Multi-agent cooperative localization method based on event triggering under limited resources

Abstract

The invention discloses a multi-agent co-localization method based on event triggering under limited resources, which comprises the following steps: executing a distributed co-localization algorithm based on relative measurement by utilizing a kinetic equation and an observation equation of a multi-agent system, and updating an estimation state and a covariance matrix of each agent; traversing k intelligent agents which are neighbor to the intelligent agent i, and calculating a relative covariance matrix between the state estimation value of the intelligent agent i and the state estimation value of the neighbor; when it is determined that a triggering condition is met based on the relative covariance and a set event triggering condition, communication is started between the intelligent agents, after information fusion operation of covariance crossing is carried out, next round of iteration updating operation is carried out on the estimation state and the covariance matrix of each intelligent agent, and otherwise, the next round of iteration updating operation is directly carried out; according to the invention, under the constraint of limited resources, the resource consumption can be effectively reduced, and the multi-agent cooperative positioning precision can be maintained.

Description

Technical Field

[0001] The present invention relates to the cross - technical field of multi - agent systems and filtering technologies, and particularly to an event - triggered multi - agent cooperative localization method under limited resources. Background Art

[0002] In the current era of rapid technological development, sensor technology, microcomputer technology, and communication technology are advancing by leaps and bounds. With its significant advantages of high reliability and low cost, the multi - agent system has successfully broken through the scope of theoretical research and deeply integrated into many key fields such as military strategic deployment and daily life services. Its active presence can be seen in scenarios such as unmanned aerial vehicle formations performing complex tasks, satellite clusters constructing space networks, surveillance and exploration for efficient resource management, smart grids ensuring stable energy supply, and smart agriculture promoting the process of agricultural modernization.

[0003] In the practical application and theoretical deepening process of various multi - agent systems, high - precision position information has become the core cornerstone for the stable and efficient operation of the system. Whether in the theoretical research and practical scenarios such as the precise cooperative flight of multi - agent formations or the precise tactical cooperation in capture operations, accurately mastering the position information of each agent is the key prerequisite to ensure the effective execution of control instructions.

[0004] However, traditional positioning methods, such as Global Positioning System (GPS) and Simultaneous Localization and Mapping (SLAM) technologies, expose many insurmountable shortcomings when facing the unique requirements of multi - agents. For example, the limitation of communication bandwidth hinders the transmission of positioning data among a large number of agents, the accuracy is difficult to reach the ideal level in complex dynamic environments, and the high equipment purchase and operation costs also severely restrict their large - scale popularization and application in multi - agent systems. Fundamentally, this determines that these traditional technologies cannot be simply and directly grafted into the multi - agent system architecture.

[0005] In view of this, it is urgent to develop a distributed positioning method specifically for multi-agent systems. As a cutting-edge positioning strategy based on distributed filtering, the core task of collaborative positioning is to innovatively reshape the distributed architecture of traditional centralized filtering, aiming to ensure that the positioning accuracy is not lost while fully matching the distributed architecture characteristics of multi-agent systems. The current mainstream collaborative positioning methods mainly cover two major strategy systems: loose coupling and tight coupling. Although the loose coupling strategy reduces the communication overhead to a certain extent with the help of the covariance crossover algorithm and achieves the basic consistency of positioning results, its positioning accuracy is too conservative and it is difficult to meet the application scenarios with strict accuracy requirements; the tightly coupled strategy requires real-time tracking of cross-information between nodes, and due to the limitations of its technical architecture, it is impossible to effectively decouple this information, which leads to its reliance on the storage of huge historical information and rigid requirements for global communication.

[0006] In the current research perspective, how to ensure that positioning accuracy is always maintained at a high standard and that the estimation results are highly consistent under the premise of abandoning global communication is still a cutting-edge problem that needs to be solved urgently. At the same time, it cannot be ignored that the energy supply of multi-agent systems is usually limited, and in the process of filtering iterations, frequent information measurement and communication operations will consume a lot of energy rapidly. Therefore, in-depth exploration of how to cleverly balance the subtle relationship between positioning accuracy and energy loss under the harsh conditions of energy limitation undoubtedly has extremely important practical application value and theoretical research significance, which will also become a key breakthrough point in promoting the positioning technology of multi-agent systems to a new level.

[0007] For example, in the related technology, the patent application document with publication number CN116124149A proposes to determine the pose estimation and error covariance of the agent based on the state equation and covariance propagation, determine the global relative orientation angle by measuring the local relative azimuth angle, and then fuse the two pose estimation values. It mainly solves the pose estimation fusion problem of multi-agent systems without common orientation when the mutual covariance is unknown, achieves algorithm complexity reduction and pose estimation consistency guarantee, but this solution is not suitable for actual scenarios with limited resources. Summary of the invention

[0008] The technical problem to be solved by the present invention is how to effectively reduce resource consumption and maintain the accuracy of multi-agent collaborative positioning under the constraints of limited resources.

[0009] The present invention solves the above technical problems by the following technical means:

[0010] A multi-agent collaborative positioning method based on event triggering under limited resources is proposed, and the method includes:

[0011] Execute a distributed cooperative localization algorithm based on relative measurement using the dynamic equation and observation equation of the multi-agent system, and update the estimated state and covariance matrix of each agent;

[0012] Traverse the k agents that are neighbors of agent i, and calculate the relative covariance matrix between the estimated state of agent i itself and the estimated states of its neighbors;

[0013] Based on the relative covariance and the set event trigger condition, when the trigger condition is met, communication is initiated between the agents and information fusion operation of covariance intersection is performed, and then the estimated state and covariance matrix of each agent are updated in the next round of iterative update operation; otherwise, the next round of iterative update operation is directly performed.

[0014] Further, before executing the distributed cooperative localization algorithm based on relative measurement using the dynamic equation and observation equation of the multi-agent system and updating the estimated state and covariance matrix of each agent, the method further includes:

[0015] Construct the dynamic equation of the multi-agent system, and perform linearization processing on the dynamic equation to obtain the linearized dynamic equation;

[0016] Construct the observation equation of the multi-agent system, and perform linearization processing on the observation equation to obtain the linearized observation equation. Further, the formula of the linearized dynamic equation is expressed as:

[0017] s i (k)≈A i (k - 1)s i (k - 1)+B i (k - 1)u i (k - 1)+η i (k - 1)

[0018] In the formula: s i (k) represents the estimated state of agent i at time k, s i (k - 1) represents the estimated state of agent i at time k - 1; u i (k - 1) represents the control input at time k - 1; η i (k - 1) represents the input noise at time k - 1, A i (k - 1), B i (k - 1) are the Jacobian matrices of the nonlinear equation f i at s i (k - 1), u i (k - 1) respectively.

[0019] Further, the formula of the linearized observation equation is expressed as:

[0020] z ij (k)≈C ij (k)[s i (k) T s j (k) T T +μ ij (k)

[0021] Where: z ij (k) represents the relative measurement value of agent i and agent j at time k, i≠j; C ij (k) represents the Jacobian matrix of the observation equation at s i (k),s j (k); s i (k) represents the estimated state of agent i at time k, s j (k) represents the estimated state of agent j at time k, s i (k) T and s j (k) T are the transposed vectors corresponding to s i (k) and s j (k) respectively, and T is the matrix transpose symbol; μ ij (k) represents the measurement noise at time k.

[0022] Furthermore, the distributed cooperative localization algorithm based on relative measurement is performed by using the dynamic equation and the observation equation of the multi-agent system to update the estimated state and covariance matrix of each agent, including:

[0023] Each agent predicts the state estimate value of itself at the next moment based on its own state at the previous moment and the linearized dynamic equation locally, and updates the covariance matrix of the state estimate value;

[0024] Each agent performs relative measurements on its neighbor nodes respectively based on the linearized observation equation, and calculates the state estimate value of the relative measurement based on the state estimate value of itself at the next moment;

[0025] Based on the state value of the relative measurement at the previous moment and the covariance matrix of its own state at the previous moment, calculate the Kalman gain at the next moment;

[0026] Based on the Kalman gain at the next moment and the measurement error of the state estimate value of the relative measurement, update the state estimate value of itself at the next moment and the covariance matrix of the state prediction value of itself at the next moment respectively.

[0027] ​Furthermore, each agent predicts the estimated value of its own state at the next moment based on its own state at the previous moment and the linearized dynamic equation, and updates the covariance matrix of the estimated value of the state, including:

[0028] The predicted estimated value of its own state at the next moment is:

[0029]

[0030] In the formula: is the estimated value of its own state at the next moment, are respectively the components of the estimated value vector of the state of agent i at the next moment ; is a function of the state components of agent i, where takes the estimated value of the state of agent i at the current moment as the input; is the state prediction function.

[0031] The covariance matrix of the updated estimated value of the state is:

[0032]

[0033] In the formula: is the covariance matrix of the estimated value of its own state at the next moment, F i (k) is the state transition matrix related to agent i, is the covariance matrix of the estimated value of the state of agent i itself at the current moment, G i (k) is the noise drive matrix, and Q is the covariance matrix of the system noise.

[0034] Furthermore, the Kalman gain at the next moment is calculated based on the state value of the relative measurement at the previous moment and the state of its own at the previous moment, and the formula is expressed as:

[0035]

[0036] In the formula: is the covariance matrix of the state of its own at the previous moment, H i (k) is the observation matrix, M i (k) is the intermediate calculation matrix, R is the covariance matrix of the observation noise.

[0037] Furthermore, based on the Kalman gain at the next moment and the measurement error of the estimated value of the relative measurement, the covariance matrices of the estimated value of its own state at the next moment and the predicted value of its own state at the next moment are updated respectively, and the formula is expressed as:

[0038]

[0039] Wherein: is the updated state estimate value, is the state estimate value of itself at the next moment, K(k + 1) is the Kalman gain at the (k - 1)th moment, is the measurement error, is the corresponding covariance matrix, is the updated covariance matrix, H i (k + 1) is the observation matrix related to agent i at the (k + 1)th moment.

[0040] Furthermore, when it is determined that the trigger condition is satisfied based on the relative covariance and the set event trigger condition, communication is initiated between agents and information fusion operation of covariance intersection is performed, and then the estimated state and covariance matrix of each agent are subjected to the next round of iterative update operation; otherwise, the next round of iterative update operation is directly performed, including:

[0041] Compare the relative covariance with the set event trigger condition to determine whether it satisfies represents the mth type of relative covariance matrix between agent i and agent j at the kth moment, and trace() is a function for finding the trace of a matrix;

[0042] If so, search for and solve the formula to obtain the parameter ω that satisfies the minimization of the objective function * , where ω is a variable weight parameter in the solution formula and can take different values during the solution process, is another type of relative covariance matrix between agent i and agent j at the kth moment, different from to distinguish different types:

[0043] Based on the parameter ω * perform the information fusion operation of covariance intersection to obtain the fused covariance matrix and estimated state, and then let k = k + 1 to perform the next round of iterative update operation;

[0044] If not, directly let k = k + 1 to perform the next round of iterative update operation.

[0045] Furthermore, the information fusion operation of covariance intersection based on the parameter ω * to obtain the fused covariance matrix and estimated state includes:

[0046] Substitute the parameter ω * into the following formula to obtain the fused covariance matrix and estimated state:

[0047]

[0048] Where: P new (k) is the fused covariance matrix, is the element of the fused covariance matrix P new (k), reflecting the variance of the state estimate of agent i itself, reflecting the variance of the state estimate of agent j itself, reflecting the covariance between the state estimates of agent i and agent j; is the joint estimated state vector of agent i and agent j after fusion, are the estimated state vectors of agent i and agent j after fusion respectively, is the state information vector related to agent i, is the state information vector related to agent j;

[0049] Using P new (k) to replace the corresponding elements related to fusion in, including replacing some elements in the covariance matrix that describe the uncertainty and correlation of the state estimates of agent i and agent j, so as to update to the fused uncertainty description;

[0050] Using to replace the corresponding part of the state estimate vector in, and updating the fused joint estimated state to the state estimates of agent i and agent j, so as to obtain the fused covariance matrix and estimated state for subsequent iterative update and other operations.

[0051] The advantages of the present invention are as follows:

[0052] (1) The present invention is a distributed cooperative positioning algorithm based only on relative measurement. During the entire positioning process, each agent only relies on local measurement information and does not need to communicate, greatly reducing the energy consumption required for positioning, providing an energy-efficient positioning solution for systems with limited resources; and by introducing the covariance intersection algorithm, while ensuring the estimation consistency of each agent, fully considering the information complementarity between different nodes, and further improving the positioning accuracy through an intelligent information fusion mechanism, thus achieving a more accurate position estimate.

[0053] (2) The present invention cleverly integrates the event-triggered control strategy. Only when the trigger condition is met, will the nodes start communication and perform the information fusion operation of covariance intersection. By flexibly adjusting the event trigger threshold, this system can dynamically adjust the balance relationship between the positioning accuracy and the system energy loss according to different energy-constrained environments, enabling it to adapt to various complex and changeable actual application scenarios.

[0054] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a schematic flow chart of a multi-agent collaborative positioning method based on event-triggering under limited resources proposed in an embodiment of the present invention;

[0056] Figure 2 is a complete schematic flow chart of the multi-agent collaborative positioning method based on event-triggering under limited resources in an embodiment of the present invention;

[0057] Figure 3 is a schematic diagram of the movement trajectories of multi-agents in an embodiment of the present invention;

[0058] Figure 4 is an estimated error graph of the state of Agent 1 in an embodiment of the present invention;

[0059] Figure 5 is a comparison graph of the estimated states of Agent 1 and Agent 2 in an embodiment of the present invention;

[0060] Figure 6 is the trace value of the estimated covariance in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] As Figure 1 shown, an embodiment of the present invention proposes a multi-agent collaborative positioning method based on event-triggering under limited resources, and the method includes the following steps:

[0063] S10. Execute a distributed collaborative positioning algorithm based on relative measurement by using the dynamic equation and observation equation of the multi-agent system, and update the estimated state and covariance matrix of each agent;

[0064] The embodiment only has a distributed collaborative positioning algorithm based on relative measurement. During the entire positioning process, each agent only depends on local measurement information and does not need to communicate, greatly reducing the energy consumption required for positioning and providing an energy-efficient positioning solution for systems with limited resources.

[0065] S20. Traverse the k agents that are neighbors of agent i, and calculate the relative covariance matrix between the estimated value of agent i's own state and the estimated values of its neighbors' states;

[0066] S30. Based on the relative covariance and the set event trigger condition, when it is determined that the trigger condition is met, communication is initiated between the agents and information fusion operations of covariance intersection are performed, and then the estimated state and covariance matrix of each agent are updated in the next round of iterative update operations; otherwise, the next round of iterative update operations are directly performed.

[0067] In this embodiment, by introducing the covariance intersection algorithm, on the basis of ensuring the estimation consistency of each agent, the information complementarity between different nodes is fully considered, and the positioning accuracy is further improved through an intelligent information fusion mechanism, so as to achieve a more accurate position estimation.

[0068] As a further preferred technical solution, as Figure 2 shown, before the step S10: performing a distributed cooperative positioning algorithm based on relative measurement by using the dynamic equation and the observation equation of the multi-agent system to update the estimated state and covariance matrix of each agent, the method further includes the following steps:

[0069] S1. Construct the dynamic equation of the multi-agent system, and perform linearization processing on the dynamic equation to obtain the linearized dynamic equation;

[0070] Specifically, in this embodiment, a dynamic equation applicable to the multi-agent system is constructed. Considering a multi-agent system including n agents in a d-dimensional space, this system consists of m anchor nodes V l =[v1,...,v m and n - m follower nodes V f =[v m+1 ,...,v n , where the anchor nodes know their own states, while the states of the follower nodes are unknown, and these nodes cooperate to complete various tasks.

[0071] To describe the motion state of the agents, the following discrete-time nonlinear model is constructed:

[0072] s i (k)=f i (s i (k - 1),u i (k - 1))+η i (k - 1),

[0073] where, s i (k) represents the estimated state of agent i at time k, s i(k - 1) represents the estimated state of agent i at time k - 1; u i (k - 1) represents the control input of agent i at time k - 1; η i (k - 1) represents the input noise of agent i at time k - 1; the nonlinear equation f i represents the state transition equation of the system, i ∈ {1, 2,..., n}.

[0074] It should be noted that the input noise η i is independent and identically distributed Gaussian white noise, and the noises η i (m), η i (k), m ≠ k are linearly independent, and the noises η i (m), η j (m), i ≠ j are also linearly independent.

[0075] Furthermore, for the convenience and accuracy of subsequent calculations and algorithm implementation, the above - mentioned nonlinear model is linearized by using the first - order Taylor expansion, and the following linear model is obtained:

[0076] s i (k) ≈ A i (k - 1)s i (k - 1)+B i (k - 1)u i (k - 1)+η i (k - 1),

[0077] where A i (k - 1), B i (k - 1) are the Jacobi matrices of the nonlinear equation f i at s i (k - 1), u i (k - 1) respectively.

[0078] In this example, there are 3 agents that are neighbor nodes of each other in the system. Among them, agent 3 is an anchor node with known state, and periodically broadcasts its own state information to neighbor nodes; agents 1 and 2 are follower nodes with unknown states. During the experiment, the movement trajectories of the three agents are as Figure 3 shown, and this trajectory graph clearly shows the position changes of the agents during the experiment. The system constructed in this embodiment is:

[0079]

[0080] where the state s i (k) = [x i (k), y i (k), θi (k)] T ,[η x ,η y ,η t T are three linearly independent Gaussian noises, x i (k), y i (k), θ i (k) are the abscissa, ordinate, and heading angle of agent i at time k, respectively, η x , η y , η t are the input errors in the x - coordinate direction, y - coordinate direction of the agent, and related to time t, respectively. v i (k - 1) is the linear velocity of agent i at time k - 1, ω i (k - 1) is the angular velocity of agent i at time k - 1, θ i (k - 1) is the heading angle of agent i at time k - 1, and T is the sampling period.

[0081] The above - mentioned system is linearized, and the state equation of the linearized system can be expressed as:

[0082] s i (k)≈s i (k - 1)+B i (k - 1)u i (k - 1)+η i (k - 1)

[0083] where u i =[v i , ω i T .

[0084] S2. Construct the observation equation of the multi - agent system and linearize the observation equation to obtain the linearized observation equation.

[0085] Specifically, in the multi - agent system, each agent is regarded as a node, and agents that are neighbors of each other can achieve relative measurement. At time k, assuming that node i measures the state of node j in its own coordinate system, the relative measurement equation can be expressed as:

[0086] z ij (k)=h ij (s i (k), s j (k))+μ ij (k)

[0087] where z ij (k) represents the relative measurement value between agent i and agent j at time k, i≠j; h ij ​​Represents the measurement equation of the system, and the measurement noise μ ij (k) is linearly independent Gaussian white noise.

[0088] Assume that the agent is equipped with distance and angle sensors. Agent i can measure the relative distance and relative azimuth of neighbor agent j, i.e., z ij (k) = [d ij (k) θ ij (k)] T . At the same time, considering that errors will inevitably occur in the distance and angle measurement processes, represent it as μ = [μ d , μ b T , and the corresponding measurement equation is:

[0089]

[0090] In the formula, d ij (k) is the relative distance between agent i and neighbor agent j at time k, θ ij (k) is the relative azimuth angle between agent i and neighbor agent j at time k, μ is the measurement error vector, μ d , μ b are the distance measurement error and angle measurement error respectively, x i (k), x j (k) are the abscissas of agent i and agent j at time k respectively, y i (k), y j (k) are the ordinates of agent i and agent j at time k respectively, z1(k) represents the relative distance measurement value between agent i and neighbor agent j at time k, and z2(k) represents the relative azimuth angle measurement value between agent i and neighbor agent j at time k.

[0091] Furthermore, in order to better fit with the subsequent algorithms, the first-order Taylor expansion is also used to linearize the above relative measurement equation, and the following linear measurement model is obtained: Linearizing the measurement equation gives

[0092] z ij (k) ≈ C ij (k) [s i (k) T s j (k) T T + μ ij (k)

[0093] In the formula: C ij (k) represents the Jacobian matrix of the observation equation at s i (k), s j (k); s​​i (k) T represents the transpose of the state vector of agent i at time k, s j (k) T represents the transpose of the state vector of agent j at time k, T is the matrix transpose symbol; μ ij (k) represents the measurement noise at time k.

[0094] As a further preferred technical solution, in step S10: The distributed cooperative localization algorithm based on relative measurement is performed by using the dynamic equation and the observation equation of the multi-agent system to update the estimated state and covariance matrix of each agent, which specifically includes the following steps:

[0095] S11. Each agent predicts the estimated value of its own state at the next moment based on its own state at the previous moment and the linearized dynamic equation locally, and updates the covariance matrix of the estimated state value;

[0096] S12. Each agent performs relative measurements on its neighbor nodes respectively based on the linearized observation equation, and calculates the estimated value of the state of the relative measurement based on the estimated value of its own state at the next moment;

[0097] S13. Calculate the Kalman gain at the next moment based on the state value of the relative measurement at the previous moment and the covariance matrix of the state of its own at the previous moment;

[0098] S14. Update the covariance matrix of the estimated value of its own state at the next moment and the predicted value of the state of its own at the next moment respectively based on the Kalman gain at the next moment and the measurement error of the estimated value of the state of the relative measurement.

[0099] Specifically, assume that the k neighbor nodes of node i can be expressed as Node i estimates the states of itself and its neighbor nodes through relative measurement and communication The input noise η and the measurement noise μ are independent Gaussian white noises with a mean of 0 and variances of Q and R respectively. The distributed cooperative localization algorithm based on relative measurement is divided into two steps: prediction and update:

[0100] (1) At the k+1 prediction step: Given that the follower node i has a clear understanding of the motion strategies of itself and its neighbor nodes, it can directly and accurately update locally using the known dynamic equation

[0101]

[0102] In the formula: is the estimated value of its own state at the next moment, are respectively the vector of the estimated value of the state of agent i at the next moment Each component of is a function related to the state component of agent i, and is the state prediction function;

[0103] Meanwhile, update the covariance matrix of the state prediction value to reflect the uncertainty of the prediction:

[0104]

[0105] where F i (k) is the state transition matrix related to agent i, is the covariance matrix of the state estimate value of agent i itself at the current moment, G i (k) is the noise driving matrix, Q is the covariance matrix of the system noise, is a function related to the overall state of agent i, is a function related to the state component of agent i and is related to the function, is a function related to the state component of agent i and is related to the function, is the noise driving matrix and is the diagonal element of

[0106] At this point, the (k + 1)-th prediction step ends.

[0107] (2) At the (k + 1)-th update step: Node i performs relative measurements on each neighbor node respectively. The specific measurement information obtained will depend on the sensors equipped on the agent, usually including relative distance information and relative azimuth information. Thus, the following relative measurement vector is obtained:

[0108]

[0109] Furthermore, define the relative measurement equation:

[0110]

[0111] Substitute the estimated value of the prediction step into the above formula, and the estimated value of the relative measurement can be obtained. To accurately measure the measurement error, define the measurement error

[0112] and its covariance can be calculated by the following formula:

[0113]

[0114] On this basis, the Kalman gain expression can be further derived:

[0115]

[0116] In the formula, is the covariance matrix of its own state at the previous moment, and H i (k) is the observation matrix, and M i (k) is the intermediate calculation matrix. R is the covariance matrix of the observation noise.

[0117] (3) Update of state and covariance matrix: Based on the Kalman gain at the next moment and the measurement error of the state estimate value of the relative measurement, the state estimate value of itself at the next moment and the covariance matrix of the state prediction value of itself at the next moment are updated respectively. The formula is expressed as:

[0118]

[0119] In the formula: is the updated state estimate value, is the state estimate value of itself at the next moment, K(k + 1) is the Kalman gain at the k - 1 moment, is the measurement error, is the corresponding covariance matrix, is the updated covariance matrix, and H i (k + 1) is the observation matrix at the k + 1 moment.

[0120] Preferably, if the neighbor node is not within the measurement range of node i, node can be temporarily ignored during the update process.

[0121] Meanwhile, directly set and as a component (predicted value) in the state estimate value vector of neighbor agent j by agent i at the k + 1 moment, as a component (updated value) in the state estimate value vector of neighbor agent j by agent i at the k + 1 moment. is an element (predicted value) related to the state estimate of neighbor agent j itself in the state estimate covariance matrix of neighbor agent j by agent i at the k + 1 moment, is an element (updated value) related to the state estimate of neighbor agent j itself in the state estimate covariance matrix of neighbor agent j by agent i at the k + 1 moment, is an element (predicted value) related to the correlation between the state estimates of neighbor agent j and agent i in the state estimate covariance matrix of neighbor agent j by agent i at the k + 1 moment, is an element (updated value) in the covariance matrix of agent i's state estimate for neighbor agent j at time k+1, which is related to the correlation between agent j and agent i's state estimate. Here, lowercase p represents an element in the covariance matrix. Compared with uppercase P, uppercase P represents the complete covariance matrix.

[0122] As a further preferred technical solution, the step S20: traversing k agents that are neighbors of agent i, and calculating the relative covariance matrix between the state estimation value of agent i itself and the state estimation value of its neighbors, specifically includes:

[0123] Traverse all neighbor nodes of node i, and take neighbor node j as an example to carry out subsequent operations. Consider follower node i, i∈V f Estimates of oneself and the estimated value of neighbor node j definition The covariance matrix of

[0124] As a further preferred technical solution, the step S30: when it is determined based on the relative covariance and the set event trigger condition that the trigger condition is met, the agents start communication and perform information fusion operation of covariance crossover, and then perform the next round of iterative update operation on the estimated state and covariance matrix of each agent, otherwise directly perform the next round of iterative update operation, specifically including the following steps:

[0125] S31, the relative covariance And the event trigger conditions set Compare and determine whether represents the mth type of relative covariance matrix between agent i and agent j at time k, trace() is a function for finding the matrix trace, if yes, execute step S32, if no, directly execute step S34;

[0126] It should be noted that, when setting the trigger conditions, this embodiment will fully consider the real-time performance indicators of the system, environmental factors and task requirements to make the trigger conditions more scientific and reasonable.

[0127] S32, search and solve the formula by 0.618 method or Fibonacci method Obtain the parameter ω that satisfies the minimization objective function * , where ω is the variable weight parameter in the solution formula, and different values ​​can be tried during the solution process. is another type of relative covariance matrix between agent i and agent j at time k (with Distinguish between different types);

[0128] S33, based on parameter ω* Perform information fusion operation of covariance intersection to obtain the fused covariance matrix and estimated state;

[0129] S34. Let k = k + 1 and perform the next round of iterative update operation.

[0130] As a further preferred technical solution, the parameter ω-based * Perform information fusion operation of covariance intersection to obtain the fused covariance matrix and estimated state, including:

[0131] Substitute the parameter ω * into the following formula to obtain the fused covariance matrix and estimated state:

[0132]

[0133] In the formula: P new (k) is the fused covariance matrix, are respectively the elements in the fused covariance matrix P new (k), reflects the variance of the state estimate of agent i itself, Similarly, it reflects the variance of the state estimate of agent j itself, reflects the covariance between the state estimates of agent i and agent j; is the joint estimated state vector of agent i and agent j after fusion, are respectively the estimated state vectors of agent i and agent j after fusion, is the state information vector related to agent i, is the state information vector related to agent j;

[0134] Use P new (k) to replace the corresponding elements related to fusion in, that is, replace some elements in the covariance matrix that describe the uncertainty and correlation of the state estimates of agent i and agent j to update to the fused uncertainty description; use to replace the corresponding part of the state estimate vector in, and update the fused joint estimated state to the state estimates of agent i and agent j, so as to obtain the fused covariance matrix and estimated state for subsequent iterative update and other operations.

[0135] It should be noted that in the iterative update process of this embodiment, relevant parameters will be dynamically adjusted according to the operating state and performance indicators of the system to ensure continuous optimization of the system.

[0136] Specifically, the estimation error of agent 1 for its own state is as Figure 4As shown, the changing trend of the estimation error can be visually observed through this figure, thereby evaluating the performance of the positioning algorithm. The comparison of the estimated states of Agents 1 and 2 is as follows Figure 5 As shown, it helps to analyze the estimation consistency between different agents. The trace of the estimated covariance of Agent 1 is as follows Figure 6 As shown, this figure provides a quantitative index for evaluating the uncertainty of the estimation results. By comprehensively analyzing these experimental results, the actual performance of the collaborative positioning method proposed in the present invention in this specific embodiment can be comprehensively evaluated.

[0137] In this embodiment, the event-triggered control strategy is cleverly integrated. Only when the trigger condition is met, will the nodes initiate communication and perform the information fusion operation of covariance intersection. By flexibly adjusting the event-trigger threshold This system can dynamically adjust the balance between the positioning accuracy and the system energy consumption according to different energy-constrained environments, enabling it to adapt to various complex and changing practical application scenarios.

[0138] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0139] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0140] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A multi-agent collaborative positioning method based on event triggering under limited resources, characterized in that: The method comprises: The distributed collaborative localization algorithm based on relative measurement is implemented using the dynamic equations and observation equations of the multi-agent system to update the estimated state and covariance matrix of each agent. Traverse the k agents that are neighbors of agent i, and calculate the relative covariance matrix between agent i's own state estimate and its neighbor's state estimate; When the trigger condition is determined to be met based on the relative covariance and the set event trigger condition, the agents start communicating with each other and perform information fusion operation of covariance crossover before performing the next round of iterative update operation on the estimated state and covariance matrix of each agent, otherwise the next round of iterative update operation is performed directly.

2. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 1, characterized in that: Before the distributed collaborative positioning algorithm based on relative measurement is executed by using the dynamic equations and observation equations of the multi-agent system to update the estimated state and covariance matrix of each agent, the method further includes: Construct the dynamic equation of the multi-agent system and linearize the dynamic equation to obtain the linearized dynamic equation; The observation equation of the multi-agent system is constructed and linearized to obtain the linearized observation equation.

3. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 2, characterized in that: The linearized kinetic equation is expressed as: s i (k)≈A i (k-1)s i (k-1)+B i (k-1)u i (k-1)+η i (k-1) Where: s i (k) represents the estimated state of agent i at time k, s i (k-1) represents the estimated state of agent i at time k-1; u i (k-1) represents the control input at time k-1; η i (k-1) represents the input noise at time k-1, A i (k-1),B i (k-1) are the nonlinear equations f i In s i (k-1),u i The Jacobian matrix at (k-1).

4. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 2, characterized in that: The formula of the linearized observation equation is expressed as: With ij (k)≈C ij (k)[s i (k) T s j (k) T ] T +μ ij (k) Where: z ij (k) represents the relative measurement value of agent i and agent j at time k, i≠j; C ij (k) represents the Jacobian matrix of the observation equation at si(k), sj(k); i (k) represents the estimated state of agent i at time k, s j (k) represents the estimated state of agent j at time k, s i (k) T and j (k) T They are i (k) and s j (k) The corresponding transposed vector, T is the matrix transpose symbol; μ ij (k) represents the measurement noise at time k.

5. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 1, characterized in that: The method uses the dynamic equations and observation equations of the multi-agent system to execute a distributed collaborative positioning algorithm based on relative measurement, and updates the estimated state and covariance matrix of each agent, including: Each agent predicts its own state estimate at the next moment based on its own state at the previous moment and the linearized dynamic equation, and updates the covariance matrix of the state estimate; Each agent performs relative measurements on its neighbor nodes based on the linearized observation equation, and calculates the state estimate of the relative measurement based on its own state estimate at the next moment; Calculate the Kalman gain at the next moment based on the relative measured state value at the previous moment and the covariance matrix of its own state at the previous moment; Based on the Kalman gain at the next moment and the measurement error of the relative measured state estimate, the covariance matrix of the next moment's own state estimate and the next moment's own state prediction are updated respectively.

6. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 5, characterized in that: Each agent locally predicts its own state estimate at the next moment based on its own state at the previous moment and the linearized dynamic equation, and updates the covariance matrix of the state estimate, including: The estimated state value of the next moment is predicted to be: Where: is the estimated value of its own state at the next moment, are the estimated value vectors of the state of agent i at the next moment. The various components of are functions related to the state components of agent i, respectively, where The estimated value of the state of agent i at the current moment As input; is the state prediction function; The covariance matrix of the updated state estimate is: Where: P i - (k+1) is the covariance matrix of the state estimate at the next moment, F i (k) is the state transfer matrix associated with agent i, P i + (k) is the covariance matrix of the state estimate of agent i at the current moment, G i (k) is the noise driving matrix, and Q is the covariance matrix of the system noise.

7. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 5, characterized in that: The Kalman gain at the next moment is calculated based on the relative measured state value at the previous moment and the state of the previous moment, and the formula is expressed as: K(k)=P i - (k)H i (k) T M i (k) -1 =P i - (k)H i (k) T [H i (k)P i - (k)H i (k) T +R] -1 Where: P i - (k) is the covariance matrix of its own state at the previous moment, H i (k) is the observation matrix, M i (k) is the intermediate calculation matrix, M i (k) = H i (k)P i - (k)H i (k) T +R; R is the covariance of the observation noise.

8. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 5, characterized in that: The measurement error based on the Kalman gain at the next moment and the relative measured state estimation value respectively updates the covariance matrix of the state estimation value at the next moment and the state prediction value at the next moment, and the formula is expressed as: Where: is the updated state estimate, is the estimated value of its own state at the next moment, K(k+1) is the Kalman gain at moment k-1, is the measurement error, P i - (k+1) is The corresponding covariance matrix, P i + (k+1) is the updated covariance matrix, H i (k+1) is the observation matrix related to agent i at time k+1.

9. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 1, characterized in that: When the trigger condition is determined to be met based on the relative covariance and the set event trigger condition, the agents start communicating with each other and perform the information fusion operation of covariance crossover, and then perform the next round of iterative update operation on the estimated state and covariance matrix of each agent, otherwise the next round of iterative update operation is directly performed, including: The relative covariance P i ij And the event trigger conditions set Compare and determine whether represents the mth type of relative covariance matrix between agent i and agent j at time k, and trace() is a function for finding the matrix trace. If so, search for the solution formula Obtain the parameter ω that satisfies the minimization objective function * , where ω is the variable weight parameter in the solution formula, and different values ​​can be tried during the solution process. is another type of relative covariance matrix between agent i and agent j at time k: Based on the parameter ω * Perform the information fusion operation of covariance crossover to obtain the fused covariance matrix and estimated state, then set k=k+1 to perform the next round of iterative update operation; If not, directly set k=k+1 and perform the next round of iterative update operation.

10. The event-triggered multi-agent collaborative positioning method under limited resources as claimed in claim 9, characterized in that: The parameter ω * The information fusion operation of covariance cross is performed to obtain the fused covariance matrix and estimated state, including: The parameter ω * Substitute the following formula to obtain the fused covariance matrix and estimated state: Where: P new (k) is the covariance matrix after fusion, is the covariance matrix P after fusion new (k) element, reflects the variance of agent i’s own state estimation, Similarly, it reflects the variance of agent j's own state estimation, Reflects the covariance between the state estimates of agent i and agent j; is the joint estimated state vector of the fused agent i and agent j, are the estimated state vectors of agent i and agent j after fusion, is the state information vector associated with agent i, is the state information vector related to agent j; Using P new (k) Replacement The corresponding elements related to fusion in , that is, replacing some elements in the covariance matrix that describe the uncertainty and correlation of the state estimation of agents i and j, to update the uncertainty description after fusion; adopt replace The corresponding state estimation vector part in , updates the fused joint estimation state to the state estimation of agent i and agent j, so as to obtain the fused covariance matrix and estimation state for subsequent iterative update and other operations.

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