CN104406593A

CN104406593A - Method for determining optimal route of airway of unmanned aerial vehicle

Info

Publication number: CN104406593A
Application number: CN201410725347.2A
Authority: CN
Inventors: 罗淇方; 周永权; 陈信
Original assignee: Guangxi University for Nationalities
Current assignee: Guangxi University for Nationalities
Priority date: 2014-12-03
Filing date: 2014-12-03
Publication date: 2015-03-11

Abstract

The invention provides a method for determining an optimal route of the airway of an unmanned aerial vehicle. According to the method, the threat of an operation area is more sufficiently considered, more efficient global searching ability is achieved and a more accurate flying route is provided for the unmanned aerial vehicle. The method comprises the following steps: by adopting a quantum encoding mode, changing the state of a basic quantum bit by using a quantum rotating gate and a quantum not-gate, and further updating the position of a bat individual. Because of the diversity of the quantum state, a quantum bat algorithm (QBA) is relatively high in global searching ability and an available or even optimal route avoiding the threat and limiting conditions can be found for the unmanned aerial vehicle. The experiment result shows that the quantum bat algorithm is an effective and stable method for solving the airway route planning problem of the unmanned aerial vehicle, and the search performance of the quantum bat algorithm is superior to that of other swarm intelligence algorithms.

Description

Method for determining optimal path of unmanned aerial vehicle airway

Technical Field

The invention relates to a method for determining an aircraft airway, in particular to a method for determining an optimal path of an unmanned aerial vehicle airway.

Background

Unmanned Combat Aircraft (UCAV) is a modern aviation weaponry equipment that is one of the potentially necessary trends for future war acts because it can perform dangerous, repetitive tasks in remote and hazardous environments. The goal of the unmanned aerial vehicle routing problem is to find an optimal or near optimal flight path between the initial position and the desired destination with minimal threat cost, subject to certain constraints. In recent years, the problem of unmanned aerial vehicle route planning is widely researched in military and civil fields. Partial intelligent algorithms have been applied to this problem, such as chaotic artificial bee Colony Algorithm (CABC), Genetic Algorithm (GA), particle swarm optimization algorithm (PSO), Differential Evolution (DE), chaotic prey biopsychological algorithm (CPBBO), ant colony Algorithm (ACO), Firefly Algorithm (FA), Artificial Neural Network (ANN), and the like.

The Bat Algorithm (BA) was proposed by x.s.yang in 2010, which was derived from a simulation of the process of searching for, predating food by bats in nature using the principle of echo location. When searching for food, the bat sends out ultrasonic wave pulses, and the sound intensity of the pulses is the largest, so that the ultrasonic waves are facilitated to propagate for a longer distance. During flying to a prey, the sound intensity of the pulses is gradually reduced, and the frequency of the pulses is gradually increased, so that the bat can more accurately acquire the position of food. The bat algorithm has been widely applied in various fields, such as global engineering optimization problem, constraint optimization problem, structure optimization problem, and discrete steel structure size optimization problem. And G.G.Wang applies a basic Bat Algorithm (BA) and an improved bat algorithm (MBA) fused with a variation strategy to solve the unmanned aerial vehicle route planning problem. In the improved bat algorithm (MBA), mutation operations in differential evolution are added to the bat algorithm to speed up the global convergence speed.

The basic bat algorithm in the prior art adopts a real number coding method, and comprises the following specific steps:

the first step is as follows: the mathematical model for the unmanned aerial vehicle air route planning problem (UCAV) is established as follows:

i.e., a threat source model of UCAV, in which a starting point of a route is defined as S and a target point is defined as T. There are many threat areas (e.g., radar, missile, artillery, etc.) within the unmanned aerial vehicle's mission area. The threat areas are all represented in a circular area mode, the closer to the center of the circular area, the more vulnerable the threat areas are, and the more vulnerable the threat areas are, the more non-attacked the threat areas are; the flight mission is to find an optimal route between S and T under the premise of considering all threat areas.

(1) The treatment method is shown in the attached figure 1;

1. connecting S and T;

2. divide ST into D +1 segments (i.e., D nodes), labeled L respectively₁,L₂,...,L_k,...L_D；

3. A vertical line of ST is made at each node, forming a set of discrete points:

C＝{S,L₁(x(1),y(1)),L₂(x(2),y(2)),...,L_k(x(k),y(k)),...L_D(x (D), y (D)), and T, which connect the points in sequence, form a path.

(2) Coordinate system transformation

To speed up the search, the ST can be considered as the x-axis for each discrete point (x)_k,y_k) For coordinate transformation

Where θ is the angle at which the x-axis of the original coordinate system rotates counterclockwise to be parallel to ST, (x)_s,y_s) Representing the coordinates in the original coordinate system. Thus, the x coordinate can be expressed asThe set of discrete points C can be converted to:

C'＝{0,L₁(y'(1)),L₂(y'(2)),...,L_k(y'(k)),...L_D(y'(D)),0}

secondly, establishing a performance evaluation function as follows:

the evaluation of the flight path mainly comprises a threat cost J_tAnd oil cost J_f

<math> <mrow> <msub> <mi>J</mi> <mi>t</mi> </msub> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>L</mi> </munderover> <msub> <mi>w</mi> <mi>t</mi> </msub> <mi>dl</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mi>J</mi> <mi>f</mi> </msub> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mi>L</mi> </munderover> <msub> <mi>w</mi> <mi>f</mi> </msub> <mi>dl</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein, w_tAnd w_fThe current path point represents the threat cost and the oil cost of each route respectively, and L is the total length of the route.

With a relatively accurate approximation strategy, the threat cost per route (between two discrete points) is approximated as the sum of five points:

wherein N is_tIs the number of threat regions, L_iIs the length of the ith sub-section, d_0.1,i,kIs the distance from 1/10 minutes point on the i subsection to the kth threat, t_kIs the threat level of the kth threat.

Assuming that the speed of UCAV is a constant, the oil cost can be equated to a total length L.

The final total cost is:

J＝kJ_t+(1-k)J_f (5)

where k is 0.5 (varying from 0 to 1), representing the flexibility of the designer, where k approaches 1, the path is shorter, and k approaches 1, the path is longer.

The third step: determining velocity updates and location updates for bats

Assuming that the search space is n-dimensional, the bat i has a position at time tAt a speed ofThen the position at time t +1And velocityThe update formula is as follows:

v_{i}^{t + 1} = v_{i}^{t} + (x_{i}^{t} - best) f_{i}^{t} - - - (7)

x_{i}^{t + 1} = x_{i}^{t} + v_{i}^{t + 1} - - - (8)

wherein f is_i，f_max，f_minRespectively represents the frequency of the sound wave emitted by the bat i at the current moment, and the maximum value and the minimum value of the frequency of the sound wave. Beta is epsilon [0,1 ∈]Is a randomly generated number. best represents the current globally optimal solution.

For a bat group with the size of n, a bat can be randomly selected from the bat group, and the corresponding position of the bat is updated according to the formula (4), and the process can be understood as a local search process, namely, a new solution is generated in the selected solution.

x_new(i)＝x_old+A^t (9)

Wherein x is_oldRepresenting a solution, A, randomly selected from the current optimal solution set^tRepresenting the average value of i batloudness just before time t, the elements of the random vector being the interval [ -1,1]The random number of (2).

The fourth step: determining loudness and pulse rate

Generally, when the bat starts to search, the pulse sound intensity is strong and the pulse frequency is low, and in the process of flying to food, the pulse sound intensity is gradually reduced, and the pulse frequency is gradually increased. The bat i pulse sound intensity a (i) and the pulse r (i) can be updated according to the following formulas (5) (6):

r^t+1(i)＝r⁰(i)×[1-exp(-γt)] (10)

A^t+1(i)＝αA^t(i) (11)

wherein alpha is more than 0 and less than 1, and lambda is a constant value when being more than 0. When a (i) is 0, it means that bat i has just found a game and temporarily stops making any sound, and it is not difficult to find: when t → ∞ a^t(i)→0,r^t(i)＝r⁰(i)。

Fifthly, the basic bat algorithm is implemented according to the following steps

Step1 initialization basic parameters: group size N, pulse sound intensity attenuation coefficient alpha, pulse frequency increase coefficient gamma, maximum pulse frequency r⁰Maximum pulse sound intensity A and maximum iteration number iterMax;

step 2 defining the pulse frequency Q_i∈[Q_min,Q_max]And a velocity v;

step 3 initialization of the bat position x_iAnd find the currentOf (d) an optimal solution f_min；

Step 4, entering the main circulation if rand < r_iRespectively updating the speed and the current position of the bat according to formulas (7) and (8), otherwise, randomly disturbing the position of the bat, and entering the step 5;

step 5, if rand < A_iAnd f (x)_i) If the solution is less than f (x), the new solution is received and the new solution flies to the position after updating;

step 6 if f (x)_i)＜f_minReplacing the former optimum bat and adjusting the pulse sound intensity A according to the formulas (10), (11)_iAnd the frequency r of the pulses_i；

Step 7, evaluating the bat group to find out the best bat and the position thereof;

step 8, if the termination condition of the algorithm is met (the maximum search times are reached or the search precision is met), the Step 9 is carried out; otherwise, entering step 4, and searching for the next time;

and Step 9, outputting the optimal individual value and the global optimal solution.

Wherein rand is a random number uniformly distributed over [0,1 ].

The applicant of the patent of the invention finds that the basic bat algorithm adopts a real number coding method through a plurality of practices, wherein the diversity of the population is limited, so that the algorithm is easy to fall into local optimization. Once the local optimal solution is entered, the jump-out is difficult, and in practice, the jump-out is often not possible at all. However, in the actual course determination process of the unmanned aerial vehicle, the threat of the combat area can be considered more fully, the global search capability is more efficient, and a more accurate flight path can be provided for the unmanned aerial vehicle and the unmanned aerial vehicle cannot be trapped in local optimization.

Disclosure of Invention

The invention aims to solve the technical problem of providing a method for determining the optimal route of the air route of the unmanned aerial vehicle, which can fully consider the threat of a combat area, has more efficient global search capability and can provide more accurate flight route for the unmanned aerial vehicle.

In order to solve the technical problems, the technical scheme provided by the invention is as follows: a method for determining an optimal path of an unmanned aerial vehicle airway comprises the following steps:

firstly, encoding the bat individuals by adopting the probability amplitude of the qubits on the basis of a basic bat algorithm, namely updating the probability amplitude of the qubits by using a quantum revolving gate, and adopting a quantum not gate as a variation operation to avoid premature convergence of the algorithm; there are two probability magnitudes for each qubit, and thus, each bat can represent two positions of the optimization space;

secondly, in quantum computation, the smallest information unit is stored in a qubit, and the state of the qubit can be '0', or '1', or any state between '0' and '1'; the state of a qubit can be represented as follows:

|Ψ>＝α|0>+β|1> (12)

wherein α and β satisfy:

|α|²+|β|²＝1 (13)

wherein | α |²And | β | |)²Respectively represent a trend state |0>And |1>The probability of (d);

an n-ary qubit can be defined as:

the quantum rotating gate is defined as follows:

the quantum not gate is defined as follows:

third, generating initial population

The algorithm uses the following coding scheme:

wherein, theta_ijIs the argument, and it can be seen from the formula (17) that each bat corresponds to two positions of the problem space, corresponding to the quantum state |0>And |1>The probability amplitude of (c):

P_ic＝(cos(θ_i1),cos(θ_i2),...,cos(θ_in)) (18)

P_is＝(sin(θ_i1),sin(θ_i2),...,sin(θ_in)) (19)

the fourth step, solving the spatial transformation

In order to calculate the fitness of an individual and evaluate the quality of the individual, the solution space of a population needs to be converted; each probability amplitude of an individual qubit corresponds to one solution of the solution space of the problem, i.e. each bat corresponds to two solutions of the optimization problem;

wherein,from quantum state |0>Amplitude of probability ofIs obtained byIs formed by quantum state |1>Amplitude of probability ofObtaining;

the fifth step, updating the strategy

In the Quantum Bat Algorithm (QBA), the amplitude and angle increment of the qubit is updated by adopting an updating strategy of the Bat Algorithm (BA), and the updating process is as follows:

Δθ_ij(t+1)＝Δθ_ij(t)+Δθ_g*Q(i)*stepnow (22)

θ_ij(t+1)＝θ_ij(t)+Δθ_ij(t+1) (23)

wherein, Delta theta_ijAnd theta_ijArgument increment and argument respectively;

<math> <mrow> <mi>stepnow</mi> <mo>=</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>Maxgen</mi> <mo>-</mo> <mi>gen</mi> <mo>)</mo> </mrow> <mi>w</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>Maxgen</mi> <mo>)</mo> </mrow> <mi>w</mi> </msup> </mfrac> <mrow> <mo>(</mo> <msub> <mi>σ</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>σ</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>σ</mi> <mi>e</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow> </math>

herein, the parameter values in equation (25) are: w is 2, σ_e＝0，σ_s＝2；

And (3) updating the probability amplitude by using a quantum revolving gate:

two new positions are obtained:

sixth, mutation strategy

In the Quantum Bat Algorithm (QBA), in order to prevent the algorithm from falling into local optima prematurely, a variation strategy is adopted herein to increase the diversity of the population, the variation strategy being implemented by a quantum not gate; if rand () < p_mIf so, executing quantum NOT gate operation and exchanging the two probability values; wherein p is_mIs the variation probability;

after the method is adopted, the invention has the following beneficial effects: the algorithm uses the concept of quantum bits as a coding method. The quantum rotating gate is used for changing the state of the quantum bit, and the quantum not gate is used for realizing the variation of the quantum bit so as to avoid premature convergence. Due to the diversity of quantum states, the global search capability of QBA is effectively improved, and bats are prevented from getting into local optimum prematurely. Simulation results show the robustness and effectiveness of the proposed algorithm. QBA can more fully consider the threat in the area of battle, obtain more accurate flight path for unmanned aerial vehicle (UCAV).

Drawings

Fig. 1 is a diagram of an unmanned aerial vehicle combat area model in a basic bat algorithm.

FIG. 2 is a flow chart of a threat cost calculation method in a basic bat algorithm.

Fig. 3 is a graph of the results when the first class example D is 10.

Fig. 4 is a graph of the results when the first class example D is 15.

Fig. 5 is a graph of the results when the first class example D is 20.

Fig. 6 is a graph of the results when the first class example D is 25.

Fig. 7 is a graph of the results when the first class example D is 30.

Fig. 8 is a graph of the results when the first class example D is 35.

Fig. 9 is a fitness map when the first class example D is 10.

Fig. 10 is a fitness map when the first class example D is 15.

Fig. 11 is a fitness map when the first class example D is 20.

Fig. 12 is a fitness map when the first class example D is 25.

Fig. 13 is a fitness map when the first class example D is 30.

Fig. 14 is a fitness map when the first class example D is 35.

Fig. 15 is a graph of the results when the second class of examples D-5.

Fig. 16 is a graph of the results when the second class example D is 10.

Fig. 17 is a graph of the results when the second class of examples D-15.

Fig. 18 is a graph of the results for the second class of examples, D-20.

Fig. 19 is a graph of the results when the second class of examples D-25.

Fig. 20 is a graph of the results when the second class of examples D-30.

Fig. 21 is a graph of the results when the second class of examples D is 35.

Fig. 22 is a graph of the results for the second class of examples, D-40.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

With reference to fig. 1 to 22, a method for determining an optimal path of an unmanned aerial vehicle route includes the following steps:

|Ψ>＝α|0>+β|1> (12)

wherein α and β satisfy:

|α|²+|β|²＝1 (13)

an n-ary qubit can be defined as:

the quantum rotating gate is defined as follows:

the quantum not gate is defined as follows:

third, generating initial population

The algorithm uses the following coding scheme:

P_ic＝(cos(θ_i1),cos(θ_i2),...,cos(θ_in)) (18)

P_is＝(sin(θ_i1),sin(θ_i2),...,sin(θ_in)) (19)

the fourth step, solving the spatial transformation

the fifth step, updating the strategy

Δθ_ij(t+1)＝Δθ_ij(t)+Δθ_g*Q(i)*stepnow (22)

θ_ij(t+1)＝θ_ij(t)+Δθ_ij(t+1) (23)

And (3) updating the probability amplitude by using a quantum revolving gate:

two new positions are obtained:

sixth, mutation strategy

the Quantum Bat Algorithm (QBA) is converted into a computer execution flow as follows:

the simulation experiment concerning the algorithm according to the present invention is as follows

1 simulation platform

In order to verify the correctness and effectiveness of the algorithm in solving the actual problem, a quantum bat algorithm, a basic bat algorithm and a differential evolution algorithm are subjected to a comparative test experiment. A simulation test platform: matlab R2012 (a); a CPU: AMD Athlon (tm) IIX 4640 Processor, dominant frequency: 3.00 GHz; RAM: 3 GB; operating the system: windows 7.

2 parameter setting

The parameter settings of the bat algorithm are as follows:

after 20 independent experimental comparisons, the following settings are made for each parameter in the algorithm:

in the basic bat algorithm, according to experience, the parameters are generally set as follows: search pulse frequency range of [0,2 ]]Maximum pulse frequency r⁰The maximum pulse sound intensity a is 0.5, the pulse sound intensity attenuation coefficient α is 0.95, and the pulse frequency increase coefficient γ is 0.05.

In the differential evolution algorithm, the scaling factor F is 0.5, and the crossover probability CR is 0.9.

The basic parameters in the quantum bat algorithm are the same as the basic bat algorithm, and the range of the quantum argument is set as theta_ij∈[-π,π]. Wherein, the other parameters in the formula (25) are respectively set as: w is 2, σ_e＝0，σ_s＝2。

3 results and analysis of the experiments

Two test examples are adopted to verify the performance of the QBA algorithm in solving the unmanned aerial vehicle route planning problem. In the test experiments in this section, the population size is set to 30 for Popsize, and 200 for max iterations of the three algorithms.

TABLE 1 relevant information for threat regions for a first set of test cases

The unmanned aerial vehicle route planning problem is to find an optimal or suboptimal route with the minimum threat cost, and when D takes different values, different optimization results of the problem can be obtained. As can be seen from the experimental results of table 2, initially, the accuracy of the flight path starts to decrease as the division dimension D increases, but when the division dimension D exceeds 30. For the first set of test cases, we can set the more appropriate segmentation dimension D to 20. In table 2, the optimal value, the average value, and the worst value of the Quantum Bat Algorithm (QBA) are all better than those of the Bat Algorithm (BA) and the Differential Evolution (DE). Therefore, the optimization performance of the algorithm provided by the method is obviously superior to that of a Bat Algorithm (BA) and Differential Evolution (DE). The result of the standard deviation shows that the Quantum Bat Algorithm (QBA) has the strongest robustness and can stably and effectively solve the optimization problem.

TABLE 2 Experimental results for the first set of test cases

From fig. 3 to fig. 8, we can see that the flight path is divided into D equally divided units. The drone attempts to evade the threat zone to find a route with the least threat cost. From the convergence graphs of the three algorithms of fig. 9 to fig. 14, it can be seen that the convergence speed of the Quantum Bat Algorithm (QBA) is the fastest and is not easy to fall into local optimum. Analysis of the experimental results of table 2 reveals that the optimization performance (i.e., flight path) of the algorithm is not simply a direct proportional relationship with the segmentation dimension D. The better the result is not optimized for larger segmentation dimensions D.

In the following test examples, to more fully verify the validity of the quantum bat algorithm, QBA and a plurality of intelligent algorithms were used^[12]Comparative experiments were performed and the results are shown in tables 4, 5 and 6. In the test experiments in this section, the population size was set to Popsize 30, and the maximum number of iterations for each algorithm was 200 for Maxgen.

TABLE 3 relevant information for second set of test case threat regions

TABLE 4 optimal solutions for different dimensions for the second set of test cases

TABLE 5 worst solution for different dimensions for the second set of test cases

TABLE 6 average solutions for different dimensions for the second set of test cases

Fig. 15 to 22 are the results of the Quantum Bat Algorithm (QBA) optimization for the second class of test examples. It can be seen from the figure that, aiming at different division dimensions D, QBA can find a path avoiding a threat area for the unmanned aerial vehicle, so that the threat cost is as low as possible to ensure the safety of the aircraft.

Due to the diversity of particle states, the quantum bat algorithm has strong global search capability. As can be seen from the experimental results of the second set of test examples in tables 4, 5 and 6, the quantum bat algorithm can achieve better optimal solutions under different division dimensions D, with the average solution being slightly worse than the mixed Bat Algorithm (BAM) only in two cases, D25 and D40, and being worse than the Differential Evolution (DE) only in 5 cases, and the worst solution being worse than the BAM only in 5 cases. The optimal solution, the worst solution and the average solution are comprehensively evaluated, and the comprehensive search performance of the Quantum Bat Algorithm (QBA) is superior to that of other 10 algorithms. Compared with the basic Bat Algorithm (BA), the optimization performance is improved by times, and compared with the hybrid Bat Algorithm (BAM), the optimization performance is also obviously improved. For the problem of unmanned aerial vehicle (UCAV) route planning, the quantum bat algorithm has higher optimizing precision, so that a more optimal flight route can be obtained.

A novel Quantum Bat Algorithm (QBA) path planning problem for unmanned combat aircraft is presented. QBA has an extremely strong global search capability in terms of probability due to its diversity. Simulation experiments show that the proposed algorithm is a feasible and effective way to plan the path of the unmanned fighter. The QBA can find a safe flight path by minimizing the threat of node connection costs for the empty room with the lowest fuel costs.

The invention and its embodiments have been described above, without limitation. In summary, those skilled in the art should appreciate that methods and embodiments similar to those described above can be devised without departing from the spirit and scope of the present invention.

Claims

1. A method for determining an optimal path of an unmanned aerial vehicle airway is characterized in that: it comprises the following steps:

|Ψ>＝α|0>+β|1> (12)

wherein α and β satisfy:

|α|²+|β|²＝1 (13)

an n-ary qubit can be defined as:

the quantum rotating gate is defined as follows:

the quantum not gate is defined as follows:

third, generating initial population

The algorithm uses the following coding scheme:

P_ic＝(cos(θ_i1),cos(θ_i2),...,cos(θ_in)) (18)

P_is＝(sin(θ_i1),sin(θ_i2),...,sin(θ_in)) (19)

the fourth step, solving the spatial transformation

the fifth step, updating the strategy

Δθ_ij(t+1)＝Δθ_ij(t)+Δθ_g*Q(i)*stepnow (22)

θ_ij(t+1)＝θ_ij(t)+Δθ_ij(t+1) (23)

And (3) updating the probability amplitude by using a quantum revolving gate:

two new positions are obtained:

sixth, mutation strategy