Multi-agent system distributed positioning method and system based on relative position measurement

Abstract

The invention discloses a multi-agent system distributed positioning method and system based on relative position measurement, and the method comprises the steps: obtaining the position information of a leader node and the orientation angles of all nodes for a multi-agent system which is composed of n + 1 nodes and moves at a constant speed, and the n + 1 nodes comprise one leader node and n follower nodes; performing relative position measurement on each follower node and a neighbor node thereof under a local coordinate system, and communicating with the neighbor node; each follower node obtains a position estimation value based on the measured relative position, the orientation angle and the communication information and converges to a real position in finite time, so that all follower nodes realize distributed positioning in the finite time; under the condition that speed measurement and system control input are not needed, finite time positioning of the distributed system is achieved only based on relative position measurement.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent positioning, and in particular to a multi-agent system distributed positioning method and system based on relative position measurement. Background Art

[0002] A multi-agent system is composed of a series of intelligent agents that collaborate through communication and measurement to complete complex tasks that would be difficult for a single agent to accomplish. Multi-agent collaboration can expand the system's perception range and offer enhanced scalability, allowing it to adapt to diverse requirements. Therefore, research on multi-agent systems, based on technologies such as robotics and sensors, holds great promise for broad application.

[0003] Current research on localization methods for multi-agent systems can generally be categorized into two approaches: centralized and distributed. The centralized approach requires a control center, which, through communication and other means, obtains the status, measurement, and other data of all agents in the system and processes this data uniformly. This approach places high demands on the stability of the control center; a failure in the control center risks paralyzing the entire system. In contrast, a distributed approach, in which each node measures, calculates, and stores local data, offers advantages such as low communication costs, high fault tolerance, and strong robustness.

[0004] Among the numerous studies on distributed localization from the perspective of deterministic systems, most have focused on static systems. In practical applications, such as patrolling, search and rescue, and military operations, multi-agent systems are often dynamic. Current research on dynamic systems has addressed the source localization problem in dynamic multi-agent systems and the localization problem of slow-moving targets with unknown speeds using distributed methods. However, these studies do not address the localization problem of the dynamic system itself and cannot achieve localization of each agent. In existing distributed localization research for dynamic multi-agent systems, some proposed algorithms require rigidity conditions and only achieve exponential or asymptotic convergence. However, the real-time nature of dynamic systems places higher demands on the convergence speed of localization algorithms. Therefore, achieving distributed finite-time localization for dynamic multi-agent systems is an urgent problem that needs to be solved.

[0005] In related technology, patent application publication number CN118778656A designs a controller based on a saturated input function. Leveraging fixed-time stability theory and homogeneous theory, this approach ensures that a multi-agent system completes formation control tasks, rather than positioning, within a fixed timeframe. Formation control involves moving multiple agents according to a preset geometric formation, primarily involving control strategies and collision avoidance. Traditional formation positioning, on the other hand, involves obtaining the position information of each object in the formation through various positioning techniques and methods, and then processing and analyzing it to accurately determine the position of each object in the formation. Formation control relies on formation positioning as a foundation, and control strategies must rely on individual position information to determine whether they are in the target formation. For example, if a drone cannot determine its relative position to neighboring drones, it will be difficult to achieve correct coordinated adjustments. Therefore, the proposed solution in this document focuses on designing formation control under the premise of measurable positioning information. The paper “Distributed Surrounding Tracking Control of Unknown Dynamic Targets by Second-Order Multi-Agent Systems, Chen Wenting, Master’s Thesis, Beijing University of Chemical Technology” proposes modeling the target velocity as an unknown dynamic exogenous signal, using local relative position measurement and communication to establish a distributed observer, using each agent’s estimation of the target’s relative position and velocity, and designing an adaptive control law based on this. After the agent responsible for surrounding tracking locates the target robot, the control of the agent’s tracking and surrounding is realized. Summary of the Invention

[0006] The technical problem to be solved by the present invention is how to achieve finite-time positioning of a distributed system based only on relative position measurement without the need for speed measurement and system control input.

[0007] The present invention solves the above technical problems through the following technical means:

[0008] A distributed positioning method for a multi-agent system based on relative position measurement is proposed, the method comprising:

[0009] For a uniformly moving multi-agent system consisting of n+1 nodes, obtain the position information of the leader node and the orientation angles of all nodes. The n+1 nodes include a leader node and n follower nodes.

[0010] Each follower node measures its relative position with its neighbor nodes in the local coordinate system and communicates with the neighbor nodes;

[0011] Each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, so that all follower nodes can achieve distributed positioning within a limited time.

[0012] Furthermore, obtaining the location information of the leader node and the orientation angles of all nodes includes:

[0013] Use GPS to obtain the location information of the leader node;

[0014] Use the compass to get the heading angle of each node.

[0015] Furthermore, each follower node measures a relative position with its neighboring node in its own coordinate system and communicates with the neighboring node, including:

[0016] Construct an undirected communication topology graph between n follower nodes and a directed communication topology graph between n+1 nodes;

[0017] Based on the directed communication topology graph, each follower node measures its relative position with its neighbor nodes in the local coordinate system and communicates with the neighbor nodes to transfer the position estimation information.

[0018] Furthermore, each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, including:

[0019] Based on the designed position estimator, each follower node obtains the position estimation value of the follower node based on the relative position, orientation angle and communication information. The formula of the position estimator is expressed as:

[0020]

[0021] Where: is the estimated position of the i-th follower node The first derivative of is the estimated position of the j-th follower node, is the relative position of the i-th follower node measured in the local coordinate system; is the estimated velocity of the ith follower node, is the estimated velocity of the i-th follower node The first derivative of is the estimated velocity of the j-th follower node The first derivative of ; coefficients μ1, μ2, k1, k2>0; 0<α1<1, sig α () is the derivative function of the sign function sgn, sgn() is the standard sign function; β i , γ i 、z i is the symbol of the operation process, N i is the set of all neighboring nodes of agent i; βi The first derivative of γ i The first derivative of a ij is the element value in the adjacency matrix; is the rotation matrix about the orientation angle.

[0022] Furthermore, the rotation matrix The public statement is:

[0023]

[0024] Where θ i is the orientation angle of the i-th follower node.

[0025] Furthermore, the first-order derivative of the speed estimate of the leader node satisfies

[0026] Furthermore, the represents the position estimation error observer; represents the speed error observer.

[0027] Furthermore, the position estimator converges to the true position of the follower node within a finite time based on the position estimate of the follower node itself. Design for purpose.

[0028] Furthermore, after each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, the method further includes:

[0029] The position estimator is numerically simulated and verified using MATLAB, and experimentally verified using an experimental platform built with a QbBot-2e robot.

[0030] In addition, the present invention also proposes a multi-agent system distributed positioning system based on relative position measurement, comprising:

[0031] An information acquisition module is used to obtain the position information of the leader node and the orientation angles of all nodes for a uniformly moving multi-agent system consisting of n+1 nodes, where the n+1 nodes include a leader node and n follower nodes;

[0032] The relative position measurement module is used to control each follower node to measure the relative position with its neighboring nodes in the local coordinate system and communicate with the neighboring nodes;

[0033] The position estimator is used to control each follower node to obtain its position estimate based on the measured relative position, orientation angle and communication information and converge to its true position within a limited time, so that all follower nodes can achieve distributed positioning within a limited time.

[0034] The advantages of the present invention are:

[0035] For a uniform motion multi-agent system, the present invention designs a distributed finite-time positioning method based only on relative position measurement without the need for speed measurement and system control input, thereby realizing the finite-time positioning of the system. Compared with asymptotic convergence and exponential convergence, the finite-time convergence speed is faster, which can better meet the real-time requirements of the dynamic system.

[0036] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic flow chart of a distributed positioning method for a multi-agent system based on relative position measurement proposed in one embodiment of the present invention;

[0038] Figure 2 A topological relationship diagram between intelligent agents in one embodiment of the present invention;

[0039] Figure 3 A position estimation error diagram according to an embodiment of the present invention;

[0040] Figure 4 A motion trajectory diagram of a multi-agent system in one embodiment of the present invention;

[0041] Figure 5 A motion trajectory diagram of each intelligent agent in an embodiment of the present invention;

[0042] Figure 6 A topological relationship diagram between robots in one embodiment of the present invention;

[0043] Figure 7 is a position estimation error curve diagram of each robot in one embodiment of the present invention;

[0044] Figure 8 A diagram showing the motion trajectory of a robot in one embodiment of the present invention;

[0045] Figure 9 This is a structural diagram of a distributed positioning system for a multi-agent system based on relative position measurement proposed in one embodiment of the present invention. DETAILED DESCRIPTION

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0047] like Figure 1 As shown, an embodiment of the present invention proposes a distributed positioning method for a multi-agent system based on relative position measurement, the method comprising the following steps:

[0048] S10. For a uniformly moving multi-agent system composed of n+1 nodes, obtain position information of a leader node and orientation angles of all nodes, where the n+1 nodes include a leader node and n follower nodes.

[0049] Specifically, suppose the multi-agent system consists of 6 agents, and the topological relationship between the agents is as follows: Figure 2 As shown, node 0 represents the leader node, which can be located in real time, nodes 1 to 5 are follower nodes, and the edges between the nodes represent the direction of information flow.

[0050] It should be noted that the leader node can directly obtain location information through GPS and other means, while the location information of the follower node can be obtained by measuring the relative position with the neighboring node and communicating with it based on the lidar, and then estimating the position.

[0051] It should be noted that the orientation angles of all nodes can be measured using a compass or other methods.

[0052] S20, each follower node measures the relative position of its neighbor node in the local coordinate system and communicates with the neighbor node;

[0053] It should be noted that the local coordinate system here can be understood as the follower node's own coordinate system; the follower's neighbor nodes can be known through its communication topology diagram. If there are connected lines between nodes, it means that they are neighbor nodes and can communicate.

[0054] S30. Each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, so that all follower nodes achieve distributed positioning within a limited time.

[0055] It should be noted that the communication information refers to the position estimation information transmitted between an agent and its neighboring agents.

[0056] This embodiment designs a distributed finite-time positioning method based solely on relative position measurement for a uniformly moving multi-agent system, without the need for speed measurement or system control input. The position of the follower node is estimated solely with the help of relative position information and orientation angle, achieving finite-time positioning of the system. Compared with asymptotic convergence and exponential convergence, the finite-time convergence speed is faster, which can better meet the real-time requirements of the dynamic system. The distributed positioning method for the multi-agent system proposed in this embodiment achieves self-positioning of the follower agent. In the absence of GPS or other external positioning means, the position of each agent is estimated through relative position measurement. The only information sources required are the GPS position information of the leader and the relative position information and orientation angle information of the follower measured by the lidar. The designed distributed positioning method uses the above information to estimate the position of each subsequent follower agent and ultimately achieves precise positioning.

[0057] As a further preferred technical solution, step S20: each follower node measures the relative position of its neighbor node in its own coordinate system and communicates with the neighbor node, specifically including the following steps:

[0058] S21. Construct an undirected communication topology graph between n follower nodes and a directed communication topology graph between n+1 nodes;

[0059] S22. Based on the directed communication topology graph, each follower node measures the relative position of its neighboring nodes in its own coordinate system and communicates with the neighboring nodes.

[0060] Specifically, let the directed graph consisting of n+1 nodes (including n follower nodes and one leader node) be G, and for each follower node, there is at least one directed path starting from the leader node and ending at the follower node; let the subgraph consisting of n follower nodes be G0, and the topological relationship between n followers is an undirected graph. The adjacency matrix and degree matrix of the subgraph G0 are respectively and in, is an n-order real matrix, a ij is the matrix element in the i-th row and j-th column of the adjacency matrix, indicating whether the i-th agent can communicate with the j-th agent. If j is a neighboring node of i, then a ij =1, if j is not a neighbor of i, then a ij = 0. Then calculate the Laplacian matrix of the undirected graph G0 The topological relationship between the follower node and the leader node is expressed using a matrix Indicates that, here B={a 10 ,a 20 ,…,an0}, if leader node 0 is a neighbor node of follower node i, then a i0 =1, otherwise a i0 = 0, record the Laplace matrix of the directed graph G

[0061] It should be noted that the structure of a multi-agent system can be abstracted as a graph structure, where each agent is represented by a node in the graph and the interactions between agents are represented as edges in the graph. This embodiment constructs the Laplacian matrix of the directed graph G and the Laplacian matrix of the undirected graph G0 to describe the formation structure and the transmission of communication information between agents.

[0062] As a further preferred technical solution, in step S30, each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, including:

[0063] Based on the designed position estimator, each follower node obtains the position estimate of the follower node based on the relative position, orientation angle and communication information, where the position estimator is expressed as:

[0064]

[0065] Where: is the estimated position of the i-th follower node The first derivative of is the estimated position of the j-th follower node, is the relative position of the i-th follower node measured in the local coordinate system; is the estimated velocity of the ith follower node, is the estimated velocity of the i-th follower node The first derivative of is the estimated velocity of the j-th follower node The first derivative of ; coefficients μ1, μ2, k1, k2>0, 0<α1<1, (These value ranges are based on the global finite-time stability Lemma 2.1); sig α () is the derivative function of the symbolic function sgn, sig α (x)=|x| α sgn(x),α∈(0,1); sgn() is the standard sign function, β i , γ i 、z i is the symbol of the operation process, N i is the set of all neighboring nodes of agent i, β i The first derivative of γ i The first derivative of a ij is the element value in the adjacency matrix, indicating whether the i-th agent has a communication connection with the j-th agent; is the rotation matrix about the orientation angle.

[0066] It should be noted that, as can be seen from the position estimator designed in this embodiment, position estimation can be achieved by only using the relative positions of neighbor nodes in the local coordinate system.

[0067] As a further preferred technical solution, the rotation matrix The public statement is:

[0068]

[0069] Where θ i is the orientation angle of the i-th follower node.

[0070] As a further preferred technical solution, since the designed position estimation method is used to estimate the position of the follower node, the first-order derivative of the speed estimation value of the leader node satisfies

[0071] As a further preferred technical solution, the distributed positioning method proposed in this embodiment utilizes only local relative position measurement information, eliminating the need for velocity measurement and system control input. However, for finite-time algorithms, velocity information is generally required. Therefore, in this embodiment, the absence of velocity measurement refers to not directly measuring velocity using a velocity sensor, but rather calculating velocity by observing the relative position offset over a specified period of time.

[0072] Specifically, represents the position estimation error observer; represents the speed error observer.

[0073] As a further preferred technical solution, the position estimator converges to the true position of the follower node within a limited time based on the position estimate of the follower node itself. For target design, T represents bounded time.

[0074] Specifically, the true position of agent i is represented by p i =(x i ,y i ) T The estimated position is expressed as The estimated error is T Represents the transpose symbol.

[0075] In this embodiment, when the follower node measures and communicates relative positions with neighboring nodes, a position estimation algorithm is designed for each follower node. Each follower node implements the position estimation algorithm so that all follower nodes can achieve distributed positioning within a limited time, that is, their own position estimation value converges to the true position within a limited time.

[0076] Specifically, the proof process of using the position estimator to realize the positioning of the agent within a limited time is as follows:

[0077] Definition 1.1: For a given vector X = (x1, x2, ..., x n ) T ,definition:

[0078] sgn(X)=(sgn(x1),sgn(x2),...,sgn(x n )) T ,

[0079] sig α (X)=sgn(X)|X| α =(sgn(x1)|x1| α ,sgn(x2)|x2| α ,...,sgn(x n )|x n | α ) T ,

[0080] Where |x| α =(|x1| α ,|x2| α ,...,|x n | α ) T .

[0081] For nonlinear systems If there exists a function T x (x0):Ω / {0}→(0,∞), so that for any t∈[0,T x (x0)], the following conditions are met:

[0082] (1) When t→T x (x0),

[0083] (2) When t>T x (x0), x(t,x0) is always equal to zero.

[0084] Then the system is locally finite-time stable if Ω=D=R n, then the system is called globally finite-time stable.

[0085] Lemma 1.1: For the system:

[0086]

[0087] If there exists a continuous scalar function V(x):U→R, satisfying:

[0088] (1) V(x) is a positive definite function;

[0089] (2) There exists c>0 and α∈(0,1), an open domain U0∈U at the origin such that x∈U0{0}:

[0090]

[0091] Then, the origin is the finite time stable equilibrium point. n When , the origin is the global finite-time stable equilibrium point. That is, within the finite time T, V(x) converges to zero, where

[0092]

[0093] Assumption 1.1: The topological relationship between n followers is an undirected graph.

[0094] Assumption 1.2: For each follower, there exists at least one directed path starting from the leader and ending at that follower.

[0095] Assumption 1.3: The orientation angles of all agents can be measured using a compass or other means.

[0096] The topological relationship here is that all agents can face each other through the communication topology and measurement topology, that is, if j and i are neighbors, then j and i can measure each other's relative positions and communicate with each other.

[0097] Problem 1.1: For a uniformly moving multi-agent system consisting of n+1 nodes, where all agents can directly measure their own orientation, design a position estimation algorithm for each follower using each agent's relative position measurement of its neighboring nodes in its own coordinate system and communication information with neighboring nodes, so that all followers can achieve distributed positioning within a finite time, that is, their position estimates converge to their true positions within a finite time, as follows:

[0098]

[0099] Where T represents bounded time.

[0100] Lemma 2.1: Consider the following system:

[0101]

[0102] Where x1,x2∈R n , M is a symmetric positive definite matrix. If l1>0, l2>0, 0<α1<1, Then the system (2.2) is globally finite-time stable.

[0103] To address Problem 1.1, a finite-time distributed localization algorithm is designed for a follower in a uniform motion system. The proposed localization algorithm adopts a second-order estimator model and uses only relative position measurement information and communication information. The specific details are as follows:

[0104]

[0105] Among them, the coefficients μ1, μ2, k1, k2>0, 0<α1<1, represents the estimated velocity of agent i, Represents about θ i The rotation matrix of represents the relative position measured in the local coordinate system of agent i. Here, the position estimator is used for the follower, and for the leader,

[0106] Theorem 3.1: Under the conditions that Assumptions 1.1-1.3 hold, using position estimators (2.3)-(2.7), each agent in a uniform motion multi-agent system can be positioned within a finite time, that is, each agent's estimated position converges to its true position.

[0107] Proof: According to the coordinate transformation theory, equation (2.7) can be transformed into the following equation using the rotation matrix:

[0108]

[0109] Here, the definition Because leaders can obtain their real-time location, And because all intelligent agents move at a uniform speed, ≡ represents the identity sign, indicating that all possible values are completely equal. Therefore, equations (2.3)-(2.4) can be rewritten as:

[0110]

[0111] Substitute equation (2.10) into equation (2.6), and obtain We can get:

[0112]

[0113] To write it in matrix form, first define it as follows: but:

[0114]

[0115] Where, represents the Kronecker product, and I2 represents the identity matrix.

[0116] Then, combined with Definition 1.1, Equations (2.9), (2.10), (2.5) and (2.11) can be written as follows:

[0117]

[0118] Redefine Then X=Z, and after substituting into equations (2.13)-(2.16), we can obtain:

[0119]

[0120] Let e x =β-X,e y =γ-Y, then equations (3.17)-(3.20) can be written as follows:

[0121]

[0122] Next, let’s first prove that e in (2.23) and (2.24) x and e y It will converge to zero in a finite time. For the following system composed of scalars x and y:

[0123]

[0124]

[0125] Design the following Lyapunov function:

[0126]

[0127] After expanding the function, we can get:

[0128]

[0129] It can be seen that the Lyapunov function here is a continuous bounded scalar function about x and y, V ≥ 0, if and only if x = y = 0, V = 0, so V is a positive definite function.

[0130] Taking the derivative of formula (2.28), we can get the following formula:

[0131]

[0132] It is used here The derivative of If you remember A careful observation of formula (2.29) shows that formula (2.29) can be written as follows:

[0133]

[0134] Remember the matrix The maximum and minimum eigenvalues of the matrix Q are denoted as λ max (Q) and λ min (Q), similarly, the maximum eigenvalue and minimum eigenvalue of the matrix P are also expressed as λ max (P) and λ min (P). It can be seen that the matrices P and Q are both symmetric matrices. According to the quadratic standard inequality

[0135]

[0136] in, Represents a vector The second norm of , we can get:

[0137]

[0138] Also because All from (2.32) we can get

[0139]

[0140] According to Lemma 1.1, V will be in finite time T t Converges to zero, where T t for:

[0141]

[0142] So, when t≥T t , x,y will converge to zero.

[0143] In Equations (2.23) and (2.24), each element of the vector can be written in the form of the system Equations (2.25) and (2.26), so when t ≥ T t , e x and e y will converge to zero. Therefore, equations (2.21)-(2.22) become the following forms:

[0144]

[0145] According to assumptions 1.1 and 1.2, the topological relationship between all followers in the multi-agent system is an undirected graph, so the corresponding Laplace matrix L f is a positive definite matrix. According to Lemma 2.1, X,Y will converge to zero in a finite time. According to X,Y and L f The positive definiteness of , and will also converge to zero. Therefore, within a finite time, the estimated position of agent i will converge to the true position p i , estimated speed Will also converge to the true velocity value

[0146] This completes the proof that the agent can locate itself within a limited time using the position estimator.

[0147] Note that the distributed positioning algorithm proposed in this embodiment uses only local relative position measurement information and does not require velocity measurement (system control input). However, for finite-time algorithms, velocity information is generally required. Essentially, Equations (2.5) and (2.6) in this algorithm are observers that can observe velocity errors. Therefore, this algorithm uses observers instead of velocity measurements.

[0148] As a further preferred technical solution, in step S30: after each follower node obtains its position estimate based on the measured relative position, orientation angle, and communication information and converges to its true position within a limited time, the method further includes the following steps:

[0149] The effect of the position estimator was numerically simulated and verified using MATLAB, and experimentally verified using an experimental platform built with a QbBot-2e robot.

[0150] Specifically, suppose the multi-agent system consists of 6 agents, and the topological relationship between the agents is as follows: Figure 2 As shown in the figure, node 0 represents the leader, which can be located in real time. Nodes 1 through 5 are followers, and the edges between nodes represent the direction of information flow. The initial positions of the six agents 0 through 5 are set to (0,0), (2,0), (1,-1), (0,2), (1,3), and (2,2). Each agent moves at a constant speed, and the positioning algorithm for followers 1 through 5 estimates the initial positions of (4,-1), (1,0), (0,3), (4,5), and (1,1).

[0151] The finite time distributed positioning algorithm is numerically simulated and verified using MATLAB. The simulation results are as follows: Figures 3 to 5 As shown, Figure 3is the estimation error of the five followers. It can be seen from the figure that before 4 seconds, the estimation error of each follower basically converges to zero, verifying the reliability of the positioning algorithm of the present invention. Figure 4 is the total graph of the actual motion trajectory and estimated trajectory of each agent, Figure 5 It is a schematic diagram of the actual motion trajectory and estimated trajectory of each intelligent agent. Figure 4 and Figure 5 The red color represents the actual path of the agent, the red circle represents the actual path starting point, the cyan star represents the actual path ending point, the green represents the curve formed by the estimated position, and the green circle represents the estimated initial value. Figure 4 and Figure 5 It can be seen that after a period of time, the estimated position of each agent basically coincides with the actual position, which has a good positioning effect.

[0152] In addition, experimental verification was conducted using an experimental platform built with QbBot-2e robots. In this experimental platform, each robot communicates with a central computer, which processes data using MATLAB. It should be noted that the central computer only performs calculations on behalf of the robots, but each robot's data is still processed individually, thus essentially adopting a distributed approach. Each robot is equipped with a lidar, which measures relative position and uses the result of positioning using SLAM as the actual position. The lidar model is the SLAMTEC RPLIDAR A2M8, with a sampling rate of 8k / s and an angular resolution of 0.45°. The ranging accuracy is: when the actual distance is less than 3 meters, the error is less than 1%; when the actual distance is less than 5 meters, the error is less than 2%; when the actual distance is less than 16 meters, the error is less than 2.5%.

[0153] The implementation method consists of 4 robots, and the topological results are as follows Figure 6 As shown, robot 0 is the leader and can perform real-time positioning, and the other robots are followers and perform self-positioning using the distributed positioning method proposed in this embodiment.

[0154] Figure 7 The position estimation error curves of each robot are shown. It can be seen that the position estimation errors of the three followers basically converge to zero at 2 seconds. Figure 8 The actual motion trajectory and estimated motion estimate of each agent are displayed. It can be seen that after a certain period of time, the estimated motion trajectory of each agent basically coincides with the actual motion trajectory. This verifies the effectiveness of the distributed positioning algorithm proposed in this embodiment.

[0155] In addition, if Figure 9 As shown, another embodiment of the present invention further proposes a multi-agent system distributed positioning system based on relative position measurement, characterized in that it includes:

[0156] An information acquisition module 10 is configured to acquire position information of a leader node and orientation angles of all nodes for a uniformly moving multi-agent system consisting of n+1 nodes, wherein the n+1 nodes include a leader node and n follower nodes;

[0157] The relative position measurement module 20 is used to control each follower node to measure the relative position with its neighbor node in the local coordinate system and communicate with the neighbor node;

[0158] The position estimator 30 is used to control each follower node to obtain its position estimation value based on the measured relative position, orientation angle and communication information and converge to its true position within a limited time, so that all follower nodes can achieve distributed positioning within a limited time.

[0159] Furthermore, in this embodiment, the information acquisition module 10 can be configured to include a location information acquisition unit and a heading angle acquisition unit, wherein the location information acquisition unit is used to acquire the location information of the leader node, and the heading angle acquisition unit is used to acquire the heading angles of all nodes. The location information acquisition unit uses a GPS module, and the heading angle acquisition unit uses a compass.

[0160] As a further preferred technical solution, the relative position measurement module 20 includes:

[0161] A topology graph construction unit, used to construct an undirected communication topology graph between n follower nodes and a directed communication topology graph between n+1 nodes;

[0162] The communication measurement unit is used to measure the relative position of each follower node of the laser radar with its neighboring nodes in its own coordinate system through the communication topology relationship and communicate with the neighboring nodes.

[0163] As a further preferred technical solution, the position estimation formula of the position estimator 30 is expressed as:

[0164]

[0165] Where: is the estimated position of the i-th follower node The first derivative of is the estimated position of the j-th follower node, is the relative position of the i-th follower node measured in the local coordinate system; is the estimated velocity of the ith follower node, is the estimated velocity of the i-th follower node The first derivative of is the estimated velocity of the j-th follower node The first derivative of ; coefficients μ1, μ2, k1, k2>0; 0<α1<1, sig α () is the derivative function of the sign function sgn, sgn() is the standard sign function; β i , γ i 、z i is the symbol of the operation process, N i is the set of all neighboring nodes of agent i; β i The first derivative of γ i The first derivative of a ij is the element value in the adjacency matrix; is the rotation matrix about the orientation angle.

[0166] As a further preferred technical solution, the position estimator 30 converges to the true position of the follower node within a limited time based on the position estimate of the follower node itself. Design for purpose.

[0167] As a further preferred technical solution, the system also includes a verification module for performing numerical simulation verification using MATLAB, and performing experimental verification using an experimental platform built by the QbBot-2e robot.

[0168] It should be noted that other embodiments or specific implementation methods of the multi-agent system distributed positioning system based on relative position measurement described in the present invention can refer to the above-mentioned method embodiments and will not be repeated here.

[0169] It should be noted that the logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device), or in conjunction with such instruction execution system, apparatus, or device. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by an instruction execution system, apparatus, or device, or in conjunction with such instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection portion having one or more wires (electronic device), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and portable compact disc read-only memory (CDROM). Furthermore, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing it in another suitable manner if necessary, and then storing it in a computer memory.

[0170] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0171] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0172] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0173] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A distributed positioning method for a multi-agent system based on relative position measurement, characterized in that: include: For a uniformly moving multi-agent system consisting of n+1 nodes, obtain the position information of the leader node and the orientation angles of all nodes. The n+1 nodes include a leader node and n follower nodes. Each follower node measures its relative position with its neighbor nodes in the local coordinate system and communicates with the neighbor nodes; Each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, so that all follower nodes can achieve distributed positioning within a limited time.

2. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 1, characterized in that: The obtaining of the location information of the leader node and the orientation angles of all nodes includes: Use GPS to obtain the location information of the leader node; Use the compass to get the heading angle of each node.

3. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 1, characterized in that: Each follower node measures the relative position of its neighboring nodes in its own coordinate system and communicates with the neighboring nodes, including: Construct an undirected communication topology graph between n follower nodes and a directed communication topology graph between n+1 nodes; Based on the directed communication topology graph, each follower node measures the relative position of its neighbor nodes in its own coordinate system and communicates with the neighbor nodes.

4. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 1, wherein: Each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, including: Based on the designed position estimator, each follower node obtains the position estimate of the follower node based on the relative position, orientation angle and communication information: Where: is the estimated position of the i-th follower node The first derivative of is the estimated position of the j-th follower node, is the relative position of the i-th follower node measured in the local coordinate system; is the estimated velocity of the ith follower node, is the estimated velocity of the i-th follower node The first derivative of is the estimated velocity of the j-th follower node The first derivative of ; coefficients μ1, μ2, k1, k2>0; 0<α1<1, sig α () is the derivative function of the sign function sgn, sgn() is the standard sign function; β i , γ i 、z i is the symbol of the operation process, N i is the set of all neighboring nodes of agent i; β i The first derivative of γ i The first derivative of a ij is the element value in the adjacency matrix; is the rotation matrix about the orientation angle.

5. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 4, characterized in that: The rotation matrix The public statement is: Where θ i is the orientation angle of the i-th follower node.

6. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 4, characterized in that: The first-order derivative of the leader node's velocity estimate satisfies 7. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 4, characterized in that: represents the position estimation error observer; represents the speed error observer.

8. The distributed positioning method for a multi-agent system based on relative position measurement according to claim 4, characterized in that: The position estimator converges to the true position of the follower node in a finite time based on the position estimate of the follower node itself. Design for purpose.

9. The distributed positioning method for a multi-agent system based on relative position measurement according to any one of claims 1 to 8, characterized in that: After each follower node obtains its position estimate based on the measured relative position, orientation angle and communication information and converges to its true position within a limited time, the method further includes: The effect of the position estimator was numerically simulated and verified using MATLAB, and experimentally verified using an experimental platform built with a QbBot-2e robot.

10. A multi-agent system distributed positioning system based on relative position measurement, characterized in that: include: An information acquisition module is used to obtain the position information of the leader node and the orientation angles of all nodes for a uniformly moving multi-agent system consisting of n+1 nodes, where the n+1 nodes include a leader node and n follower nodes; The relative position measurement module is used to control each follower node to measure the relative position with its neighboring nodes in the local coordinate system and communicate with the neighboring nodes; The position estimator is used to control each follower node to obtain its position estimate based on the measured relative position, orientation angle and communication information and converge to its true position within a limited time, so that all follower nodes can achieve distributed positioning within a limited time.

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