A formation leader selection algorithm based on rotorcraft UAVs

Abstract

The present invention proposes a formation leader selection algorithm based on rotorcraft UAVs. The present invention takes a certain UAV as the navigator as a premise, and based on this, converts the states of multiple UAVs into the relative motion state of the navigator in the algorithm. The method proposed by the present invention realizes the formation control of UAVs through the linear quadratic regulator (LQR) algorithm, selects a suitable navigator for the formation of UAVs, and optimizes the time to form a target formation and the GA algorithm to solve the combination mapping problem between UAVs and target formations.

Description

Technical Field

[0001] The present invention relates to a formation leader selection algorithm based on unmanned aerial vehicles (UAVs), which is mainly used to flexibly deploy multiple UAVs according to tasks and different terrains, efficiently determine the UAV formation leader, and accordingly form a UAV formation that meets the needs. Background Art

[0002] After decades of development, unmanned aerial vehicle (UAV) technology has gradually improved and even matured. At the same time, UAVs are increasingly widely used, playing an increasingly important role in many military and civilian tasks such as battlefield surveillance and reconnaissance, border patrols, forest fire detection, and public safety monitoring. Compared with a single UAV, multi-UAV formation operations have more advantages in terms of large-scale surveillance, combat distance, and attack capabilities, and the success rate of executing UAV missions is also higher. In addition, multiple UAV formations can be flexibly deployed, and different formations can be formed according to mission requirements and different terrains or tasks. Therefore, how to efficiently generate UAV target formations within a limited time or a shorter distance has attracted the attention of many researchers. Summary of the invention

[0003] Purpose of the invention: As unmanned aerial vehicles (UAVs) are increasingly used, they play an increasingly important role in many military and civilian missions. When UAVs perform missions, how to select a suitable leader for the formation of UAVs and minimize the time to form a target formation has become a major technical problem.

[0004] Technical solution: To achieve the above technical effects, the technical solution proposed by the present invention is:

[0005] The formation leader selection algorithm method based on a rotary-wing UAV is characterized by comprising the steps of:

[0006] (1) Constructing the system model: A leader-based formation system consists of M drones, using the collection In this set, one of them is selected as the leader and the other drones are followers. The shape of the target formation is prioritized rather than its position. Assuming that the shape of the target formation is predetermined and the position of the target formation is determined by the position of the currently selected leader, the goal is to select a set of drones. One of the drones acts as a leader and the others act as followers to minimize the spawning time of the drone formation:

[0007] 1) The state of each drone is represented as:

[0008]

[0009] Among them, p i =[x i ,yi ],v i =[v xi , v yi ] and u i =[u xi ,u yi ]∈R 2 represents the position vector, velocity vector and control input of the ith UAV, s i =[x i y i v xi v yi ] represents the motion state of the i-th UAV. For simplicity, we will use p i , v i and u i Indicates the status of the first drone

[0010] 2) Assuming that the lth UAV is the leader, it can be obtained from (1) that its state is represented by p1, v1 and s1, then the position and velocity matrix of the follower UAV can be expressed as:

[0011]

[0012] Among them, when the lth drone is the leader, represents the position of the jth follower,

[0013] 3) The currently selected leader position p l The total position set of the target formation corresponding to the determined follower drone is expressed as:

[0014]

[0015] When the leader drone is arranged in the target formation at a position k (1≤k≤M); represents the mth target position, when the first UAV is the leader and its position is arranged as k, 1≤m≤M-1, l∈M, k∈M, represents a one-to-one mapping set from the current target formation to followers;

[0016] 4) The target mapping relationship is:

[0017]

[0018] Where N = (M-1)!, and 1≤n≤N represents one of the target mapping relationships;

[0019] 5) The relative motion state is:

[0020]

[0021] Based on the selected leader UAV l , leader position ranking k and target mapping relationship in represents the relative position matrix between all followers and the target formation, represents the relative velocity matrix of all followers and the leader, Will and Combined to form the relative state matrix, Represents the relative motion state of the ith follower relative to the leader;

[0022] 6) Formation time of the entire system in a formation:

[0023]

[0024] The time set of all followers in the formation is The maximum time of all followers in the formation is considered as the formation time;

[0025] 7) The best leader and the shortest formation time are:

[0026]

[0027] Where l represents the selection of different UAV minimum formation time as the optimization variable of the leader. Finally, the minimum value of formula (7) is The leader is considered the best leader and gets the least formation time;

[0028] (2) The model constructed based on the above leader selection algorithm mainly includes two sub-problems: UAV formation control and target mapping relationship. The UAV formation control problem is solved by combining LQR with the above model method, mainly focusing on speed and position control. The target formation mapping problem is to solve the one-to-one mapping relationship between the current follower and the target formation position;

[0029] 1) In the first sub-problem of the leader selection algorithm, LQR is an optimized dynamic controller designed based on state space technology. The system model is a linear system given in state space form, and its objective function is a quadratic function of the state and control input. The vector matrix form of the system state space is

[0030]

[0031] Where A represents the state matrix of the system, B represents the output matrix, C represents the input matrix, D represents the direct transfer matrix of the input, x, y, and u represent the state vector, output vector, and input vector respectively;

[0032] 2) In this system, assuming that The drones are leaders, and their positions are in the following order: The state vector x of the jth follower contains four state variables - position, speed in a two-dimensional coordinate system, and input variable u. It includes two variables as control inputs. The arrival of the drone at the target formation position and the convergence of the speeds of the follower and the leader are two conditions required for the formation of multiple drones to reach a stable state. Assume that the jth follower corresponds to the mth target formation position The expected output is:

[0033]

[0034] Among them, the initial state Expected input U j =[0 0] T , convert the states of multiple drones into the relative motion state of the leader. Therefore, both the initial state vector and the output state vector in the state equation must be changed. From formula (5), we can get: Y j =[0 0 0 0] T , U j =[0 0] T ;

[0035] 3) The state space description of the j-th follower can be obtained by formula (1), expressed as:

[0036]

[0037] 4) The optimization objective function or cost function based on the LQR algorithm is defined as:

[0038]

[0039] Where Q represents the state weight and positive semidefinite matrix, R represents the control weight and positive definite matrix;

[0040] 5) LQR defines the state feedback controller u and the state feedback matrix K, which can be expressed as

[0041] u=-Kx (12)

[0042] Substituting u into the previous system state equation, it can be expressed as:

[0043]

[0044] Then, the value of the feedback matrix K is calculated by solving the Riccati equation, and the initial state and simulation time interval are set. The system is simulated using the K feedback matrix. Finally, through system simulation, the total state and formation time of each UAV under the current mapping relationship between the leader and the target formation can be obtained;

[0045] 6) In the second sub-problem of the leader selection algorithm, the time complexity of the mapping problem between followers and target formations is O(n!). As the scale of UAVs and data increases, genetic algorithm (GA) is one of the best tools to find a satisfactory solution;

[0046] 7) Applying the GA algorithm to the model, the solution represents a mapping relationship According to the population size G from the set Randomly select a population The fitness function is the formation time of the corresponding mapping relationship when the leader drone and its order are determined by k Since GA is equivalent to reducing the set , so the constraints of problem (7) will also change, and problem (7) can be rewritten as:

[0047]

[0048] in, As the number of iterations and genetic operator operations continue to change. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a principle flow chart of the UAV formation leader selection algorithm.

[0050] Figure 2 It is a schematic diagram of the relative motion state conversion process of the UAV.

[0051] Figure 3 This is a schematic diagram of the UAV target formation process.

[0052] Figure 4 It is a schematic diagram comparing the formation time of the present invention and the optimal solution.

[0053] Figure 5 It is a comparison chart of the execution time of the optimal solution and the UAV formation leader selection algorithm. DETAILED DESCRIPTION

[0054] The present invention will be further described below in conjunction with the accompanying drawings.

[0055] Figure 1 This is the principle flow chart of the UAV formation leader selection algorithm. Based on LQR and GA, the main steps of the UAV formation leader selection algorithm are as follows:

[0056] 1) Define the minimum formation time and leader drone number;

[0057] 2) Determine whether the current set of drones has been traversed. If not, record the current drone's position and dormitory, and obtain the relative speed of all followers; if completed, obtain the minimum formation time and the corresponding drone leader number;

[0058] 3) Determine whether the GA algorithm population iteration has ended. If not, obtain the target formation position, and then obtain the corresponding positions between all followers and the formation. Then, obtain the current consumption time and state according to the LQR algorithm, update the global information variable, and update the population through the GA genetic operator, and then perform the next population iteration. If the iteration has ended, take the next drone as the leader and return to step 2).

[0059] Figure 2 It is a schematic diagram of the relative motion state conversion process. Figure 2 (a) shows the initial state of the leader selection algorithm. Figure 2 The black arrows in (b) indicate the relative states of the follower and the leader.

[0060] Figure 3 It is a schematic diagram of the formation process of the drone target formation. Assuming that the leader is stationary and generates the drone formation in a relative state, Figure 3 (a) represents the initial state of the formation, Figure 3 (b) indicates the formation completion status. The blue dots represent the target formation and the green dots represent the drones.

[0061] Figure 4 : is a comparison diagram between the present invention and the optimal solution regarding the formation time. Figure 4 As shown in the figure, the formation time of the target formation of the UAV leader selection algorithm proposed in the present invention is close to the optimal solution, except when the number of UAVs is 8, so the algorithm proposed in the present invention can achieve approximately the same optimal time. In addition, after comparing the formation time of the algorithm proposed in the present invention with the average formation time of the other two scenarios, the algorithm proposed in the present invention significantly reduces the formation time of the target formation, where LU-ave and Optimal-ave represent the average formation time of the target formation in the two scenarios, respectively.

[0062] Figure 5 It is a comparison chart of the execution time of the optimal solution and the UAV formation leader selection algorithm. In the scenario of a small number of UAV formations, the algorithm proposed in the present invention executes slowly because of the population size and number of iterations of the GA algorithm.

[0063] However, as the number of drones increases, the time complexity of the optimal solution will greatly increase. When the number of drones exceeds 10, the optimal solution cannot be coded and run on MATLAB because the content space occupied is too large. Obviously, the algorithm proposed in the present invention can solve this problem well.

[0064] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A formation leader selection algorithm method based on a rotary-wing UAV, characterized in that: Includes steps: (1) Constructing the system model: A leader-based formation system consists of M drones, using the collection In this set, one of them is selected as the leader and the other drones are followers. The shape of the target formation is prioritized rather than its position. Assuming that the shape of the target formation is predetermined and the position of the target formation is determined by the position of the currently selected leader, the goal is to select a set of drones. One of the drones acts as a leader and the others act as followers to minimize the spawning time of the drone formation: 1) The state of each drone is represented as: Among them, p i =[x i ,y i ],v i =[v xi , v yi ] and u i =[u xi ,u yi ]∈R 2 represents the position vector, velocity vector and control input of the ith UAV, s i =[x i y i v xi v yi ] represents the motion state of the i-th UAV. For simplicity, we will use p i , v i and u i Indicates the status of the first drone 2) Assuming that the lth UAV is the leader, it can be obtained from (1) that its state is represented by p1, v1 and s1, then the position and velocity matrix of the follower UAV can be expressed as: Among them, when the lth drone is the leader, represents the position of the jth follower, 3) The currently selected leader position p l The total position set of the target formation corresponding to the determined follower drone is expressed as: When the leader drone's position in the target formation is arranged as k, 1≤k≤M; represents the mth target position, when the lth UAV is the leader and its position is arranged as k, 1≤m≤M-1, l∈M, k∈M, represents a one-to-one mapping set of current target formations to followers; 4) The target mapping relationship is: Where N = (M-1)!, and 1≤n≤N represents one of the target mapping relationships; 5) The relative motion state is: Based on the selected leader UAV l , leader position ranking k and target mapping relationship in represents the relative position matrix between all followers and the target formation, represents the relative velocity matrix of all followers and the leader, Will and Combined to form the relative state matrix, Represents the relative motion state of the ith follower relative to the leader; 6) Formation time of the entire system in a formation: The time set of all followers in the formation is The maximum time of all followers in the formation is considered as the formation time; 7) The best leader and the shortest formation time are: Where l represents the selection of different UAV minimum formation time as the optimization variable of the leader. Finally, the minimum value of formula (7) is The leader is considered the best leader and gets the least formation time; (2) The model constructed based on the above leader selection algorithm mainly includes two sub-problems: UAV formation control and target mapping relationship. The UAV formation control problem is solved by combining LQR with the above model method, mainly focusing on speed and position control. The target formation mapping problem is to solve the one-to-one mapping relationship between the current follower and the target formation position; 1) In the first sub-problem of the leader selection algorithm, LQR is an optimized dynamic controller designed based on state space technology. The system model is a linear system given in state space form, and its objective function is a quadratic function of the state and control input. The vector matrix form of the system state space is Where A represents the state matrix of the system, B represents the output matrix, C represents the input matrix, D represents the direct transfer matrix of the input, x, y, and u represent the state vector, output vector, and input vector respectively; 2) In this system, assuming that the first The UAV is the leader, and its position order is k, The state vector x of the jth follower contains four state variables - position, speed in a two-dimensional coordinate system, and input variable u. It includes two variables as control inputs. The arrival of the drone at the target formation position and the convergence of the speeds of the follower and the leader are two conditions required for the formation of multiple drones to reach a stable state. Assume that the jth follower corresponds to the mth target formation position The expected output is: Among them, the initial state Expected input U j =[0 0] T , convert the states of multiple drones into the relative motion state of the leader. Therefore, both the initial state vector and the output state vector in the state equation must be changed. From formula (5), we can get: Y j =[0 0 0 0] T , U j =[0 0] T ; 3) The state space description of the j-th follower can be obtained by formula (1), expressed as: 4) The optimization objective function or cost function based on the LQR algorithm is defined as: Where Q represents the state weight and positive semidefinite matrix, R represents the control weight and positive definite matrix; 5) LQR defines the state feedback controller u and the state feedback matrix K, which can be expressed as u=-Kx(12) Substituting u into the previous system state equation, it can be expressed as: Then, the value of the feedback matrix K is calculated by solving the Riccati equation, and the initial state and simulation time interval are set. The system is simulated using the K feedback matrix. Finally, through system simulation, the total state and formation time of each UAV under the current mapping relationship between the leader and the target formation can be obtained; 6) In the second sub-problem of the leader selection algorithm, the time complexity of the mapping problem between followers and target formations is O(n!). As the scale of UAVs and data increases, genetic algorithm (GA) is one of the best tools to find a satisfactory solution; 7) Applying the GA algorithm to the model, the solution represents a mapping relationship, 1≤n≤N, according to the population size G from the set Randomly select a population The fitness function is the formation time of the corresponding mapping relationship when the leader drone and its order are determined by k Since GA is equivalent to reducing the set , so the constraints of problem (7) will also change, and problem (7) can be rewritten as: in, As the number of iterations and genetic operator operations continue to change.

2. The method for selecting a leader of a formation based on a rotary-wing UAV according to claim 1, characterized in that: The UAVs are abstracted as particles in a two-dimensional coordinate system. Assuming that the shape of the target formation is predetermined, the two sub-problems of UAV formation control and target mapping relationship are solved based on LQR and GA algorithms, and a leader selection algorithm for UAV formation is proposed.

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