CN116149363A - Energy consumption optimization method for formation transformation of multi-unmanned aerial vehicle system - Google Patents
Energy consumption optimization method for formation transformation of multi-unmanned aerial vehicle system Download PDFInfo
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Abstract
The invention relates to an energy consumption optimization method for formation transformation of a multi-unmanned aerial vehicle system, which comprises the steps of firstly adopting an improved particle swarm optimization algorithm, setting a proper objective function by designing the flight distance and climbing height cost of an unmanned aerial vehicle, solving a linear programming in each iteration to obtain an optimal assignment solution of the current position of each particle, calculating the adaptability of the particle swarm in the iteration process, and finally obtaining an optimal solution of the problem by comparing the adaptability of the particle swarm; after the optimal scheme of unmanned aerial vehicle cluster formation switching is obtained, aiming at the problem of multi-task conflict that unmanned aerial vehicles need to reach a target point and avoid collision, a zero-space-based behavior control algorithm is introduced to reasonably resolve the multi-task conflict, so that each unmanned aerial vehicle is prevented from collision when driving to the target point. The method not only can optimize the energy consumption of formation transformation of the multi-unmanned aerial vehicle system, but also can ensure that unmanned aerial vehicles can reach target points without collision in the flight process, and ensure the safety of formation flight.
Description
Technical Field
The invention relates to the field of intelligent robots, in particular to an energy consumption optimization method for formation transformation of a multi-unmanned aerial vehicle system.
Background
In recent years, with the continuous popularization of the application range of unmanned aerial vehicles, the difficulty of tasks executed by unmanned aerial vehicles is increasing, and single unmanned aerial vehicles cannot cope with the changes of the tasks. Compared with a single unmanned aerial vehicle, the unmanned aerial vehicle cluster has the characteristics of redundancy, robustness, expandability and the like, and meanwhile has more excellent coordination, intelligence and autonomy. Therefore, the method is gradually deepened in the fields of life, entertainment, military and transportation. Unmanned aerial vehicle formation control is an important research field of a multi-unmanned aerial vehicle system, in the field of natural science, scholars are inspired by large-scale cluster actions of insects, birds, fishes and the like, and have collective actions through interaction among individuals, and strong robustness and cost effectiveness are shown. In this process we can use these ideas to develop autonomous unmanned control systems, so scientists apply this biological swarming behavior to unmanned formation studies.
Unmanned aerial vehicle formation transformation is an important research direction of unmanned aerial vehicle formation control, and unmanned aerial vehicle formation transformation mainly refers to that a certain number of unmanned aerial vehicles move positions according to transformation requirements to form a new formation shape, wherein the problem of energy consumption optimization is particularly critical, so that the unmanned aerial vehicle formation transformation is under increasingly extensive attention and gradually becomes a focus problem in research.
In this regard, scholars have developed various related studies. The existing Hungary algorithm can solve the problem of assigning the optimal solution for the total distance of switching. However, the flight path allocated by part of unmanned aerial vehicles is overlong, or the climbing height allocated by a single unmanned aerial vehicle is overlarge, and the consumption of electric quantity of the unmanned aerial vehicle in the flight process is larger than that of the unmanned aerial vehicle when hovering, so that the electric quantity of the individual unmanned aerial vehicle drops rapidly in advance compared with other unmanned aerial vehicles in formation switching, and the whole formation is problematic in that the flight time is shortened.
Disclosure of Invention
The invention aims to provide an energy consumption optimization method for formation transformation of a multi-unmanned-plane system, which not only can optimize the energy consumption for formation transformation of the multi-unmanned-plane system, but also can ensure that unmanned plane can reach target points without collision in the flight process and ensure the safety of formation flight.
In order to achieve the above purpose, the invention adopts the following technical scheme: according to the energy consumption optimization method for formation transformation of the multi-unmanned aerial vehicle system, the multi-unmanned aerial vehicle system is taken as a research object, aiming at the problem that the whole formation flight time is shortened due to the fact that the unmanned aerial vehicle is excessively long in partial unmanned aerial vehicle distribution path in the formation switching process, firstly, an improved particle swarm optimization algorithm is adopted, the flight distance and climbing height cost of the unmanned aerial vehicle are designed, a proper objective function is set, the optimal assignment solution of the current position of each particle is obtained through solving a linear program in each iteration, the adaptability of the particle swarm in the iteration process is calculated, and finally the optimal solution of the problem is obtained through the comparison of the particle swarm adaptability; after the optimal scheme of unmanned aerial vehicle cluster formation switching is obtained, in order to ensure that each unmanned aerial vehicle safely reaches each target point under the condition of no collision, aiming at the problem of multi-task collision that the unmanned aerial vehicle needs to reach the target point and avoid collision, a control algorithm based on zero space behavior is introduced to reasonably resolve the multi-task collision, so that each unmanned aerial vehicle is ensured to avoid collision when driving to the target point.
Further, constructing a mathematical model of the assignment problem by using the distance cost and the climbing height cost of unmanned aerial vehicle formation switching, solving a model equation as a linear programming problem, and solving an optimal assignment solution X under the current condition;
the unmanned aerial vehicle is regarded as a person, and the unmanned aerial vehicle target point is regarded as a work item; if the ith unmanned aerial vehicle is allocated to the jth target point, the cost c ij The purpose of assigning the problem is to solve how to allocate the unit cost so as to minimize the total cost; the mathematical model of the assignment problem is:
wherein c= (C) ij ) A coefficient matrix for the assignment problem; taking the distance cost and climbing height cost of unmanned aerial vehicle formation switching as consideration targets as coefficient matrixes;
thus, the elements of the coefficient matrix are:
wherein ,
and pj Starting position of unmanned plane i and position of target point j, respectively, < >>
And->
The heights of the starting position and the target point position of the unmanned aerial vehicle under the global coordinate system are respectively shown, and b is a climbing height factor; the elements of the coefficient matrix are divided into two parts, wherein the first part is the Euclidean distance cost from the ith unmanned aerial vehicle to the jth target point, and the second part is the climbing height cost from the ith unmanned aerial vehicle to the jth target point;
and solving the equation as a linear programming problem, solving an optimal assignment solution X under the current condition, and substituting the optimal assignment solution X into a particle swarm optimization algorithm to calculate the fitness.
Further, under the assignment condition that the solution is X, an objective function is designed, and a solution result with the minimum final fitness is obtained through iteration of particle swarm, so that an optimal solution with small climbing energy consumption and small overall offset distance and balanced energy consumption in unmanned aerial vehicle formation switching assignment tasks is obtained;
in the iterative process of particle swarm, the speed and position update formula of the particles is as follows:
wherein ω is an inertial factor, its value is non-Negative; c 1 and c2 C is the acceleration constant 1 Learning factors, c, for each individual particle 2 Social learning factors for each particle; r is (r) 1 and r2 Is a normalized random number; variable p best For storing the best position found so far for the ith particle, if the condition is met
Update its location +.>
f is the objective function or fitness function maximized in each iteration cycle; variable g best For storing the optimal position obtained in the population of particles; during this optimization, the movement of the particles is distributed over the search space in different directions;
the iteration process of the particle swarm is continued until the particle swarm reaches the global optimum, and in each iteration, the position and the speed are updated according to formulas (3) and (4);
the solved optimal assignment solution X will be used to determine the objective function size of the particle at any point; in the case of assignment of solution to X, the objective function is as shown in equation (5):
wherein n is the total number of unmanned aerial vehicles; dis= (dis) ij )＝||p i -p j || 2 Representing Euclidean distances from n unmanned aerial vehicles to n target points respectively for n multiplied by n dimensions; dis (dis) max and dismin The maximum distance and the minimum distance of all unmanned aerial vehicles flying under the assigned condition X are respectively; k (k) 1 And k is equal to 2 Is a weight coefficient, and k 1 +k 2 ＝1；
The objective function in equation (5) is also decomposed into two parts, the first part calculating the average flight distance under the assignment X, the second part calculating the maximum flight distance and the minimum flight distance among all unmanned aerial vehicles under the assignment XScalar of difference by adjusting the appropriate k 1 And k is equal to 2 Is to integrate two optimization targets, k 1 The larger the overall offset distance, k, of the unmanned aerial vehicle cluster will be reduced 2 The larger the difference value of the flight distances among the unmanned aerial vehicle cluster individuals is, the more the overall energy consumption of the unmanned aerial vehicle cluster is balanced;
and (3) solving a solution result with the minimum final fitness through iteration of the particle swarm, so as to obtain an optimal solution with small climbing energy consumption and small total offset distance and balanced energy consumption in the unmanned aerial vehicle formation switching assignment task.
Further, after the optimal solution for unmanned aerial vehicle cluster formation switching is obtained, in order to ensure that each unmanned aerial vehicle safely reaches each target point under the condition of no collision, the unmanned aerial vehicle is decomposed into two sub-tasks in formation switching: moving to a target point and avoiding collision; aiming at the problem that the collision between unmanned aerial vehicles can cause multi-task collision, a zero-space-based behavior control algorithm is introduced to reasonably resolve the multi-task collision, so that each unmanned aerial vehicle is prevented from collision when driving to a target point;
in the zero-space behavior control, each basic task is distributed with different priorities, and the composite task is fused into a final task output according to the priorities of the basic tasks; the basic task is defined by a task function ρ ε R a A definition, wherein a is the dimension of the unmanned aerial vehicle task space; the task function ρ is expressed as:
ρ＝g(x) (6)
wherein g (x) is a function of x; the partial derivative of its corresponding task function ρ is:
wherein J (x) is a jacobian matrix of the task, and v is a speed vector of the unmanned aerial vehicle; desired speed of output V d Calculated by converting the local linear mapping into a least squares formula:
wherein ,ρd Is the reference position of the object to be measured,
is the pseudo-inverse of the jacobian matrix; integration of the reference velocity will result in drift of the reference position of the agent, taking the form of closed loop inverse kinematics for compensating the drift:
where Λ is the positive definite matrix of constant gain,
is a task error;
the composite task speed for a plurality of tasks is calculated by the following formula:
wherein 
Zero space for task 1; therefore, by projecting the low-priority task to the zero space of the high-priority task, the conflict part between the task speed output instructions is eliminated, and the speed output of the global task is obtained;
the time for completing the whole formation switching process is calculated as follows:
wherein ,dmax Planning the furthest flight distance, v, in an unmanned aerial vehicle group max For the unmanned aerial vehicle individual allowable maximum flying speed, calculating the reference track of each unmanned aerial vehicle by the formula (11):
obtaining an expected track of the ith unmanned aerial vehicle to the jth target point about t through the (12)
Is an expression of (2); will be
As a task function of each unmanned aerial vehicle going to the target point, the task output is expressed as follows by the formula (9):
in the formula (13)
For the derivative of the task function->
The position deviation of the moving task at the time t is the position deviation of the moving task at the time t;
ρ ai as a collision avoidance task function, it can be expressed as:
ρ ia ＝||p i -p j || (14)
equation (14) represents the distance between the ith unmanned aerial vehicle and the jth unmanned aerial vehicle closest to the ith unmanned aerial vehicle, and the output of the task can be expressed as:
in (16)
Is the derivative of the desired collision avoidance function, +.>
D S Is the safety distance for collision prevention;
the distance from the nearest unmanned aerial vehicle to the unmanned aerial vehicle can be detected in real time by a sensor of the unmanned aerial vehicle body; when the measured distance is smaller than the safety distance, the priority of the collision avoidance task is higher than that of the moving task, and at the moment, the moving task is partially executed when the collision avoidance task is executed:
otherwise only the move task is performed:
v ir ＝v im (17)。
compared with the prior art, the invention has the following beneficial effects: the invention provides an energy consumption optimization method for multi-unmanned aerial vehicle system formation transformation, which aims at solving the problem of non-uniform energy consumption of the multi-unmanned aerial vehicle system formation transformation by taking a multi-unmanned aerial vehicle system as a research object. Meanwhile, the particle swarm optimization algorithm is skillfully combined with the zero-space behavior control, after the optimal scheme of unmanned aerial vehicle cluster formation switching is solved, the unmanned aerial vehicles are ensured to safely reach respective target points under the condition of no collision, so that the unmanned aerial vehicle cluster performance is effectively improved, and the automation degree of unmanned aerial vehicle collaborative work is increased.
Drawings
FIG. 1 is a diagram of a particle's movement in a search space in the background;
FIG. 2 is a diagram of an iterative process of a particle swarm optimization algorithm in the background art;
fig. 3 is a conventional particle swarm algorithm multi-unmanned cluster formation switching diagram in an embodiment of the present invention;
fig. 4 is a diagram of a conventional particle swarm algorithm formation switching situation in an embodiment of the present invention;
fig. 5 is a diagram of a cluster formation switching of multiple unmanned aerial vehicles with improved particle swarm algorithm in an embodiment of the present invention;
FIG. 6 is a diagram of improved particle swarm algorithm formation switching in an embodiment of the present invention;
fig. 7 is a diagram of change of formation switching distance of unmanned aerial vehicle without collision avoidance task in the embodiment of the invention;
fig. 8 is a diagram of change of formation switching distance of unmanned aerial vehicle with collision avoidance task in the embodiment of the invention;
fig. 9 is a functional block diagram of a method implementation of an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The embodiment provides an energy consumption optimization method for formation transformation of a multi-unmanned-plane system, which is characterized in that the method takes the multi-unmanned-plane system as a research object, aims at the problem that the whole formation flight time is shortened due to the fact that the power consumption is relatively fast due to the fact that part of unmanned planes are excessively long in the formation switching process, firstly, an improved Particle Swarm Optimization (PSO) algorithm is adopted, a proper objective function is set through designing the flight distance and climbing height cost of the unmanned planes, an iterative optimization method of the particle swarm is utilized, the optimal assignment solution of the current position of each particle is obtained through solving a linear programming in each iteration, the adaptability of the particle swarm in the iteration process is calculated, and finally, the optimal solution of the problem is obtained through comparison of the particle swarm adaptability; after the optimal scheme of unmanned aerial vehicle cluster formation switching is obtained, in order to ensure that each unmanned aerial vehicle safely reaches respective target points under the condition of no collision, aiming at the problem of multi-task collision that the unmanned aerial vehicle needs to reach the target points and avoid collision, a zero-space behavior control algorithm (NSBC) based on is introduced to reasonably resolve the multi-task collision, so that each unmanned aerial vehicle is ensured to avoid collision when driving to the target points. The implementation principle of the method is shown in fig. 9, and the method can be roughly divided into three parts, namely task allocation design, improved particle swarm optimization algorithm optimizing and unmanned aerial vehicle cluster formation switching behavior control design.
1. Design of task allocation
According to the invention, firstly, a mathematical model of an assignment problem is constructed by using the distance cost and the climbing height cost of unmanned aerial vehicle formation switching, a model equation is used as a linear programming problem to solve, and an optimal assignment solution X under the current condition is obtained.
In the present invention, the drone is considered a person and the drone target point is considered a work item. If the ith unmanned aerial vehicle is allocated to the jth target point, the cost c ij The objective of assigning the problem is to solve for how the allocation can minimize the total cost that results. The mathematical model of the assignment problem is:
wherein c= (C) ij ) To assign a coefficient matrix for the problem. To give an example of an assignment problem, only a coefficient matrix of the problem needs to be given. The solving thought of the invention takes the distance cost and climbing height cost of unmanned aerial vehicle formation switching as consideration targets as coefficient matrixes.
Therefore, the elements of the coefficient matrix are designed as:
wherein ,
and pj Starting position of unmanned plane i and position of target point j, respectively, < >>
And->
The heights of the starting position and the target point position of the unmanned aerial vehicle under the global coordinate system are respectively, b is a climbing height factor, and the situation that the index value is overlarge can be prevented by properly adjusting b. The elements of the coefficient matrix are divided into two parts, wherein the first part is the Euclidean distance cost from the ith unmanned aerial vehicle to the jth target point, the second part is the climbing height cost from the ith unmanned aerial vehicle to the jth target point, the climbing cost can be greatly increased by introducing the index, the descending height change cost cannot be greatly influenced, and the coefficient matrix is suitable for simulating the climbing height cost of the unmanned aerial vehicle.
And solving the equation as a linear programming problem, solving an optimal assignment solution X under the current condition, and substituting the optimal assignment solution X into a particle swarm optimization algorithm to calculate the fitness.
2. Improved Particle Swarm Optimization (PSO) algorithm optimization
On the basis of the first part, under the assignment condition that the solution is X, an objective function is designed, and the optimal solution with small climbing energy consumption and small total offset distance and balanced energy consumption in unmanned aerial vehicle formation switching assignment tasks can be obtained by solving the solution result with the minimum final fitness through iteration of particle swarm.
Aiming at the problem of collaborative switching planning of multiple unmanned aerial vehicles and multiple target formation, the key is how to ensure the optimal flight distance of each Unmanned Aerial Vehicle (UAV) and average overall energy consumption. Particle Swarm Optimization (PSO) is a swarm intelligence algorithm whose inspiration comes from clustering of birds or shoal learning, for solving nonlinear, non-convex, or combinatorial optimization problems that occur in many scientific and engineering fields.
In the particle swarm algorithm, a random search method is adopted, and swarm intelligence is utilized for solving. This search is done by a set of randomly generated possible solutions. This set of possible solutions is called a population, and each possible solution is called a particle.
In the particle swarm optimization algorithm, the search of particles is affected by two learning methods. Each particle is learning from other particles, and also learns its own experiences during exercise. Learning to others may be referred to as social learning, while learning from their own experiences may be referred to as cognitive learning. As a result of social learning, a particle stores in its memory the best solution for all particle accesses in the population, we call g best . Through cognitive learning, a particle stores in its memory the best solution it has visited by itself so far, called p best . The particle swarm algorithm is a simple and effective meta-heuristic method and can be applied to multi-variable function optimization with a plurality of local optimal points. Each particle shares or exchanges information obtained during a respective search process using a group of cooperating particles. In this approach, each agent is at a velocity v in the search space k Movement, and this movement depends on two factors:
(1) Itself previous best position p best 。
(2) The best position g previously obtained in all particles best 。
In the iterative process of particle swarm, the speed and position update formula of the particles is as follows:
wherein ω is an inertia factor, and when ω is a non-negative value, the global optimizing ability is strong, and when ω is a small value, the local optimizing ability is weak, and when ω is a non-negative value, the global optimizing ability is weak, and when ω is a small value, the local optimizing ability is weak. c 1 and c2 C is the acceleration constant 1 Learning factors, c, for each individual particle 2 For the social learning factor of each particle, c is generally taken 1 ＝c 2 ∈[0，4]。r 1 and r2 Is a normalized random number, and their range is (0-1). Variable p best For storing the best position found so far for the ith particle, if the condition is met
Update its location +.>
Where f is the objective function or fitness function that is maximized in each iteration cycle. Variable g best For storing the best positions obtained in the population of particles. During this optimization, the movement of the particles is distributed over the search space in different directions, as shown in fig. 1.
The iterative process of particle swarm is shown in fig. 2. This process continues until global optimum is reached and in each iteration the position and velocity are updated according to equations (3), (4); in real-time operation, the objective function typically changes due to changes in particle location conditions.
The objective function needs to be designed for the unmanned aerial vehicle formation switching optimization problem. The optimal assignment solution X solved in part one will be used to determine the objective function size of the particle at any point; in the case of assignment of solution to X, the objective function is as shown in equation (5):
wherein n is the total number of unmanned aerial vehicles; dis= (dis) ij )＝||p i -p j || 2 Representing Euclidean distances from n unmanned aerial vehicles to n target points respectively for n multiplied by n dimensions; dis (dis) max and dismin The maximum distance and the minimum distance of all unmanned aerial vehicles flying under the assigned condition X are respectively; k (k) 1 And k is equal to 2 For the weight coefficient, should beGuarantee k 1 +k 2 ＝1。
The objective function in equation (5) is also decomposed into two parts, the first part calculating the average flight distance under assignment X, the second part calculating the scalar of the difference between the maximum flight distance and the minimum flight distance in all unmanned aerial vehicles under assignment X, by adjusting the appropriate k 1 And k is equal to 2 Is to integrate two optimization targets, k 1 The larger the overall offset distance, k, of the unmanned aerial vehicle cluster will be reduced 2 The larger the difference value of the flight distances among the unmanned aerial vehicle cluster individuals is reduced, and the overall energy consumption of the unmanned aerial vehicle cluster is balanced.
And (3) solving a solution result with the minimum final fitness through iteration of the particle swarm, so as to obtain an optimal solution with small climbing energy consumption and small total offset distance and balanced energy consumption in the unmanned aerial vehicle formation switching assignment task.
3. Unmanned aerial vehicle cluster formation switching behavior control design
After the optimal scheme of unmanned aerial vehicle cluster formation switching is obtained, each unmanned aerial vehicle needs to be ensured to safely reach each target point under the condition of no collision. Thus, the drone breaks down into two subtasks in the formation switch: moving to the target point and avoiding collision. Aiming at the problem that the collision between unmanned aerial vehicles can cause multi-task collision in the flight process, a zero-space-based behavior control algorithm (NSBC) is introduced to reasonably resolve the multi-task collision, so that each unmanned aerial vehicle is prevented from collision when driving to a target point;
in the zero-space behavior control, different priorities are allocated to each basic task, and the composite task is fused into a final task output according to the priorities of the basic tasks. The basic task is defined by a task function ρ ε R a Definition, where a is the dimension of the unmanned aerial vehicle task space, in this embodiment a=3. The task function ρ is expressed as:
ρ＝g(x) (6)
wherein g (x) is a function of x; the partial derivative of its corresponding task function ρ is:
wherein J (x) is a jacobian matrix of the task, and v is a speed vector of the unmanned aerial vehicle; desired speed of output V d Calculated by converting the local linear mapping into a least squares formula:
wherein ,ρd Is the reference position of the object to be measured,
is the pseudo-inverse of the jacobian matrix; integration of the reference velocity will result in drift of the reference position of the agent, taking the form of closed loop inverse kinematics for compensating the drift:
where Λ is the positive definite matrix of constant gain,
is a task error.
The composite task speed for a plurality of tasks is calculated by the following formula:
wherein 
Zero space for task 1; therefore, the conflict part between the task speed output instructions is eliminated by projecting the low-priority task to the zero space of the high-priority task, and the speed output of the global task is obtained.
Considering unmanned aerial vehicle formation switching application background, when the unmanned aerial vehicle reaches the airspace point of the unmanned aerial vehicle, and other unmanned aerial vehicles still do not reach, the unmanned aerial vehicle that has reached needs to hover and waits, and the advantage of unmanned aerial vehicle when corresponding speed is fast, long-time hover and wait can influence the holistic execution condition of unmanned aerial vehicle crowd.
The time for completing the whole formation switching process is calculated as follows:
wherein ,dmax Planning the furthest flight distance, v, in an unmanned aerial vehicle group max For the unmanned aerial vehicle individual allowable maximum flying speed, calculating the reference track of each unmanned aerial vehicle by the formula (11):
obtaining an expected track of the ith unmanned aerial vehicle to the jth target point about t through the (12)
Is an expression of (2); will be
As a task function of each unmanned aerial vehicle going to the target point, the task output is expressed as follows by the formula (9):
in the formula (13)
For the derivative of the task function->
Move any one at time tPositional deviation of the business.
ρ ai As a collision avoidance task function, it can be expressed as:
ρ ia ＝||p i -p j || (14)
equation (14) represents the distance between the ith unmanned aerial vehicle and the jth unmanned aerial vehicle closest to the ith unmanned aerial vehicle, and the output of the task can be expressed as:
in (16)
Is the derivative of the desired collision avoidance function, +.>
D S Is the safe distance for collision prevention.
The distance from the nearest unmanned aerial vehicle to the unmanned aerial vehicle can be detected in real time by a sensor of the unmanned aerial vehicle body; when the measured distance is smaller than the safety distance, the priority of the collision avoidance task is higher than that of the moving task, and at the moment, the moving task is partially executed when the collision avoidance task is executed:
otherwise only the move task is performed:
v ir ＝v im (17)
4. simulation contrast and analysis
In the simulation examples given below, the modified particle swarm algorithm (algorithm two) using the formulas (2), (5) is compared with the conventional particle swarm algorithm (algorithm one) that does not consider energy balance. For convenience of energy consumption index comparison, the unit energy consumption of the climbing distance is assumed to be twice of the unit energy consumption of the horizontal distance and the unit energy consumption of the falling distance, and the hovering energy consumption is not considered in the simulation because each unmanned aerial vehicle keeps uniform motion in formation switching and reaches each target point at the same time.
In the simulation, unmanned aerial vehicle cluster formation composed of 18 unmanned aerial vehicles is adopted to switch, and unmanned aerial vehicle coordinate information of an initial graph and a terminal graph is set as follows:
x1＝[50，40，30，40，40，40，30，20，10，10，10，40，40，45，30，20，10，0]
y1＝[0，0，0，9，18，27，25，25，25，21，28，37，46，46，46，46，46，46]
z1＝[10，10，10，19，28，37，35，35，35，31，38，47，56，56，56，56，56，56]
target graphic coordinate information:
x2＝[50，40，30，20，10，0，0，40，30，20，10，0，10，20，30，40，50，50]
y2＝[0，0，0，0，0，0，3.5，9，18，27，37，46，46，46，46，46，46，42]
z2＝[10，10，10，10，10，10，13.5，19，28，37.5，47，56，56，56，56，56，56，52]
the simulation result of the particle swarm algorithm (algorithm one) using the conventional optimization of only the total flight distance is shown in fig. 3. Fig. 4 shows an algorithm-multi-unmanned aerial vehicle formation switching situation, and it can be seen that the "F" and the "Z" are kept at the same level before and after switching, and half of unmanned aerial vehicles are not displaced. Under the condition, although the total displacement distance of the unmanned aerial vehicles is smaller, the energy consumption gap among the unmanned aerial vehicles is large, the energy consumption of the individual unmanned aerial vehicles is large, and the task execution efficiency of the unmanned aerial vehicle cluster is greatly reduced due to the wooden barrel effect.
The simulation result of the particle swarm algorithm (algorithm II) for optimizing the overall flight energy consumption balance is shown in fig. 5, and as shown in the switching situation of the unmanned aerial vehicle cluster formation of algorithm II in fig. 6, the unmanned aerial vehicle formation is slightly deviated as a whole in order to match with the overlong flight distance of the unmanned aerial vehicle 8-10 due to the addition of the optimization target for balancing the energy consumption in the formula (5). Because the formula (2) adds the ascending cost coefficient, compared with the result of the traditional algorithm, the unmanned aerial vehicle changes the selection, and the target point which can be reached through descending movement is preferentially selected.
By comparison of tables 1 to 3, the units in the tables are the distance units and the energy consumption units in the simulation, respectively. The overall flight distance of the algorithm relative to the algorithm unmanned aerial vehicle cluster is increased by about 8%, but the maximum energy consumption of the algorithm two unmanned aerial vehicles is 77% of the maximum energy consumption of the algorithm one unmanned aerial vehicle, and the energy consumption is extremely reduced by 39%, so that the overall working efficiency of the unmanned aerial vehicle cluster is greatly improved.
TABLE 1
| |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Algorithm-energy consumption | 0.543 | 0.543 | 0.543 | 0.543 | 33.25 | 16.84 | 40.78 | 5.35 | 32.11 |
| Algorithm two energy consumption | 6.835 | 6.835 | 10 | 11.5 | 8.9 | 18.83 | 5.17 | 31.5 | 26.7 |
| |
10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Algorithm-energy consumption | 32.11 | 18 | 15.3 | 0.543 | 4.94 | 0.543 | 0.543 | 0.543 | 0.543 |
| Algorithm two energy consumption | 26.7 | 25.46 | 22.7 | 6.8 | 9.7 | 6.8 | 6.8 | 6.8 | 6.8 |
TABLE 2
| |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Algorithm a distance | 1.8 | 1.8 | 1.8 | 1.8 | 33.6 | 17.23 | 40.88 | 4.71 | 31.87 |
| Algorithm two distance | 5.92 | 5.92 | 8.3 | 10.5 | 8.7 | 17.42 | 5.2 | 30.8 | 26 |
| |
10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Algorithm a distance | 31.87 | 12.49 | 11.77 | 1.8 | 3.23 | 1.8 | 1.8 | 1.8 | 1.8 |
| Algorithm two distance | 26 | 17.23 | 18.53 | 5.92 | 9.63 | 5.92 | 5.92 | 5.92 | 5.92 |
TABLE 3 Table 3
| Average distance | Average energy consumption | Extremely poor distance | Extremely poor energy consumption | |
| Algorithm one | 11.325 | 11.3 | 39.08 | 40.24 |
| Algorithm two | 12.16 | 13.6 | 25.6 | 24.67 |
In order to ensure that unmanned aerial vehicle clusters arrive at a destination at the same time under the condition of collision avoidance, the report adopts zero-space-based behavior control, and the overall formation switching task is completed through fusion of the moving task and the collision avoidance task.
The simulation is compared by adding the collision avoidance task (16) and the non-added collision avoidance task as a control algorithm. The safety distance for collision avoidance is set to 6 distance units. The change of formation switching between unmanned aerial vehicles with and without collision avoidance tasks is shown in fig. 7 and 8, respectively. By comparison, the distance between unmanned aerial vehicles under the behavior control frame without the collision prevention task breaks through the safety distance, and the safety of task execution is affected. Under the action control frame with collision avoidance tasks, the distance between unmanned aerial vehicles is kept above the safety distance, the safety in the switching of dynamic formation is ensured, and the purpose of avoiding collision between unmanned aerial vehicles is achieved.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (4)
1. The energy consumption optimization method for the formation transformation of the multi-unmanned-plane system is characterized by taking the multi-unmanned-plane system as a research object, aiming at the problem that the whole formation flight time is shortened due to the fact that the unmanned plane is excessively long in partial unmanned plane distribution path in the formation switching process, firstly, an improved particle swarm optimization algorithm is adopted, the flight distance and climbing height cost of the unmanned plane are designed, a proper objective function is set, the optimal assignment solution of the current position of each particle is obtained by solving linear programming in each iteration, the fitness of the particle swarm in the iteration process is calculated, and finally the optimal solution of the problem is obtained by comparing the particle swarm fitness; after the optimal scheme of unmanned aerial vehicle cluster formation switching is obtained, in order to ensure that each unmanned aerial vehicle safely reaches each target point under the condition of no collision, aiming at the problem of multi-task collision that the unmanned aerial vehicle needs to reach the target point and avoid collision, a control algorithm based on zero space behavior is introduced to reasonably resolve the multi-task collision, so that each unmanned aerial vehicle is ensured to avoid collision when driving to the target point.
2. The energy consumption optimization method for multi-unmanned aerial vehicle system formation transformation according to claim 1, wherein a mathematical model of an assignment problem is constructed by using distance cost and climbing height cost of unmanned aerial vehicle formation switching, a model equation is used as a linear programming problem to solve, and an optimal assignment solution X under the current condition is obtained;
the unmanned aerial vehicle is regarded as a person, and the unmanned aerial vehicle target point is regarded as a work item; if the ith unmanned aerial vehicle is allocated to the jth target point, the cost c ij The purpose of assigning the problem is to solve how to allocate the unit cost so as to minimize the total cost; the mathematical model of the assignment problem is:
wherein c= (C) ij ) A coefficient matrix for the assignment problem; taking the distance cost and climbing height cost of unmanned aerial vehicle formation switching as consideration targets as coefficient matrixes;
thus, the elements of the coefficient matrix are:
wherein ,
and pj Starting position of unmanned plane i and position of target point j, respectively, < >>
And->
The heights of the starting position and the target point position of the unmanned aerial vehicle under the global coordinate system are respectively shown, and b is a climbing height factor; the elements of the coefficient matrix are divided into two parts, wherein the first part is the Euclidean distance cost from the ith unmanned aerial vehicle to the jth target point, and the second part is the climbing height cost from the ith unmanned aerial vehicle to the jth target point;
and solving the equation as a linear programming problem, solving an optimal assignment solution X under the current condition, and substituting the optimal assignment solution X into a particle swarm optimization algorithm to calculate the fitness.
3. The energy consumption optimization method for multi-unmanned aerial vehicle system formation transformation according to claim 2, wherein under the assignment condition of solving for X, an objective function is designed, and the optimal solution with small climbing energy consumption, small overall offset distance and balanced energy consumption in unmanned aerial vehicle formation switching assignment task is obtained by iteration of particle swarm and obtaining the solution result with the minimum final fitness;
in the iterative process of particle swarm, the speed and position update formula of the particles is as follows:
wherein ω is an inertial factor, its value being non-negative; c 1 and c2 C is the acceleration constant 1 Individual learning factors for each particleSon, c 2 Social learning factors for each particle; r is (r) 1 and r2 Is a normalized random number; variable p best For storing the best position found so far for the ith particle, if the condition is met
Update its location +.>
f is the objective function or fitness function maximized in each iteration cycle; variable g best For storing the optimal position obtained in the population of particles; during this optimization, the movement of the particles is distributed over the search space in different directions;
the iteration process of the particle swarm is continued until the particle swarm reaches the global optimum, and in each iteration, the position and the speed are updated according to formulas (3) and (4);
the solved optimal assignment solution X will be used to determine the objective function size of the particle at any point; in the case of assignment of solution to X, the objective function is as shown in equation (5):
wherein n is the total number of unmanned aerial vehicles; dis= (dis) ij )＝||p i -p j || 2 Representing Euclidean distances from n unmanned aerial vehicles to n target points respectively for n multiplied by n dimensions; dis (dis) max and dismin The maximum distance and the minimum distance of all unmanned aerial vehicles flying under the assigned condition X are respectively; k (k) 1 And k is equal to 2 Is a weight coefficient, and k 1 +k 2 ＝1；
The objective function in equation (5) is also decomposed into two parts, the first part calculating the average flight distance under assignment X, the second part calculating the scalar of the difference between the maximum flight distance and the minimum flight distance in all unmanned aerial vehicles under assignment X, by adjusting the appropriate k 1 And k is equal to 2 Is to integrate two optimization targets, k 1 The larger the overall offset distance, k, of the unmanned aerial vehicle cluster will be reduced 2 The larger the difference value of the flight distances among the unmanned aerial vehicle cluster individuals is, the more the overall energy consumption of the unmanned aerial vehicle cluster is balanced;
and (3) solving a solution result with the minimum final fitness through iteration of the particle swarm, so as to obtain an optimal solution with small climbing energy consumption and small total offset distance and balanced energy consumption in the unmanned aerial vehicle formation switching assignment task.
4. A method of optimizing energy consumption for formation transformation of multiple unmanned aerial vehicle systems according to claim 3, wherein after obtaining an optimal solution for formation switching of unmanned aerial vehicle clusters, in order to ensure that each unmanned aerial vehicle safely reaches its own target point without collision, the unmanned aerial vehicle is decomposed into two sub-tasks during formation switching: moving to a target point and avoiding collision; aiming at the problem that the collision between unmanned aerial vehicles can cause multi-task collision, a zero-space-based behavior control algorithm is introduced to reasonably resolve the multi-task collision, so that each unmanned aerial vehicle is prevented from collision when driving to a target point;
in the zero-space behavior control, each basic task is distributed with different priorities, and the composite task is fused into a final task output according to the priorities of the basic tasks; the basic task is defined by a task function mu E R a A definition, wherein a is the dimension of the unmanned aerial vehicle task space; the task function ρ is expressed as:
ρ＝g(x) (6)
wherein g (x) is a function of x; the partial derivative of its corresponding task function ρ is:
wherein J (x) is a jacobian matrix of the task, and v is a speed vector of the unmanned aerial vehicle; desired speed of output V d Calculated by converting the local linear mapping into a least squares formula:
wherein ,ρd Is the reference position of the object to be measured,
is the pseudo-inverse of the jacobian matrix; integration of the reference velocity will result in drift of the reference position of the agent, taking the form of closed loop inverse kinematics for compensating the drift:
where Λ is the positive definite matrix of constant gain,
is a task error;
the composite task speed for a plurality of tasks is calculated by the following formula:
wherein 
Zero space for task 1; therefore, by projecting the low-priority task to the zero space of the high-priority task, the conflict part between the task speed output instructions is eliminated, and the speed output of the global task is obtained;
the time for completing the whole formation switching process is calculated as follows:
wherein ,dmax Is unmanned planePlanning the furthest flight distance in the group, v max For the unmanned aerial vehicle individual allowable maximum flying speed, calculating the reference track of each unmanned aerial vehicle by the formula (11):
obtaining an expected track of the ith unmanned aerial vehicle to the jth target point about t through the (12)
Is an expression of (2); will->
As a task function of each unmanned aerial vehicle going to the target point, the task output is expressed as follows by the formula (9):
in the formula (13)
For the derivative of the task function->
The position deviation of the moving task at the time t is the position deviation of the moving task at the time t;
ρ ai as a collision avoidance task function, it can be expressed as:
ρ ia ＝||p i -p j || (14)
equation (14) represents the distance between the ith unmanned aerial vehicle and the jth unmanned aerial vehicle closest to the ith unmanned aerial vehicle, and the output of the task can be expressed as:
in (16)
Is the derivative of the desired collision avoidance function, +.>
D S Is the safety distance for collision prevention;
the distance from the nearest unmanned aerial vehicle to the unmanned aerial vehicle can be detected in real time by a sensor of the unmanned aerial vehicle body; when the measured distance is smaller than the safety distance, the priority of the collision avoidance task is higher than that of the moving task, and at the moment, the moving task is partially executed when the collision avoidance task is executed:
otherwise only the move task is performed:
v ir ＝v im (17)。
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