence is obtained by inverse mapping of equation (15). The optimal solution is selected by the fitness function value in the formula (16). In order to better approach to the optimal solution, a greedy threshold value xi is selectedG0.4, [0,1 ]]Random number r between3Comparing with greedy threshold, and taking when individual position exceeds threshold
Figure BDA0002424595230000112
When the threshold value is not reached, take
Figure BDA0002424595230000113
Equation (17) is an update equation for the individual positions of CGWO.
After the position is updated, the iteration times are increased by one, and whether the maximum iteration times t are exceeded or not is judgedmaxIf the optimal solution is not exceeded, the searching is continued, and if the optimal solution is exceeded, the searched optimal solution is returned, and the algorithm is ended.
S5: and establishing a distributed model predictive control framework based on chaos grey wolf optimization.
(1) Designing a cost function
Formation constraint schematic diagram as shown in fig. 4, the expected formation shape is an isosceles right triangle, and the expected distance between the unmanned planes is constrained to be
Figure BDA0002424595230000121
The angle is constrained to
Figure BDA0002424595230000122
The reference trajectory is set to a circle having a center of [ x ]tj,ytj]＝[8000,0]Radius Rtj6000 m. And writing a distributed cost function of each unmanned aerial vehicle according to the formula (22), and carrying out algorithm optimization based on the cost function.
(2) Distributed model predictive control framework designed based on chaos grey wolf optimization
In distributed MPC, time-domain T is predictedpControl interval is δ 4sT0.5s, the rolling time domain control time is tc＝t0+δTc, c is belonged to {0,1, 2. }, and at each control time tcThe CGWO algorithm is used to solve the FHOCP problem, and the flow is shown in fig. 5.
At each control time tcFirst with the previous prediction period [ t ]c-1,tc-1+Tp]And initializing the control input of the unmanned aerial vehicles in the formation by the optimal control track. Each drone then receives information from its neighbors, generating an estimated control trajectory, as shown in fig. 6. The estimated state trajectory is calculated based on two parts, one part being the control trajectory of the neighboring drone in the previous prediction period and the other part being the control trajectory of the non-neighbors in the previous two prediction periods, since the information from the non-neighbors is indirectly transmitted from the neighbors. Based on the estimated state and the estimated control track from the neighbor, each unmanned aerial vehicle in the formation calculates the distributed cost function of the unmanned aerial vehicle, and finds the current prediction period [ t [ [ t ]c,tc+Tp]The predicted control trajectory of (1). Finally, an optimal control sequence is obtained through chaos grey wolf optimization, and a first control interval [ t ] is usedc,tc+1]To update the state of each drone. Until the formation reaches the expected area, the simulation is finished, in the example, the expected area x is 8000m, and y is within 1km around-6000 m.
S6: and outputting a result of the unmanned aerial vehicle formation control method.
The invention adopts three unmanned planes to carry out formation control. The three airplanes are enabled to maintain the expected formation, and the formation center can carry out formation flying according to the reference track.
The unmanned aerial vehicle formation track of the embodiment is shown in fig. 7, wherein x is the x-axis direction in the horizontal plane, and y is the y-axis direction in the horizontal plane; (ii) a The state of the unmanned aerial vehicles in the formation is shown in fig. 8, wherein v is the flight speed of the unmanned aerial vehicles in the horizontal plane, a is the flight acceleration of the unmanned aerial vehicles in the horizontal plane, theta is the course angle of the unmanned aerial vehicles, and omega is the angular acceleration of the unmanned aerial vehicles; the distance between the unmanned aerial vehicle formation center and the reference track is shown in fig. 9, pOdThe distance between the unmanned aerial vehicle formation center and the expected position of the formation center is shown, and the unmanned aerial vehicle formation center can track a reference track according to the graph; the distance between drones is shown in fig. 10, p12Is the distance, p, between UAV1 and UAV213Is the distance, p, between UAV1 and UAV323For the distance between the UAV2 and the UAV3, it can be seen from the figure that the distance between the drones can satisfy the desired distance constraint, and form a desired formation; the angular constraints of formation of drones are shown in figure 11,
Figure BDA0002424595230000131
the angular constraint between UAV1 and UAV3,
Figure BDA0002424595230000132
for the angular constraint between UAV2 and UAV3, it can be seen that the angular constraint between drones can satisfy the desired angular constraint; fig. 7-11 show that the unmanned aerial vehicle formation control method provided by the invention has a good effect, and can enable unmanned aerial vehicles to form a formation to fly according to a desired formation according to a reference track. The invention also carries out a comparison experiment with Particle Swarm Optimization (PSO), the cost function pair of the two is shown in FIG. 12, and the CGWO proposed by the invention converges faster than PSO for the formation control example.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature includes the first feature being directly under and obliquely below the second feature, or simply meaning that the first feature is at a lesser elevation than the second feature.
In the present invention, 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. The term "plurality" means two or more unless expressly limited otherwise.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. An unmanned aerial vehicle formation control method based on chaos grey wolf optimization is characterized by comprising the following steps:
s1: establishing an unmanned aerial vehicle formation model:
if N unmanned aerial vehicle do the flight of level, be in the same two-dimensional plane promptly, every unmanned aerial vehicle can be regarded as a particle, every unmanned aerial vehicle's motion model is:
Figure FDA0003023508000000011
wherein p isi＝[pix,piy]TIs the position of drone i, pixIs the coordinate of unmanned plane i on the x-axis, piyIs the coordinate of drone i on the y-axis,
Figure FDA0003023508000000012
is pixThe first derivative of (a), representing the speed of drone i in the direction of the x-axis,
Figure FDA0003023508000000013
is piyIs a first derivative of (a), representing the velocity of the drone i in the direction of the y-axis, viAnd thetaiIs the flight speed and heading angle of drone i,
Figure FDA0003023508000000014
is thetaiThe first derivative of (a) is,
Figure FDA0003023508000000015
is viFirst derivative of, omegaiAnd aiRepresenting the angular velocity and acceleration of drone i;
s2: establishing an unmanned aerial vehicle kinetic equation under the condition of communication limitation:
for the nonlinear model predictive control problem, the unmanned plane kinetic equation is expressed as:
Figure FDA0003023508000000016
wherein the content of the first and second substances,
Figure FDA0003023508000000017
is the system state trajectory, n is the number of state quantities,
Figure FDA0003023508000000018
is the first derivative of z (t),
Figure FDA0003023508000000019
is the system control trajectory, m is the number of control quantities, t0Is the initial time, z0Is the initial state trajectory of the system;
for the problem of distributed model predictive control, the decoupling time-invariant nonlinear dynamics of an unmanned aerial vehicle i belonging to V is equivalent to that:
Figure FDA00030235080000000110
the above system vector is represented as: z is (z)1,z2,…,zN)，u＝(u1,u2,...,uN)，f(z,u)＝(f1(z1,u1),f2(z2,u2),...,fN(zN,uN))，
Figure FDA00030235080000000111
Is zi(t), V is a set of N drones;
under the limited condition of communication, it can only be integrated with unmanned aerial vehicle i
Figure FDA00030235080000000112
In (3) neighbor drone communication, in the set
Figure FDA00030235080000000113
The number of unmanned aerial vehicles in is NiFor the unmanned aerial vehicles which are not neighbors in the formation, the unmanned aerial vehicle i can only indirectly receive corresponding information through the neighbors,
Figure FDA00030235080000000114
represents a set of drones that are not neighbors of drone i;
in distributed model predictive control, drone j is a neighboring drone to drone i,
Figure FDA0003023508000000021
the control trajectory and state trajectory of the neighboring drone of drone i are represented as: u. of-i(t)＝{uj(t) } and z-i(t)＝{zj(t) }, the kinetic equation is:
Figure FDA0003023508000000022
drone k is a non-neighbor drone to drone i,
Figure FDA0003023508000000023
Figure FDA0003023508000000024
is a set of neighboring drones of drone j, the control trajectory and state trajectory of the non-neighboring drones of drone i being denoted u～i(t)＝{uk(t) } and z～i(t)＝{zk(t) }, the kinetic equation is:
Figure FDA0003023508000000025
wherein the content of the first and second substances,
Figure FDA0003023508000000026
is z-i(t) first derivative;
Figure FDA0003023508000000027
is z～i(t) first derivative;
s3: initializing parameters of the chaotic grayish optimization algorithm:
let the total number of wolf clusters be NgThe search space is D dimension, the maximum iteration number is tmax；
S4: designing a chaos gray wolf optimization algorithm:
s4-1: a gray wolf optimization algorithm;
let the position vector of the ig wolf be
Figure FDA0003023508000000028
Figure FDA0003023508000000029
Representing the position of the wolf in D-dimensional space, the hunting process of the igth wolf is represented as:
Dig＝|Cig·Xp(tg)-Xig(tg)| (6)
Xig(tg+1)＝Xp(tg)-Aig·Dig (7)
wherein, tgFor the current number of iterations, Xig(tg) For the position vector of the ig wolf in the current iteration, Xig(tg+1) is the position vector of the ith wolf in the next iteration, DigIs a distance vector, Xp(tg) A position vector representing a prey, also representing an optimal solution, a coefficient vector AigAnd CigObtained by the following expression:
Aig＝2a·r1-a (8)
Cig＝2·r2 (9)
wherein r is1And r2Is [0,1 ] in D-dimensional space]Random vector of (a) 2-2tg/tmax，tmaxIs the maximum iteration number;
the wolf pack leader is considered to know the position of the prey more, the most preferable first three solutions are wolf α, β and δ, which are regarded as the leader of the wolf pack and are closer to the position of the prey, the position vector of the leader wolf is taken as the position vector of the prey in formulas (6) and (7), and the process of hunting by the other wolfs following the leader is represented as:
Figure FDA0003023508000000031
Figure FDA0003023508000000032
wherein, Xα(tg),Xβ(tg) And Xδ(tg) Is the position vector of wolf alpha, beta and delta, X(1)(tg+1),X(2)(tg+1) and X(3)(tg+1) is the position vector of the next iteration calculated when the position of the prey is based on the three head wolfs, Aα,Aβ,AδAnd Cα,Cβ,CδThe coefficients of the positions of the prey are wolf alpha, beta and delta respectively;
s4-2: a chaotic grayish wolf optimization algorithm;
during initialization, chaotic mapping is used for generating 2 XN ordered by fitness valuegSelecting an odd number term as an initial solution, and simultaneously generating a by a chaotic operator;
including the optimal solution for each individual in the search mechanism:
Figure FDA0003023508000000033
wherein the content of the first and second substances,
Figure FDA0003023508000000034
represents the individual optimal solution of the igth wolf,
Figure FDA0003023508000000035
is composed of
Figure FDA0003023508000000036
The position vector of the next iteration is calculated,
Figure FDA0003023508000000037
is composed of
Figure FDA0003023508000000038
Position vector of current iteration, AbAnd CbIs composed of
Figure FDA0003023508000000039
Corresponding coefficient vectors, in order to emphasize the roles of the three head wolfs in the search mechanism, the location update process is:
Figure FDA00030235080000000310
wherein, omega represents the non-leading wolf in the wolf group, f (·) is the fitness function of the individual, Xα(tg+1),Xβ(tg+1) and Xδ(tg+1) are the position vectors of wolf α, β and δ, respectively, at the next iteration;
then, introducing a chaos optimization strategy in a search mechanism, and integrating a greedy strategy of a differential evolution method into a chaos search strategy;
s4-2-1: limiting the search range to [ Xmin,Xmax]Is mixing Xig(tg+1) to range (0,1), the mapping formula being:
Figure FDA0003023508000000041
s4-2-2: the number of iterations is CmaxA series of chaotic variables θ (q), q ═ 1,2maxIterative computation is carried out by chaotic mapping, and then a chaotic sequence can be obtained by inverse mapping:
Figure FDA0003023508000000042
s4-2-3: selecting an optimal solution from the chaotic solution sequence based on the fitness,
Figure FDA0003023508000000043
the solution with the optimal fitness in the chaotic solution sequence of the next iteration is the ig wolf:
Figure FDA0003023508000000044
s4-2-4: defining greedy threshold as xiGObtaining a new position updating equation:
Figure FDA0003023508000000045
wherein r is3Is [0,1 ]]A random number in between;
s5: establishing a distributed model predictive control framework based on chaos grey wolf optimization:
s5-1: designing a cost function;
the distributed cost function of the ith unmanned aerial vehicle is as follows:
Fi(zi(t),ui(t))＝wi1Fi1(zi(t),ui(t))+wi2Fi2(zi(t),ui(t))+wi3Fi3(zi(t),ui(t)) (18)
wherein, wi1,wi2And wi3Is a constant value of the weight, and,
Fi1(zi(t),ui(t)) represents the formation distance constraint:
Figure FDA0003023508000000046
wherein the content of the first and second substances,
Figure FDA0003023508000000047
is the set of adjacent unmanned aerial vehicles in the formation of unmanned aerial vehicles, and for each unmanned aerial vehicle i in the formation, if any, the adjacent unmanned aerial vehicles
Figure FDA0003023508000000048
Then define
Figure FDA0003023508000000049
And is
Figure FDA00030235080000000410
pij(t)＝pi(t)-pj(t) represents the distance between drone i and drone j, pi(t) and pj(t) are the positions of drone i and drone j respectively,
Figure FDA00030235080000000411
is the desired distance between drone i and drone j;
Fi2(zi(t),ui(t)) represents the angle constraint in the formation:
Figure FDA0003023508000000051
wherein the content of the first and second substances,
Figure FDA0003023508000000052
is the angle constraint between drone i and drone j,
Figure FDA0003023508000000053
is the desired angle constraint between drone i and drone j;
Fi3(zi(t),ui(t)) represents the tracking of the reference trajectory by the convoy:
Figure FDA0003023508000000054
wherein the content of the first and second substances,
Figure FDA0003023508000000055
is the location of the center of the formation,
Figure FDA0003023508000000056
is the expected location of the formation center;
considering the estimated control trajectory and the estimated state trajectory, the distributed cost function of each drone i is:
Figure FDA0003023508000000057
wherein the content of the first and second substances,
Figure FDA0003023508000000058
is the predicted location of the drone i,
Figure FDA0003023508000000059
is the estimated location of drone j,
Figure FDA00030235080000000510
is the estimated position of drone k;
Figure FDA00030235080000000511
is the desired distance between drone i and drone j,
Figure FDA00030235080000000512
is the desired distance between drone i and drone k,
Figure FDA00030235080000000513
is the desired distance between the center of the formation and the reference trajectory;
Figure FDA00030235080000000514
is a desired angle constraint between drone i and drone j,
Figure FDA00030235080000000515
is a predicted angle constraint between drone i and drone j;
s5-2: designing a distributed model predictive control framework based on chaos grayish wolf optimization;
in model predictive control, the prediction horizon is TpE (0, infinity), control interval deltaT∈(0，Tp]With a rolling time-domain control time tc＝t0+δTc, c is belonged to {0,1, 2. }, and at each control time tcThe problem of solving the model predictive control is the problem of finite time domain optimization control;
tcand then, the different states and control tracks of the unmanned aerial vehicle i are as follows:
Figure FDA00030235080000000516
and
Figure FDA00030235080000000517
are the predicted control trajectory and the predicted state trajectory,
Figure FDA00030235080000000518
and
Figure FDA00030235080000000519
are an optimal control trajectory and an optimal state trajectory,
Figure FDA00030235080000000520
and
Figure FDA00030235080000000521
is an estimated control trajectory and an estimated state trajectory; accordingly, the method can be used for solving the problems that,
Figure FDA0003023508000000061
and
Figure FDA0003023508000000062
is that
Figure FDA0003023508000000063
The estimated control trajectory and the estimated state trajectory of the drone,
Figure FDA0003023508000000064
and
Figure FDA0003023508000000065
is that
Figure FDA0003023508000000066
Estimating a control track and an estimated state track of the medium unmanned aerial vehicle;
at each control time tcFirst with the previous prediction period [ t ]c-1,tc-1+Tp]Initializing the control input of the unmanned aerial vehicle in the formation by the optimal control track; then, each unmanned aerial vehicle receives information from its neighbors and generates an estimated control trajectory; the estimated state trajectory is calculated based on two parts, one part is the control trajectory of the neighboring unmanned aerial vehicle in the previous prediction period, and the other part is the control trajectory of the non-neighboring unmanned aerial vehicle in the previous two prediction periods, because the information from the non-neighboring unmanned aerial vehicle is indirectly transmitted from the neighboring unmanned aerial vehicle; based on the estimated state and the estimated control track from the neighbor, each unmanned aerial vehicle in the formation calculates the distributed cost function of the unmanned aerial vehicle, and finds the current prediction period [ t [ [ t ]c,tc+Tp]The predicted control trajectory of (2); finally, an optimal control sequence is obtained through chaos grey wolf optimization, and a first control interval [ t ] is usedc,tc+1]Updating the state of each unmanned aerial vehicle by the optimal control track;
s6: outputting a result of the unmanned aerial vehicle formation control method:
and giving out an expected formation form and a reference track, finally realizing that the unmanned aerial vehicle keeps the expected formation form, and carrying out formation flying by the formation center according to the reference track.
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