An Unmanned Cluster Cooperative Formation Control Method Based on the Shortest Delay Path Network

Abstract

The present invention discloses a method for cooperative formation control of unmanned clusters based on the shortest-delay path network. The present invention models the static formation control problem of homogeneous unmanned clusters, gives the dynamic model of the unmanned clusters, and on the basis of the traditional adjacency network and the static formation control protocol based on the adjacency network, proposes the shortest-delay path network and the static formation control protocol based on the shortest-delay path network. Consider the static formation control problem of an unmanned cluster containing multiple unmanned vehicles in a two-dimensional plane. The goal of the static formation control of the unmanned cluster is to control the cluster to form a formation with a predetermined geometric relationship and to control the speed of each individual to converge to zero. It realizes the rapid and stable formation of a predetermined geometric formation by the unmanned cluster and the advancement at a predetermined speed, improves the convergence speed and practical application value, and provides an efficient and reliable formation control solution for the unmanned cluster system.

Description

Technical Field

[0001] The present invention relates to the field of UAV control, and particularly to a method for collaborative formation control of an unmanned cluster based on a time-delay shortest path network. Background Art

[0002] With the development of information technology and intelligent manufacturing technology, the functions of unmanned vehicles (including UAVs, unmanned vehicles, satellites, etc.) are becoming increasingly perfect. However, in the face of increasingly complex application environments and diverse requirements, a single intelligent unmanned vehicle is still limited in performing large and complex tasks due to its own software and hardware conditions. To make up for the limitations shown by a single device in the face of complex tasks, the concept of unmanned cluster collaborative formation is proposed, that is, multiple unmanned vehicles of the same model form a cluster to complete tasks collaboratively.

[0003] The formation control method based on multi-agent consensus theory only requires UAVs to perform local information interaction. In this method, actual physical communication links are only established between a UAV and its neighbors, and the desired formation control can be completed using relatively few communication links, which has the advantage of low communication cost compared with other methods. Also for this reason, in this method, the integrity, real-time performance, and accuracy of information are crucial. However, due to the limited communication speed and the existence of sensor measurement time, control instruction calculation time, instruction execution time, etc., time delay exists in almost all actual systems, and its impact on system stability and rapidity cannot be ignored.

[0004] To effectively address the challenges brought by time delay, by constructing a time-delay shortest path communication network, the information transmission path between UAVs is optimized to ensure that information can be transmitted within the cluster with the shortest time delay. Therefore, researching the unmanned cluster collaborative formation control technology based on a time-delay shortest path network will provide strong technical support for solving the problem of unmanned cluster collaborative control in complex task scenarios. Summary of the Invention

[0005] In view of the above deficiencies in the prior art, the present invention provides a method for collaborative formation control of an unmanned cluster based on a time-delay shortest path network.

[0006] To achieve the above invention objective, the technical solution adopted by the present invention is as follows:

[0007] A method for collaborative formation control of an unmanned cluster based on a time-delay shortest path network, comprising the following steps:

[0008] S1. Regarding the unmanned cluster as a multi-agent system, each unmanned vehicle can be regarded as an agent with second-order discrete dynamic characteristics;

[0009] S2. Construct a network communication topology model based on the shortest-delay path, and design a static formation control protocol based on the shortest-delay path network communication topology model, so that the multi-agent system forms a formation with a predetermined geometric shape and the speed of each agent converges to zero;

[0010] S3. Design a sampling-based dynamic formation control protocol considering the influence of the sampling period on the formation convergence, so that the multi-agent system forms a formation with a predetermined geometric relationship and the speed of each agent converges to the desired speed.

[0011] Further, the second-order discrete dynamic characteristics of the agent in S1 are expressed as:

[0012] x i (k + 1) = x i (k) + v i (k)

[0013] v i (k + 1) = v i (k) + u i (k), i ∈ {1, 2,..., n}

[0014] In the formula, x i represents the displacement of agent i, v i represents the speed of agent i, u i represents the control input, k is the discrete sampling point, and n is the total number of discrete points.

[0015] Further, the static formation control protocol in S2 is expressed as:

[0016]

[0017] In the formula, x i represents the displacement of agent i, v i represents the speed of agent i, γ i > 0, κ i > 0 are control parameters, represents the element in the adjacency matrix, D i represents the input delay of agent i, u i (k) is the control input, x i (k) is the displacement of agent i at the kth discrete sampling point, v i (k) is the speed of agent i at the kth discrete sampling point, is the communication delay from agent i to agent j, represents a formation with a predetermined geometric relationship.

[0018] Further, the multi-agent system under the designed static formation control protocol in S2 is expressed as:

[0019] x i (k + 1) = x i (k) + v i (k)

[0020]

[0021] where x i is the displacement of agent i, v i is the velocity of agent i, γ i > 0, κ i > 0 are control parameters, is an element in the adjacency matrix, D i is the input delay of agent i, u i (k) is the control input, x i (k) is the displacement of agent i at the k - th discrete sampling point, v i (k) is the velocity of agent i at the k - th discrete sampling point, n is the total number of discrete sampling points, is the communication delay from agent i to agent j, represents a formation with a predetermined geometric relationship.

[0022] Furthermore, the sampling - based dynamic formation control protocol in S3 is expressed as:

[0023]

[0024] where x i is the displacement of agent i, v i is the velocity of agent i, u(kT) is the control protocol considering the influence of the sampling period, T is the sampling period, γ i and κ i are control parameters, is an element in the adjacency matrix, D i is the input delay of agent i, and among them v * (k) is the desired velocity varying with the discrete time series k, n is the total number of discrete points, is the communication delay from agent i to agent j, represents a formation with a predetermined geometric relationship.

[0025] Furthermore, the agent system under the designed sampling - considered dynamic formation control protocol in S3 is expressed as:

[0026] x i ((k + 1)T) = x i (kT) + Tv i (kT)

[0027]

[0028] where x i represents the displacement of agent i, v i represents the velocity of agent i, u(kT) is the control protocol considering the influence of the sampling period, T is the sampling period, γ i >0, κ i >0 are control parameters, a ij represents the element in the adjacency matrix, D i represents the input time delay of agent i, and among them v * (k) is the desired velocity varying with the discrete time sequence k, is the communication time delay from agent i to agent j, represents the formation with a predetermined geometric relationship.

[0029] The present invention has the following beneficial effects:

[0030] (1) In solving the formation control problem of second-order discrete isomorphic unmanned clusters in a complex time-delay environment, aiming at the characteristics of transmissible and superimposable communication time delays, combining the idea of the shortest path network, by proposing the "time-delay shortest path network" model and the supporting formation control protocol, the stability and efficiency of formation formation are improved.

[0031] (2) On the basis of retaining the existing communication links, a shortest path communication network with time delay as the weight is constructed, and a formation control algorithm is designed. The formation formation conditions are optimized by frequency domain analysis and matrix theory, and the system performance is improved through simulation verification.

[0032] (3) It realizes that the unmanned cluster quickly and stably forms a predetermined geometric formation and advances at a predetermined speed, improves the convergence speed and practical application value, and provides an efficient and reliable formation control solution for the unmanned cluster system. Brief Description of the Drawings

[0033] Figure 1 It is a schematic flow chart of the cooperative formation control method for unmanned clusters based on the time-delay shortest path network.

[0034] Figure 2 It is a schematic topological diagram of the shortest path network communication model corresponding to the traditional adjacency network in the embodiment of the present invention.

[0035] Figure 3 It is a schematic multi-agent communication topology diagram based on the adjacency network in the embodiment of the present invention.

[0036] Figure 4 It is a schematic multi-agent communication topology diagram based on the time-delay shortest path network in the embodiment of the present invention.

[0037] Figure 5a This is the plane trajectory diagram of the static formation control simulation results of the embodiments of the present invention.

[0038] Figure 5b This is the X-direction velocity convergence diagram of the static formation control simulation results of the embodiments of the present invention.

[0039] Figure 5c This is the Y-direction velocity convergence diagram of the static formation control simulation results of the embodiments of the present invention.

[0040] Figure 6a This is the plane trajectory diagram of the dynamic formation control simulation results with a non-zero constant desired velocity of the embodiments of the present invention.

[0041] Figure 6b This is the X-direction velocity convergence diagram of the dynamic formation control simulation results with a non-zero constant desired velocity of the embodiments of the present invention.

[0042] Figure 6c This is the Y-direction velocity convergence diagram of the dynamic formation control simulation results with a non-zero constant desired velocity of the embodiments of the present invention.

[0043] Figure 7a This is the plane trajectory diagram of the dynamic formation control simulation results with the desired velocity varying with the time series of the embodiments of the present invention.

[0044] Figure 7b This is the X-direction velocity convergence diagram of the dynamic formation control simulation results with the desired velocity varying with the time series of the embodiments of the present invention.

[0045] Figure 7c This is the Y-direction velocity convergence diagram of the dynamic formation control simulation results with the desired velocity varying with the time series of the embodiments of the present invention.

[0046] Figure 8a This is the plane trajectory diagram of the formation control simulation results based on the adjacency network of the embodiments of the present invention.

[0047] Figure 8b This is the X-direction velocity convergence diagram of the formation control simulation results based on the adjacency network of the embodiments of the present invention.

[0048] Figure 8c This is the Y-direction velocity convergence diagram of the formation control simulation results based on the adjacency network of the embodiments of the present invention.

[0049] Figure 9a This is the plane trajectory diagram of the formation control simulation results based on the time-delay shortest path network of the embodiments of the present invention.

[0050] Figure 9b This is the X-direction velocity convergence diagram of the formation control simulation results based on the time-delay shortest path network of the embodiments of the present invention.

[0051] Figure 9c This is the Y - direction velocity convergence graph of the simulation results of the formation control based on the shortest - delay path network in the embodiments of the present invention. Detailed implementation manners

[0052] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0053] A method for collaborative formation control of unmanned clusters based on the shortest - delay path network, as Figure 1 shown, includes the following steps:

[0054] S1. Regard the unmanned cluster as a multi - agent system, and each unmanned vehicle can be regarded as an agent with second - order discrete dynamic characteristics;

[0055] The present invention models the static formation control problem of homogeneous unmanned clusters, gives the dynamic model of the unmanned cluster, and on the basis of the traditional adjacency network and the static formation control protocol based on the adjacency network, proposes the shortest - delay path network and the static formation control protocol based on the shortest - delay path network.

[0056] Consider the static formation control problem of an unmanned cluster containing n unmanned vehicles in a two - dimensional plane (the research conclusions in this context can be directly applied to the formation of ground unmanned vehicle clusters, the formation of medium - altitude unmanned aircraft clusters in three - dimensional space, etc.). The goal of the static formation control of the unmanned cluster is to control the cluster to form a formation with a predetermined geometric relationship and control the speed of each individual to converge to zero.

[0057] Regard the unmanned cluster as a multi - agent system, and each unmanned vehicle can be regarded as an agent with second - order discrete dynamic characteristics. The dynamic equation is as follows:

[0058]

[0059] where x i ∈R 2 represents the displacement of agent i, v i ∈R 2 represents the speed of agent i, and u i ∈R 2 represents the control input.

[0060] S2. Construct a network communication topology model based on the shortest delay path, and design a static formation control protocol based on the network communication topology model of the shortest delay path, so that the multi-agent system forms a formation with a predetermined geometric shape and the speed of each agent converges to zero.

[0061] The traditional model used to describe the actual communication relationship between agents is defined as an adjacency network. However, considering the widespread communication delay between agents, in order to improve the utilization degree of communication network information, increase the security and reliability of the communication network, without changing the actual physical communication network, by increasing the network information volume and reallocating communication resources, a shortest path communication network with communication delay as the weight is established, that is, the shortest delay path network.

[0062] The shortest delay path network is the shortest path network with communication delay as the weight, and its topology model is represented by a directed graph. It is represented as follows, where \(V = \{v_1, v_2, \cdots, v\) n \} is the node set of the directed graph , representing \(n\) agents participating in the formation of the unmanned cluster. For the edge set of the adjacency matrix and the communication delay between agents are defined as follows:

[0063] 1. If there is at least one directed path from node \(v\) j to node \(v\) i in the traditional adjacency network, then agent \(i\) can receive the information of \(j\). It is defined that the communication delay corresponding to each directed path is equal to the sum of the communication delays corresponding to each edge on the path. If there are multiple directed paths from agent \(j\) to agent \(i\), then the directed path with the shortest corresponding communication delay is taken as the only actual path for information transmission between agent \(j\) and agent \(i\) (if the directed paths satisfying the shortest communication delay are still not unique, any one of them can be taken). Denote this directed path as , where each ordered node pair in \(p\) ij is an edge in the adjacency network, that is Thus, the communication delay from agent \(j\) to agent \(i\) is defined, and the element

[0064] 2. If there is no directed path from node \(v\) j to node \(v\) i in the traditional adjacency network, then agent \(i\) cannot receive the information of \(j\).

[0065] According to the definition, the shortest path network communication model corresponding to the traditional adjacency network can be obtained. As Figure 2 shown, the node set of [the shortest path network] is the same as that of the adjacency network, and its edge set adds the edge (v1, v3) relative to the adjacency network, as shown by the dashed line in the figure. The adjacency matrix of [the shortest path network] and the communication delay matrix are respectively:

[0066]

[0067] The shortest path network here is not the shortest path network calculated with the weight of the edge as the weight in the traditional sense, but the shortest path network generated by calculating with the communication delay corresponding to each edge as the weight. The reason why the delay shortest path network only uses the communication delay as the weight and does not include the input delay is that the communication delay between agents has the characteristics of being transmitted and accumulated in the communication link, while the input delays of each agent are independent of each other.

[0068] The delay shortest path network has stronger connectivity than the adjacency network, but it does not delete or add any actual physical communication links. The delay shortest path network only increases the traffic and optimizes the communication path on the basis of the existing physical communication network. Next, consider the static formation control protocol based on the delay shortest path network. Under the communication model of [the delay shortest path network], for the system shown in formula (1), the following control protocol for the unmanned cluster system with static formation control is proposed: Figure 2 For the system shown in formula (1), the following control protocol for the unmanned cluster system with static formation control is proposed under the communication model of [the delay shortest path network]:

[0069]

[0070] Then, the mathematical model of the unmanned cluster system considering static formation control is:

[0071]

[0072] To meet the requirement that the system shown in formula (3) can make the unmanned cluster asymptotically form a formation with a predetermined geometric relationship and the speed of each agent converges to zero (static formation control) under the action of the control protocol shown in formula (2), the following proof is given:

[0073] Theorem 1 Consider the system (3) composed of n agents. If:

[0074] (i) The communication topology G contains a directed spanning tree,

[0075] (ii) 0 < γ i < 2,

[0076] (iii)

[0077] If all of them hold, the system shown in formula (3) can asymptotically form a formation with a predetermined geometric relationship, and the velocity of each agent converges to zero. That is, There is

[0078] Proof: For the system shown in formula (3), let There is:

[0079]

[0080] Taking the z-transform of (4) gives:

[0081]

[0082] Where and V i (z) are the z-transforms of and v i (k) respectively.

[0083] Define an n×n matrix L(z) = {l ij (z)}:

[0084]

[0085] Where L(1) = L is the Laplacian matrix of graph . Then equation (5) can be written as:

[0086]

[0087] Where

[0088] V(z) = [V1(z) T ,V2(z) T ,...,V n (z) T T , denotes the Kronecker product,

[0089] Γ = diag{γ1,γ2,...γ n},K = diag{κ1,κ2,...κ n},I 2×2 denotes the 2×2 identity matrix.

[0090] Thus, the characteristic equation about is:

[0091] ​

[0092] According to the properties of Kronecker multipliers, we can first consider

[0093] det[(z - 1) 2 I n×n +(z - 1)(Γ + KL(z)) + ΓKL(z)] = 0 (8) The characteristic equation (8) can be equivalently rewritten as

[0094] det[(z - 1)I n×n + Γ] = 0 (9) or

[0095] det[(z - 1)I n×n + KL(z)] = 0 (10) Considering equation (9), since Γ is a diagonal matrix, its solutions can be directly obtained as z i = 1 - γ i , i ∈ {1, 2,..., n}. When 0 < γ i < 2, we have |z i | = |1 - γ i | < 1, i.e., all roots of (7) are inside the unit circle.

[0096] Considering equation (10), define

[0097] D(z) = det[(z - 1)I n×n + KL(z)] (11)

[0098] Next, it will be shown that z = 1 is a simple zero of D(z), and all other zeros are inside the unit circle in the complex plane.

[0099] Let z = 1, then D(1) = det(KL(1)) = det(KL) = det(K)det(L). Since the graph G = (V, E, A) contains a directed spanning tree, the graph contains a directed spanning tree, so 0 is a simple eigenvalue of the Laplacian matrix L of the graph . Also, since K = diag{k i > 0, i = 1, 2,..., n}, we have D(1) = 0, and z = 1 is a simple zero of D(z).

[0100] When z ≠ 1, define F(z) = det(I + (1 / (z - 1))KL(z)). Next, it is shown that all zeros of F(z) are inside the unit circle. By the generalized Nyquist criterion, when (1 / (e jω - 1))KL(e jωWhen the characteristic root locus of () does not enclose the point (-1, j0) for ω ∈ [-π, π], the modulus of the zeros of F(z) is less than 1, that is, all zeros are inside the unit circle.

[0101] According to the Gerschgorin disk theorem, (1 / (e jω -1))KL(e jω ) has its characteristic roots located within the union of n disks D i , that is

[0102] λ((1 / (e jω -1))KL(e jω )) ∈ ∪ i∈{1,2,...,n} D i , ω ∈ [-π, π] (12)

[0103] where

[0104]

[0105] Since

[0106]

[0107] So (13) can be written as

[0108]

[0109] where Define

[0110]

[0111] Note that G i (ω) is the center of the disk and the characteristic root locus of (1 / (e jω -1))KL(e jω ) encloses the origin of the complex plane. Thus, as long as the point (-a, j0) with a ≥ 1 is outside the disk then the characteristic root locus of (1 / (e jω -1))KL(e jω ) does not enclose the point (-1, j0) for any ω ∈ [-π, π]. Furthermore, when a ≥ 1, if all have then it can be shown that all zeros of F(z) are inside the unit circle.

[0112] From (15), we have:

[0113]

[0114] Before proceeding with the subsequent proof, the following lemma needs to be given:

[0115] Lemma 1 For any non - negative integer N and any ω ∈ [-π, π], the following inequality holds:

[0116]

[0117] From Lemma 1 and condition (iii), we have

[0118]

[0119] Thus

[0120]

[0121] That is, when a ≥ 1, for we always have Thus, all zeros of F(z) are inside the unit circle in the complex plane.

[0122] In summary, except for the single - root z = 1, the remaining roots of equation (8) are inside the unit circle in the complex plane. From the properties of the Kronecker multiplier, except for the two roots at z = 1, the remaining roots of equation (7) are inside the unit circle in the complex plane. Therefore, and Thus, when k → ∞, equation (3) can be reduced to where 0 is an eigenvalue of the Laplacian matrix L, and 1 n =[1, 1,..., 1] T is a right - eigenvector corresponding to the eigenvalue 0. Thus the roots of can be expressed as 2 where c ∈ R Thus Proved.

[0123] S3. Consider the influence of the sampling period on the formation convergence and design a sampling - based dynamic formation control protocol to make the multi - agent system form a formation with a predetermined geometric shape relationship and the velocity of each agent converge to the desired velocity.

[0124] To be more applicable to the control problem of dynamic formation in practical scenarios, that is, if it is desired that the unmanned cluster maintains a desired velocity v * (k) and continues to move forward after forming the desired formation, and it is necessary to examine whether the sampling period has an impact on the formation convergence. Now consider a more general unmanned - cluster dynamic formation system with sampling period T:

[0125] x i ((k + 1)T)=x i (kT)+Tv i (kT)

[0126] v i v = x((k + 1)T) i x(kT) + Tu i x(kT) (17)

[0127] Propose a control protocol u(kT) applicable to (17):

[0128]

[0129] Substituting the protocol (18) into the system (17), the closed-loop system of (17) can be obtained as follows:

[0130]

[0131] where T is the sampling period, and v * x(kT) represents the desired velocity of the entire formation that can vary with the discrete time series, Propose Theorem 2 as follows:

[0132] Theorem 2: Considering the influence of the sampling period on the formation, in order to satisfy that the system (19) can make the unmanned cluster asymptotically form a formation with a predetermined geometric relationship under the action of the control protocol (18), and the velocity of each agent asymptotically converges to v * x(kT) (dynamic formation control), the following proof is given:

[0133] Consider the system (19) composed of n agents. If:

[0134] (i) The communication topology G contains a directed spanning tree,

[0135] (ii) 0 < γ i T < 2,

[0136] (ii)

[0137] both hold, then the system (17) asymptotically forms a formation with a predetermined geometric relationship, and the velocity of each agent asymptotically converges to v * x(kkT). That is, there is

[0138] Proof: First, perform a variable substitution. Let Then the system (17) can be transformed into:

[0139]

[0140] Taking the z-transform of the above equation gives:

[0141]

[0142] Among them, and are respectively and The z-transforms of, and the definition of L(z) can be seen in the proof process of Theorem 1. denotes the Kronecker product, Γ = diag{γ1, γ2,... γ n}, K = diag{κ1, κ2,... κ n}, and I 2×2 denotes the 2×2 identity matrix.

[0143] Thus, the characteristic equation of the system with respect to is as follows:

[0144]

[0145] After factorization, according to the properties of the Kronecker product, we can first consider the equations:

[0146] det[((z - 1)I n×n + TΓ] = 0

[0147] and the equation:

[0148] det[((z - 1)I n×n + TK L(z)] = 0

[0149] Following the proof process of Theorem 1, it can be proved that: if conditions (i), (ii), and (iii) are all satisfied, then where c ∈ R 2 is a constant vector.

[0150] Thus, Theorem 2 is proved.

[0151] It can be seen that the control gain parameters γ and κ of the system, the sampling period T of the system, and the in-degree of each agent in the shortest path network topology are important factors for whether the swarm can form a formation. Moreover, by adjusting the above parameters, the system can tolerate a larger input time delay D i . When the above parameters satisfy the theorem conditions, the communication time delay will not affect whether the system can finally form a formation. Even if the communication time delay takes a quite large value, the system will asymptotically form a formation. Although the communication time delay will not affect the convergence of the formation, its impact on the dynamic performance of the formation (such as the convergence speed) has to be considered.

[0152] The research object of the simulation experiment is a multi-agent system composed of four second-order unmanned vehicles (agents). The dynamic characteristics of each agent are described by Equation (17). The communication structure G among the agents is as shown in Figure 3 :

[0153] It can be seen that G contains a directed spanning tree. For ease of understanding, the weights of all edges of G are taken as 1. According to Definition 1, the adjacency matrix A of G and the communication delay assignment among the agents are as follows:

[0154]

[0155] After introducing the delay shortest path network, the communication topology of the system can be updated to Figure as Figure 4 shown. The corresponding adjacency matrix and communication delay matrix are:

[0156]

[0157] The relevant parameter settings are as follows: sampling period T = 0.1; input delays D1 = D2 = D3 = D4 = 1; control parameters γ1 = γ2 = γ3 = γ4 = 1, κ1 = κ2 = κ3 = κ4 = 0.1 in (19); the desired formation is a square, x1 * = [-50, -50] T , x2 * = [-50, 50] T , x3 * = [50, 50] T , x4 * = [50, -50] T . After verification, the above parameters meet the conditions of step S3.

[0158] Now, verify the feasibility of the formation control protocol:

[0159] (1) Static formation control simulation

[0160] The goal of static formation control is to make the 4 agents form the desired formation and the speed of each unmanned vehicle converges to 0. For system (19), set the desired speed v * = [0, 0] T , and the initial speeds and positions of the agents are randomly generated. The simulation results are as shown in Figure 5a , Figure 5b , Figure 5c . It can be seen that the 4 agents finally form the desired square formation (as shown by the dotted box in Figure 5a ), and the speed of each agent converges to zero.

[0161] (2) Dynamic formation control simulation with a non - zero constant desired speed

[0162] The goal of dynamic formation control with a non - zero constant desired speed is to make 4 agents form the desired formation, and the speeds of each agent can converge to the same preset non - zero constant value. For system (19), set the desired speed \(v\) * = [10, 8] T , and the initial speeds and positions of the agents are randomly generated. The simulation results are as shown in Figure 6a 、 Figure 6b 、 Figure 6c . It can be seen that the 4 agents finally form the desired square formation (as shown by the dashed box in Fig. 5(a)), the speed of each agent in the X - direction converges to 10, and the speed in the Y - direction converges to 8, completing the tracking of the desired speed \(v\) * = [10, 8] T .

[0163] (3) Dynamic formation control simulation with desired speed varying with time series

[0164] The goal of dynamic formation control with a non - zero constant desired speed is to make 4 agents form the desired formation, and the speeds of each agent can track the desired speed that varies with the discrete time series. For system (19), set the desired formation speed as \(v\) * (kT)=[3sin(0.2kT), 3cos(0.2kT)] T , and the initial speeds and positions of the agents are randomly generated. The simulation results are as shown in Figure 7a 、 Figure 7b 、 Figure 7c . It can be seen that the 4 agents form the desired square formation, and when the desired speed is a signal varying with the discrete time series, the control protocol proposed in this invention can still make the speeds of each agent track \(v\) * (kT)=[3sin(0.2kT), 3cos(0.2kT)] T . The above three simulation experiments verify the correctness of Theorem 2, that is, the formation control protocol of this invention is feasible.

[0165] A comparative simulation experiment is carried out between the formation control algorithm based on the delay - shortest - path network proposed in this invention and the traditional formation control algorithm based on the adjacency network to show the improvement of this algorithm on the formation speed. To reflect the advantages of the communication network proposed in this invention, a control protocol corresponding to the control protocol (18) and applicable to the traditional adjacency communication network is given first:

[0166]

[0167] First, consider a communication topology based on a traditional adjacency network, such as Figure 3 for a system, and apply a control protocol as in Equation (20). The communication delay matrix is τ, and the input delays are D1 = D2 = D3 = D4 = 1. Let the sampling period T = 0.1, set the desired formation to a square, x1 * = [-50, -50] T , x2 * = [-50, 50] T , x3 * = [50, 50] T , x4 * = [50, -50] T ; set the desired velocity v * (kT) = [3sin(0.2kT), 3cos(0.2kT)] T ; set the control parameters γ1 = γ2 = γ3 = γ4 = 1, κ1 = κ2 = κ3 = κ4 = 0.1; set the initial positions of the agents as x1 = [0, 10] T , x2 = [0, 20] T , x3 = [30, 0] T , x4 = [40, 0] T , and set the initial velocities of the agents as v1 = [7, 8] T , v2 = [5, 6] T , v3 = [3, 4] T , v4 = [1, 2] T . The simulation results are as shown in Figure 8a , Figure 8b and Figure 8c .

[0168] Next, consider a system with a communication topology incorporating a shortest - path network, such as Figure 3 . The communication delay matrix is and the input delays are D1 = D2 = D3 = D4 = 1. When the settings of other conditions are the same as those when applying the control protocol in Equation (20), the simulation results are as shown in Figure 9a , Figure 9b , Figure 9c .

[0169] As can be seen from Figure 8 and Figure 9, although the systems under both protocols can form the desired formation, the system based on the shortest - path network with the control protocol in Equation (18) has a significantly faster speed convergence rate. Thus, it can be seen that the delay - shortest communication network and the corresponding control protocol proposed in the present invention can improve the utilization rate of network information and accelerate the speed of the system to achieve formation.

[0170] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing device produce a means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks, which specify the functions of the device.

[0171] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction means that implements the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks, which specify the functions.

[0172] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks, which specify the functions.

[0173] Specific embodiments are applied in the present invention to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation on the present invention.

[0174] Those of ordinary skill in the art will realize that the embodiments described herein are for helping readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for cooperative formation control of unmanned clusters based on a network with the shortest delay path, characterized in that, Including the following steps: S1. Regarding the unmanned cluster as a multi-agent system, each unmanned vehicle can be regarded as an agent with second-order discrete dynamic characteristics; S2. Constructing a communication topology model based on the shortest-delay path network and designing a static formation control protocol based on the shortest-delay path network communication topology model, so that the multi-agent system forms a formation with a predetermined geometric shape and the speed of each agent converges to zero. Among them, the static formation control protocol is expressed as: wherein, represents the displacement of the agent ; represents the velocity of the agent ; , is a control parameter, represents an element in the adjacency matrix, represents the input time delay of the agent ; is the control input, is the displacement of the agent at the k -th discrete sampling point, is the velocity of the agent at the k -th discrete sampling point, is the communication time delay from the agent to the agent ; represents a formation with a predetermined geometric relationship, is the total number of discrete points; S3. Designing a sampling-based dynamic formation control protocol considering the influence of the sampling period on the formation convergence, so that the multi-agent system forms a formation with a predetermined geometric shape relationship and the speed of each agent converges to the desired speed. Among them, the dynamic formation control protocol is expressed as: wherein, is the control protocol considering the influence of the sampling period, is the sampling period, and are control parameters, is an element in the adjacency matrix, is the input time delay of agent , and among them , is the desired speed varying with the discrete time series .

2. The method for unmanned cluster cooperative formation control based on the network with the shortest delay path according to claim 1, wherein The second-order discrete dynamic characteristics of the agent in S1 are expressed as: wherein, represents the displacement of the agent , represents the velocity of the agent , represents the control input, is the discrete sampling point, is the total number of discrete points.

3. The method for unmanned cluster cooperative formation control based on the network with the shortest delay path according to claim 1, wherein The multi-agent system under the designed static formation control protocol in S2 is expressed as: In the formula, is the displacement of the agent . is the velocity of the agent . , is the control parameter, is the element in the adjacency matrix, is the input time delay of the agent , is the control input, is the displacement of the agent at the k -th discrete sampling point, is the velocity of the agent at the k -th discrete sampling point, is the total number of discrete sampling points, is the communication time delay from the agent i to the agent j , represents a formation with a predetermined geometric relationship.

4. The method for unmanned cluster cooperative formation control based on the network with the shortest delay path according to claim 1, wherein The agent system under the designed sampling-based dynamic formation control protocol in S3 is expressed as: In the formula, represents the displacement of the agent , represents the velocity of the agent , is the control protocol considering the influence of the sampling period, is the sampling period, , is the control parameter, represents the element in the adjacency matrix, represents the input time delay of the agent , and among them , is the desired velocity varying with the discrete time series , is the communication time delay from the agent i to the agent j , represents the formation with a predetermined geometric relationship.

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