Multi-agent cooperative positioning method and system based on double-channel event triggering mechanism

Abstract

The application provides a multi-agent cooperative positioning method and system based on a dual-channel event triggering mechanism, which comprises the following steps: establishing a discrete-time nonlinear state space model of each robot; establishing an event triggering mechanism for a channel between a sensor node and a remote estimator; performing local filtering update based on Kalman gain to obtain a local state estimation value; establishing an event triggering mechanism for a channel between the remote estimator and a fusion center; performing prediction compensation on the received local state estimation value by the fusion center to obtain a complete local compensation estimation value; constructing a quadratic optimization problem with the minimization of global estimation error covariance as the target, and calculating an optimal weighting matrix to realize distributed fusion and output a global state estimation value. The application realizes dynamic balance between communication frequency and estimation accuracy, and the event triggering mechanism significantly reduces data transmission while maintaining estimation performance.

Description

Technical Field

[0001] This paper belongs to the field of intelligent transportation technology, specifically involving a multi-agent cooperative localization method and system based on a dual-channel event triggering mechanism. Background Technology

[0002] With the rapid development of mobile robot technology, multi-robot systems have been widely used in complex scenarios such as intelligent manufacturing, disaster relief, environmental monitoring, and swarm intelligence operations. For these systems, accurate and reliable positioning capabilities are a fundamental prerequisite for achieving effective collaboration and navigation.

[0003] Existing independent localization methods, such as inertial navigation, odometry, or lidar localization, are often limited by the inherent physical properties of sensors and affected by cumulative drift in practical applications. Especially in complex environments with sparse or significant nonlinear characteristics, a single robot struggles to maintain high-precision attitude estimation over long periods. In contrast, cooperative localization technology has become a key solution, effectively mitigating these problems by utilizing observational data from other robots to suppress error growth.

[0004] However, in real-world deployment scenarios, robot swarm systems often face severe resource constraints, including insufficient communication bandwidth, limited energy budgets, and network latency. Traditional communication scheduling often employs time-triggered mechanisms (i.e., broadcasting status information at fixed sampling periods). When large-scale clusters communicate concurrently, this rigid scheduling strategy is prone to channel congestion, packet loss, and accelerated depletion of node energy, severely restricting the real-time performance and robustness of cooperative localization systems.

[0005] How to effectively reduce redundant data transmission overhead while maintaining high-precision positioning performance remains a key challenge that needs to be addressed. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this paper aims to provide a multi-agent collaborative localization method and system based on a dual-channel event triggering mechanism, which can reduce redundant data transmission while ensuring high-precision localization.

[0007] To solve the above-mentioned technical problems, the specific technical solution presented in this paper is as follows: On the one hand, this paper provides a multi-agent cooperative localization method based on a dual-channel event triggering mechanism. This method is applied to a multi-agent system composed of multiple mobile robots, and includes: Establish a discrete-time nonlinear state-space model for each robot, with each robot including multiple sensor nodes; Based on the state evolution relationship of each robot and the pre-constructed test statistic following the chi-square distribution, an event triggering mechanism for the channel between the sensor node and the remote estimator is established. When the channel between the sensor node and the remote estimator is triggered for transmission, a local state estimate is obtained by performing local filtering updates based on the Kalman gain. Based on the current local state estimate and the local state estimate most recently transmitted to the fusion center, an event triggering mechanism for the channel between the remote estimator and the fusion center is established. The fusion center receives all the local state estimates transmitted by the robot and performs predictive compensation on the local state estimates to obtain complete local compensation estimates. Based on all local compensation estimates, a quadratic optimization problem is constructed with the goal of minimizing the global estimation error covariance. The optimal weighting matrix is ​​calculated to achieve distributed fusion and output the global state estimate.

[0008] Furthermore, the discrete-time nonlinear state-space model is expressed by the following formula: ; ; in, k It is a discrete time step. Indicates that the robot is k The state vector at time t, ,in Indicates position coordinates, Indicates the direction angle. It is a nonlinear state evolution function. Indicates the first i Each sensor node in k The observation vector acquired at each time step, The corresponding nonlinear observation function; process noise and measuring noise The zero-mean Gaussian white noise was assumed to be mutually independent. The state vector transition is estimated using the following formula: ; in, and These represent constant linear velocity and angular velocity, respectively. The sampling period; Process noise and measuring noise The statistical properties of satisfy the following formula:

[0009]

[0010] in, Represents the mathematical expectation operator. Represents the process noise at time k The covariance matrix, Indicates the measurement noise of the i-th sensor node. The covariance matrix, and It is the Kronecker function.

[0011] Furthermore, the event-triggered mechanism for establishing the channel between the sensor node and the remote estimator includes: For each robot, the trigger residual vector is calculated based on the current measurement and the local state estimate from the previous transmission time. , of which is the first i Each sensor node in k The trigger residual vector at time step; According to the trigger residual vector Construct a test statistic vector that follows a chi-square distribution. And based on the chi-square quantile of the preset information level, the sensor-side event triggering conditions are established, expressed as: , ,in, For the first i Each sensor node in k The test statistics vector at time t. Indicates the first i Observation vectors of each sensor node Dimensions This indicates the preset confidence level. Describing the degrees of freedom as Confidence level is upper quantiles of the chi-square distribution; For event-triggered decision variables, This indicates that the triggering condition is met at the current moment, and the data transmission operation is executed. This indicates that the triggering conditions are not met, and the current measurement data will not be transmitted. When the sensor-side event triggering condition is activated, data transmission between the sensor node and the remote estimator is performed. Furthermore, for each robot, a trigger residual vector is calculated based on the current measurement value and the local state estimate value from the previous transmission time. ,include: The discrete-time nonlinear state-space model is linearized using the first-order Taylor series expansion method, resulting in a linearized approximate expression, which is expressed as: ; in, ,express Error in state estimation at time t. ,express The state prediction error at time t, This represents the predicted state value at time k. express k State estimate at time -1 The Jacobian matrix, representing higher-order remainder terms, is defined as follows: State evolution function exist The Jacobian matrix at the location, and This represents the observation function corresponding to the i-th sensor node. exist Jacobian matrix at the location; Based on the linearized approximation expression, the predicted state value at the current time and the corresponding prediction error covariance matrix are obtained, expressed as follows: ; ;in, This represents the predicted state value at time k. express k State estimate at time -1 This represents the prediction error covariance matrix at time k. The covariance matrix representing the process noise at time k-1; Based on the current state prediction value and the corresponding prediction error covariance matrix, the current predicted measurement value and the corresponding innovation covariance matrix are calculated and expressed as follows: ; ,in, This represents the predicted measurement value of the i-th sensor node at time k. Let represent the information covariance matrix of the i-th sensor node at time k; Based on the evolutionary relationship between the current state and the states at historical transmission times, an approximate representation of the current state vector is determined, which is expressed as: ,in, Indicates that the robot is k The state vector at time t, This represents the time when the i-th sensor node last transmitted its state measurement value. Represents the state transition matrix. , , I It is the identity matrix; The noise at time m is the process noise. The measurement difference between the current measurement and the previous measurement is calculated and expressed as: ;in, The last transmission time The measured value; Based on the measurement difference, the current state prediction value, and the corresponding prediction error covariance matrix, the trigger residual vector is determined, expressed as: , This indicates the trigger residual vector.

[0012] Furthermore, when channel-triggered transmission occurs between the sensor node and the remote estimator, a local state estimate is obtained by performing local filtering updates based on the Kalman gain, including: Determining Kalman gain using piecewise function form , represented as ,in, Let K be the Kalman gain of the i-th sensor node at time k; For event-triggered decision variables, This is the actual measured value of k at the current time. This is the corrected covariance term; The covariance of the measured difference; Based on the Kalman gain, the robot's state estimate and corresponding error covariance matrix are updated, as follows:

[0013]

[0014] in, This is the state estimate of the robot at time k. Let be the error covariance matrix at time k. It is the identity matrix. This is the covariance correction term caused by the event triggering.

[0015] Furthermore, based on the current local state estimate and the local state estimate most recently transmitted to the fusion center, an event-triggered mechanism for the channel between the remote estimator and the fusion center is established, including: The robot's state estimate is reduced in dimensionality using a dimensionality reduction matrix, which is expressed as follows: .in, It is a binary variable indicating whether to select the first state estimate. One portion, Indicates the number of elements transmitted. n Let be the total dimension of the state vector, satisfying ; Define the channel-triggered decision variable between the remote estimator and the fusion center as follows: Among them, the triggering area Defined as: , It is a predefined trigger threshold. Indicates at time The most recent local state estimate transmitted to the fusion center before the current time; Based on the triggering decision variable and the current state estimate, the local state estimate that needs to be transmitted is determined, expressed as: ,in, To determine the local state estimates that need to be transmitted.

[0016] Furthermore, the complete local compensation estimate is obtained through the following compensation formula: , in, For the compressed information received by the fusion center, , The predicted state value at the current moment. For a dimension reduction matrix, It is an identity matrix.

[0017] 8. The method according to claim 1, characterized in that, based on all local compensation estimates, a quadratic optimization problem is constructed with the objective of minimizing the global estimation error covariance, and the optimal weighting matrix is ​​calculated to achieve distributed fusion and output a global state estimate, including: Define the global fusion estimate as follows: ;in, To optimize the weighting matrix weights of the i-th sensor node, The weight matrix must satisfy the following constraints for the compensated local state estimate of the i-th sensor node at time k: , where I is the identity matrix and N is the total number of sensor nodes; Define the estimation error evolution function after compensation; Based on the compensated estimation error evolution function, the cross covariance matrix function relationship between the compensated local state estimates of any two sensor nodes is constructed. Based on the aforementioned cross-covariance matrix function relationship, a quadratic optimization problem is constructed with the goal of minimizing the global estimation error, and the optimal weighting matrix weights are obtained by solving the problem. Based on the optimal weighted matrix obtained by solving, the global state estimate is output.

[0018] On the other hand, this paper also provides a multi-agent cooperative localization system based on a dual-channel event triggering mechanism. The system is a multi-agent system composed of multiple mobile robots, and includes: The nonlinear state-space model building module is used to build a discrete-time nonlinear state-space model for each robot, and each robot includes multiple sensor nodes. The first event triggering mechanism establishment module is used to establish an event triggering mechanism for the channel between the sensor node and the remote estimator based on the state evolution relationship of each robot and the pre-constructed test statistic that follows the chi-square distribution. The gain module is used to perform local filtering updates based on Kalman gain to obtain local state estimates when the channel between the sensor node and the remote estimator is triggered for transmission. The second event triggering mechanism establishment module establishes an event triggering mechanism for the channel between the remote estimator and the fusion center based on the current local state estimate and the local state estimate most recently transmitted to the fusion center. The compensation module is used by the fusion center to receive all the local state estimates transmitted by the robot and to perform predictive compensation on the local state estimates to obtain complete local compensation estimates. The global optimal output module is used to construct a quadratic optimization problem with the goal of minimizing the global estimation error covariance based on all local compensation estimates, calculate the optimal weighting matrix, realize distributed fusion, and output the global state estimate.

[0019] Finally, this document also provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method described above.

[0020] Using the above technical solution, the multi-agent cooperative localization method and system based on a dual-channel event-triggered mechanism described in this paper establishes a discrete-time nonlinear state-space model for each robot, with each robot including multiple sensor nodes. Based on the state evolution relationship of each robot and a pre-constructed chi-square distribution test statistic, an event-triggered mechanism is established for the channel between the sensor nodes and the remote estimator. When the channel between the sensor nodes and the remote estimator triggers transmission, local filtering updates are performed based on Kalman gain to obtain local state estimates. Based on the current local state estimates and the most recent local state estimate transmitted to the fusion center, an event-triggered mechanism is established for the channel between the remote estimator and the fusion center. The fusion center receives all the local state estimates transmitted by the robots and performs predictive compensation on these local state estimates to obtain complete local compensated estimates. Based on all local compensated estimates, a quadratic optimization problem is constructed with the goal of minimizing the global estimation error covariance, and the optimal weighting matrix is ​​calculated to achieve distributed fusion and output the global state estimate. This paper achieves a dynamic balance between communication frequency and estimation accuracy through a dual-channel intelligent adaptive triggering mechanism, and the event-triggered mechanism significantly reduces data transmission volume while maintaining estimation performance.

[0021] To make the above and other objects, features and advantages of this document more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments or prior art described herein, the accompanying drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this article. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This document illustrates the steps of a multi-agent cooperative localization method based on a dual-channel event triggering mechanism, as provided in the embodiments herein. Figure 2 The implementation flowchart of the method provided in the example in this article is shown; Figure 3 A comparison diagram is shown between the actual trajectory in the simulation experiment provided in this paper and the estimated trajectory of the method proposed in this application; Figure 4 This document shows a schematic diagram of the framework of a multi-agent cooperative localization system based on a dual-channel event triggering mechanism, as provided in the embodiments herein. Figure 5 A schematic diagram of the framework of the computer device provided in the embodiments of this article is shown. Detailed Implementation

[0024] The technical solutions in the embodiments described below will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments described herein, and not all of the embodiments. Based on the embodiments described herein, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this document.

[0025] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings herein are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, apparatus, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0026] In existing multi-robot system deployment scenarios, robot swarm systems often face severe resource constraints, including insufficient communication bandwidth, limited energy budgets, and network latency. Traditional communication scheduling often employs time-triggered mechanisms (i.e., broadcasting status information at fixed sampling periods). In large-scale cluster concurrent communication, this rigid scheduling strategy easily leads to channel congestion, data packet loss, and accelerated energy depletion of nodes, severely restricting the real-time performance and robustness of cooperative positioning systems. How to effectively reduce redundant data transmission overhead while maintaining high-precision positioning performance remains a critical challenge that urgently needs to be addressed.

[0027] To address the aforementioned issues, this paper presents a multi-agent cooperative localization method based on a dual-channel event triggering mechanism, which can maintain high-precision localization performance while effectively reducing redundant data transmission overhead. Figure 1 This document illustrates the steps of a multi-agent cooperative localization method based on a dual-channel event-triggered mechanism, as provided in the embodiments. While this specification provides the operational steps described in the embodiments or flowcharts, more or fewer steps may be included based on conventional or non-inventive methods. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only possible order. In actual system or device products, the methods shown in the embodiments or accompanying drawings can be executed sequentially or in parallel. Specifically, as shown... Figure 1 As shown, the method may include: S101: Establish a discrete-time nonlinear state-space model for each robot, with each robot including multiple sensor nodes; This specification describes a method applied to a multi-agent system composed of multiple mobile robots. Each robot has multiple sensor nodes and a remote estimator. The sensors can be UWB or orientation sensors. A communication channel exists between the sensor nodes and the remote estimator. The system also has a fusion center, which serves as the system's control center, used to send corresponding control commands and other information to the multiple mobile robots. A communication signal exists between the remote estimator and the fusion center. This multi-agent system can be a drone system, an unmanned transportation system, or similar systems. Figure 2 The diagram shown illustrates the entire implementation process of this method.

[0028] A multi-agent system composed of multiple mobile robots constructs a distributed system model with N sensor nodes. Given that the robot body typically possesses complex nonlinear dynamic characteristics, and that the system performs discretized perception and control via a digital processor during actual operation, this specification's embodiments employ a discrete-time nonlinear state-space model to describe the robot's state evolution process. The discrete-time nonlinear state-space model of this system can be described as follows: ; ; in, k It is a discrete time step. Indicates that the robot is k The state vector at time t, ,in Indicates position coordinates, Indicates the direction angle. It is a nonlinear state evolution function. Indicates the first i Each sensor node in k The observation vector acquired at each time step, The corresponding nonlinear observation function; process noise at time k. and measuring noise It is assumed to be mutually independent zero-mean Gaussian white noise, where N is the total number of sensor nodes; The state vector transition is estimated using the following formula: ; in, and These represent constant linear velocity and angular velocity, respectively. The sampling period; Furthermore, process noise and measuring noise The statistical properties of satisfy the following formula:

[0029]

[0030] in, Represents the mathematical expectation operator. Represents the process noise at time k The covariance matrix, Indicates the measurement noise of the i-th sensor node. The covariance matrix, and It is the Kronecker function, which takes the value 1 if and only if the indices are the same, otherwise it is 0.

[0031] S102: Based on the state evolution relationship of each robot and the pre-constructed test statistic following the chi-square distribution, establish an event triggering mechanism for the channel between the sensor node and the remote estimator. In other words, this specification proposes an event-triggered data transmission mechanism for the communication channel between the sensor node and the remote estimator. The core objective of this mechanism is to effectively reduce the transmission of redundant measurement information and minimize communication overhead at the sensor end by monitoring measurement data in real time at the sensor side and performing data transmission operations only when trigger conditions are met.

[0032] Specifically, an event-triggered mechanism is established for the channel between the sensor node and the remote estimator, including: For each robot, the trigger residual vector is calculated based on the current measurement and the local state estimate from the previous transmission time. , of which is the first i Each sensor node in k The trigger residual vector at time step; According to the trigger residual vector Construct a test statistic vector that follows a chi-square distribution. And based on the chi-square quantile of the preset information level, the sensor-side event triggering conditions are established, expressed as: , ,in, For the first i Each sensor node in k The test statistics vector at time t. Indicates the first i Observation vectors of each sensor node Dimensions This indicates the preset confidence level. Describing the degrees of freedom as Confidence level is upper quantiles of the chi-square distribution; For event-triggered decision variables, This indicates that the triggering condition is met at the current moment, and the data transmission operation is executed. This indicates that the triggering conditions are not met, and the current measurement data will not be transmitted. When the sensor-side event triggering condition is activated, data transmission between the sensor node and the remote estimator is performed.

[0033] In other words, each robot needs to perform local state prediction during execution. To handle the nonlinear terms in the system model, this section calculates the state estimate from the previous time step at each sampling time. and state prediction value At this point, the first-order Taylor series expansion method is used to analyze the nonlinear function. and After linearization, a linearized approximate expression is obtained, which is expressed as: ; in, ,express Error in state estimation at time t. ,express The state prediction error at time t, This represents the predicted state value at time k. express k State estimate at time -1 The Jacobian matrix, representing higher-order remainder terms, is defined as follows: State evolution function exist The Jacobian matrix at the location, and This represents the observation function corresponding to the i-th sensor node. exist Jacobian matrix at the location; Based on the above linearization process, the local estimator (i.e., the sensor node) performs the state prediction process to obtain the current state prediction value and the corresponding prediction error covariance matrix, as follows: ; ; in, This represents the predicted state value at time k. express k State estimate at time -1 This represents the prediction error covariance matrix at time k. The covariance matrix representing the process noise at time k-1; Based on the current state prediction value and the corresponding prediction error covariance matrix, the current predicted measurement value and the corresponding innovation covariance matrix are calculated and expressed as follows: ; ,in, This represents the predicted measurement value of the i-th sensor node at time k. Let represent the information covariance matrix of the i-th sensor node at time k; Based on the evolutionary relationship between the current state and the states at historical transmission times, an approximate representation of the current state vector is determined, which is expressed as: ,in, Indicates that the robot is k The state vector at time t, This represents the time when the i-th sensor node last transmitted its state measurement value. Represents the state transition matrix. , , I It is the identity matrix; The noise at time m is the process noise. The measurement difference between the current measurement and the previous measurement is calculated and expressed as: ;in, The last transmission time The measured value; Based on the measurement difference, the current state prediction value, and the corresponding prediction error covariance matrix, the trigger residual vector is determined, expressed as: , This represents the trigger residual vector, used to characterize the information offset of the current measurement value relative to the state estimate value at the previous transmission time. express State estimate at time 1.

[0034] Based on the aforementioned assumption of Gaussian white noise, the triggered residual vector It approximately follows a Gaussian distribution with zero mean, i.e. Among them, the error covariance matrix The calculation formula is as follows:

[0035] Based on the above error covariance matrix Based on the distribution characteristics, a test statistic vector that follows a chi-square distribution can be constructed. This allows for the determination of whether data transmission should be performed between the sensor node and the remote estimator.

[0036] Furthermore, the remote estimator is used to update the calculated actual input measurements. Determined by the following formula:

[0037] in, The above formula, which represents the actual input measurement value transmitted by the i-th sensor node at time k, indicates that when an event is triggered, the remote estimator receives and uses the real-time measurement value of the current i-th sensor node at time k. When no event is triggered, the local estimator retains and uses the measurements transmitted from the previous time step. This effectively reduces the frequency of channel transmission.

[0038] Furthermore, S103: When the channel between the sensor node and the remote estimator is triggered for transmission, a local state estimate is obtained by performing local filtering update based on the Kalman gain; Specifically, to compensate for the measurement uncertainty introduced by the event-triggered mechanism, the Kalman gain is determined using a piecewise function. , represented as ,in, Let K be the Kalman gain of the i-th sensor node at time k; For event-triggered decision variables, This is the actual measured value of k at the current time. To comprehensively consider the corrected covariance term that accounts for both prediction error and measurement bias, its expression is: ; To measure the covariance of the difference, the desired compensation for the measurement difference can be introduced by setting the Kalman gain when no communication is triggered, thus ensuring the estimation accuracy at low communication frequencies. Based on the Kalman gain, the robot's state estimate and corresponding error covariance matrix are updated, as follows:

[0039]

[0040] in, This is the state estimate of the robot at time k. Let be the error covariance matrix at time k. It is the identity matrix. This is the covariance correction term caused by the event triggering.

[0041] S104: Based on the current local state estimate and the local state estimate most recently transmitted to the fusion center, establish an event triggering mechanism for the channel between the remote estimator and the fusion center; Specifically, the robot's state estimate is reduced in dimensionality using a dimensionality reduction matrix, which is represented as follows: .in, It is a binary variable indicating whether to select the first state estimate. One portion, Indicates the number of elements transmitted. n Let be the total dimension of the state vector, satisfying ; Define the channel-triggered decision variable between the remote estimator and the fusion center as follows: Among them, the triggering area Defined as: , It is a predefined trigger threshold. Indicates at time The most recent local state estimate transmitted to the fusion center before the current time; Based on the triggering decision variable and the current state estimate, the local state estimate that needs to be transmitted is determined, expressed as: ,in, To determine the local state estimates that need to be transmitted.

[0042] In order to solve the communication congestion problem in the channel from the remote estimator to the fusion center, this specification proposes a joint optimization method of coupled dimensionality reduction mechanism and event triggering mechanism. This method aims to compress the local estimate from the spatial dimension (i.e., dimensionality reduction) and dynamically schedule the transmission frequency from the time dimension (i.e., triggering). By eliminating redundant components and duplicate information in the local estimation sequence, the core bandwidth pressure of the fusion network can be alleviated.

[0043] S105: The fusion center receives all the local state estimates transmitted by the robot and performs prediction compensation on the local state estimates to obtain complete local compensation estimates. Since dimensionality reduction (i.e., compression) is required before data transmission, if the event-triggered mechanism for data transmission is activated, the compressed information actually received by the fusion center will be represented as follows: To ensure the integrity of the global fusion, the fusion center reconstructs the missing or untransmitted components based on the prediction information, obtaining compensated local estimates. :

[0044] in, For the compressed information received by the fusion center, , The predicted state value at the current moment. For a dimension reduction matrix, For the identity matrix, the predicted value This is used to compensate for dimensionality components discarded due to the dimensionality reduction mechanism, as well as time-series components that were not transmitted due to events not being triggered.

[0045] S106: Based on all local compensation estimates, construct a quadratic optimization problem with the goal of minimizing the global estimation error covariance, calculate the optimal weighting matrix, realize distributed fusion, and output the global state estimate. Specifically, the global fusion estimate is defined as follows: ;in, To optimize the weighting matrix weights of the i-th sensor node, The weight matrix must satisfy the following constraints for the compensated local state estimate of the i-th sensor node at time k: , where I is the identity matrix and N is the total number of sensor nodes; Define the compensation-adjusted estimation error evolution function; that is, considering the correlation between the estimation errors of different robots, we can calculate the compensation-adjusted estimation error cross-covariance matrix. First, we define the evolution process of the compensated estimation error: ; Based on the compensated estimation error evolution function, a cross-covariance matrix function relationship is constructed between the compensated local state estimates of any two sensor nodes, i.e., the local compensated estimates. and The cross covariance matrix between It can be calculated recursively using the following formula: ;in, This is the standard local filtering error cross-covariance matrix; Based on the aforementioned cross-covariance matrix function relationship, a quadratic optimization problem is constructed with the goal of minimizing the global estimation error, and the optimal weighting matrix weights are obtained by solving the problem. To achieve the optimal fusion effect, this invention constructs a quadratic optimization problem with the objective of minimizing the global estimation error, resulting in the optimal weighting matrix sequence. for:

[0046] Therefore, the final globally optimal distributed fusion estimate and its corresponding error covariance matrix are:

[0047] In this section, quadratic optimization is used to solve the distributed fusion estimation problem:

[0048] in, ,and It is A symmetric positive definite matrix. A quadratic function constructed here. It is about Since it is a convex function, it has a minimum value. This can be determined by taking the derivative and setting it to zero (i.e., ...). ), can find smallest value:

[0049] The optimal distributed estimate can be obtained through the unbiased property:

[0050] in,

[0051] The error covariance of the optimal distributed estimate is:

[0052] For the above equation, let ,and You can get Therefore, we can conclude that:

[0053] Based on the mathematical proof above, the global estimation error covariance satisfies In other words, the global fusion performance is better than the performance of any single local estimation.

[0054] Based on the optimal weighted matrix obtained by solving, the global state estimate is output.

[0055] This specification's embodiments construct a dual-channel event-triggered architecture, introducing triggering mechanisms in two core channels: "sensor-remote estimator" and "remote estimator-fusion center." In the time dimension, redundant sampling data is eliminated through event-triggered decisions; in the spatial dimension, a dimensionality reduction mechanism simplifies the vector size of local estimates. This spatiotemporal coupling optimization strategy effectively solves the data congestion problem in multi-robot systems under conditions of poor communication.

[0056] For example, the embodiments of this specification can also be used to conduct simulation experiments using the simulation software MATLAB, and a real vehicle experimental platform has been built for physical experiments. In the simulation experiment, the present invention uses a convoy of six mobile robots to simulate a two-dimensional plane, namely one central vehicle and five surrounding vehicles. The robots operate in time... k The state vector is defined as ,in Indicates position coordinates, The direction angle is represented. The discrete-time nonlinear kinematic model is described by the following equations:

[0057] The state transition is given by the following formula:

[0058] In this model, and These represent constant linear velocity and angular velocity, respectively. Sampling period. Process noise. The noise is zero-mean Gaussian white noise, and its covariance matrix is... .

[0059] Each robot is equipped with sensors for observation (such as UWB or orientation sensors). The target robot is positioned relative to the sensors. i Measured values It can be modeled as:

[0060] in , . The term indicates that it has covariance. Measurement noise. Azimuth angle Angle of travel relative to the observer Defined to reflect real airborne sensor data.

[0061] In the simulation, the parameters are set to... The total simulation time is Step. The noise covariance is measured as follows: To implement the filter, the nonlinear system equations are linearized using a first-order Taylor expansion:

[0062] in and Let be the Jacobian matrix, and its calculation formula is as follows:

[0063] Regarding the observer i Measurement Jacobian matrix It is given by the following formula:

[0064] in .

[0065] Simulation results show that, Figure 3As shown, this is a comparison between the actual trajectory in the simulation experiment and the estimated trajectory of the method proposed in this application. The error estimate after distributed fusion is lower than the local estimate, indicating that the nonlinear distributed fusion algorithm effectively alleviates the differences between local estimates from different sensors, thereby improving the overall accuracy. Furthermore, the triggering state of the event triggering mechanism differs under different thresholds, representing different moments in the measurement data transmission. Since the remote estimator does not receive data at non-triggering moments, this confirms that the event triggering mechanism can effectively reduce data transmission under communication-constrained conditions. Experimental results show that the distributed cooperative localization method based on a dual-channel event triggering strategy proposed in this invention can ensure a higher communication rate while reducing estimation errors. By adjusting the triggering threshold, the communication load can be significantly reduced without significantly reducing estimation performance.

[0066] To further verify the effectiveness of the proposed positioning method, this invention employs five TurtleBot3 mobile robots for a physical experiment. The experimental platform integrates a high-precision optical motion capture system with a host workstation running Ubuntu, and the entire platform is unified through the Robot Operating System (ROS). The five TurtleBot3 robots are deployed and move counterclockwise along a circular trajectory with a radius of 0.3 meters. Each robot is equipped with a lidar sensor for relative distance measurement and an onboard odometer for providing linear velocity, angular velocity, and heading data. To obtain the true motion state, an optical motion capture system equipped with eight high-definition cameras is used to track infrared reflective markers mounted on each robot.

[0067] Experimental data demonstrate that the proposed distributed cooperative localization algorithm based on a dual-channel event-triggered mechanism can accurately track robot motion. The fused estimation result outperforms the local estimates of the four surrounding robots individually. The experimental results are consistent with the simulation results, proving that the proposed distributed fusion method based on a dual-channel event-triggered mechanism effectively reduces communication overhead while maintaining high estimation performance.

[0068] Based on the methods described above, this paper also provides a multi-agent cooperative localization system based on a dual-channel event-triggered mechanism. This system is a multi-agent system composed of multiple mobile robots, such as... Figure 4 As shown, the system includes: The nonlinear state-space model construction module 401 is used to build a discrete-time nonlinear state-space model for each robot, and each robot includes multiple sensor nodes. The first event triggering mechanism establishment module 402 is used to establish an event triggering mechanism for the channel between the sensor node and the remote estimator based on the state evolution relationship of each robot and the pre-constructed test statistic that follows the chi-square distribution. Gain module 403 is used to perform local filtering updates based on Kalman gain to obtain local state estimates when the channel between the sensor node and the remote estimator is triggered for transmission. The second event triggering mechanism establishment module 404 establishes an event triggering mechanism for the channel between the remote estimator and the fusion center based on the current local state estimate and the local state estimate most recently transmitted to the fusion center. The compensation module 405 is used for the fusion center to receive all the local state estimates transmitted by the robot, and to perform predictive compensation on the local state estimates to obtain complete local compensation estimates. The global optimal output module 406 is used to construct a quadratic optimization problem with the goal of minimizing the global estimation error covariance based on all local compensation estimates, calculate the optimal weighting matrix, realize distributed fusion, and output the global state estimate.

[0069] This embodiment provides a computer device, the internal structure of which can be shown in the following diagram. Figure 5 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used for communication with external terminals via a network connection.

[0070] Those skilled in the art will understand that Figure 5 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0071] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0072] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the above method embodiments.

[0073] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0074] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Furthermore, any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory.

[0075] This document uses specific embodiments to illustrate the principles and implementation methods of this document. The descriptions of the embodiments above are only for the purpose of helping to understand the methods and core ideas of this document. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this document. Therefore, the content of this specification should not be construed as a limitation of this document.

Claims

1. A multi-agent cooperative localization method based on a dual-channel event triggering mechanism, characterized in that, The method is applied to a multi-agent system consisting of multiple mobile robots, and the method includes: Establish a discrete-time nonlinear state-space model for each robot, with each robot including multiple sensor nodes; Based on the state evolution relationship of each robot and the pre-constructed test statistic following the chi-square distribution, an event triggering mechanism for the channel between the sensor node and the remote estimator is established. When the channel between the sensor node and the remote estimator is triggered for transmission, a local state estimate is obtained by performing local filtering updates based on the Kalman gain. Based on the current local state estimate and the local state estimate most recently transmitted to the fusion center, an event triggering mechanism for the channel between the remote estimator and the fusion center is established. The fusion center receives all the local state estimates transmitted by the robot and performs predictive compensation on the local state estimates to obtain complete local compensation estimates. Based on all local compensation estimates, a quadratic optimization problem is constructed with the goal of minimizing the global estimation error covariance. The optimal weighting matrix is ​​calculated to achieve distributed fusion and output the global state estimate.

2. The method according to claim 1, characterized in that, The discrete-time nonlinear state-space model is expressed by the following formula: ； ； in, k It is a discrete time step. Indicates that the robot is k The state vector at time t, ,in Indicates position coordinates, Indicates the direction angle. It is a nonlinear state evolution function. Indicates the first i Each sensor node in k The observation vector acquired at each time step, The corresponding nonlinear observation function; process noise and measuring noise The zero-mean Gaussian white noise was assumed to be mutually independent. The state vector transition is estimated using the following formula: ； in, and These represent constant linear velocity and angular velocity, respectively. The sampling period; Process noise and measuring noise The statistical properties of satisfy the following formula: ； ； in, Represents the mathematical expectation operator. Represents the process noise at time k The covariance matrix, Indicates the measurement noise of the i-th sensor node. The covariance matrix, and It is the Kronecker function.

3. The method according to claim 1, characterized in that, The event-triggered mechanism for establishing the channel between the sensor node and the remote estimator includes: For each robot, the trigger residual vector is calculated based on the current measurement and the local state estimate from the previous transmission time. , of which is the first i Each sensor node in k The trigger residual vector at time step; According to the trigger residual vector Construct a test statistic vector that follows a chi-square distribution. And based on the chi-square quantile of the preset information level, the sensor-side event triggering conditions are established, expressed as: , ,in, For the first i Each sensor node in k The test statistics vector at time t. Indicates the first i Observation vectors of each sensor node Dimensions This indicates the preset confidence level. Describing the degrees of freedom as Confidence level is upper quantiles of the chi-square distribution; For event-triggered decision variables, This indicates that the triggering condition is met at the current moment, and the data transmission operation is executed. This indicates that the triggering conditions are not met, and the current measurement data will not be transmitted. When the sensor-side event triggering condition is activated, data transmission between the sensor node and the remote estimator is performed.

4. The method according to claim 3, characterized in that, For each robot, the trigger residual vector is calculated based on the current measurement and the local state estimate from the previous transmission time. ,include: The discrete-time nonlinear state-space model is linearized using the first-order Taylor series expansion method, resulting in a linearized approximate expression, which is expressed as: ； in, ,express Error in state estimation at time t. ,express The state prediction error at time t, This represents the predicted state value at time k. express k State estimate at time -1 The Jacobian matrix, representing higher-order remainder terms, is defined as follows: State evolution function exist The Jacobian matrix at the location, and This represents the observation function corresponding to the i-th sensor node. exist Jacobian matrix at the location; Based on the linearized approximation expression, the predicted state value at the current time and the corresponding prediction error covariance matrix are obtained, expressed as follows: ; ;in, This represents the predicted state value at time k. express k State estimate at time -1 This represents the prediction error covariance matrix at time k. The covariance matrix representing the process noise at time k-1; Based on the current state prediction value and the corresponding prediction error covariance matrix, the current predicted measurement value and the corresponding innovation covariance matrix are calculated and expressed as follows: ; ,in, This represents the predicted measurement value of the i-th sensor node at time k. Let represent the information covariance matrix of the i-th sensor node at time k; Based on the evolutionary relationship between the current state and the states at historical transmission times, an approximate representation of the current state vector is determined, which is expressed as: ,in, Indicates that the robot is k The state vector at time t, This represents the time when the i-th sensor node last transmitted its state measurement value. Represents the state transition matrix. , , I It is the identity matrix; The noise at time m is the process noise. The measurement difference between the current measurement and the previous measurement is calculated and expressed as: ;in, The last transmission time The measured value; Based on the measurement difference, the current state prediction value, and the corresponding prediction error covariance matrix, the trigger residual vector is determined, expressed as: , Indicates the trigger residual vector, express State estimate at time 1.

5. The method according to claim 1, characterized in that, When a channel-triggered transmission occurs between the sensor node and the remote estimator, a local state estimate is obtained by performing a local filtering update based on the Kalman gain, including: Determining Kalman gain using piecewise function form , represented as ,in, Let K be the Kalman gain of the i-th sensor node at time k; For event-triggered decision variables, This is the actual measured value of k at the current time. This is the corrected covariance term; The covariance of the measured difference; Based on the Kalman gain, the robot's state estimate and corresponding error covariance matrix are updated, as follows: ； ； in, This is the state estimate of the robot at time k. The actual input measurement value transmitted by the i-th sensor node at time k. Let be the error covariance matrix at time k. It is the identity matrix. This is the covariance correction term caused by the event triggering.

6. The method according to claim 5, characterized in that, Based on the current local state estimate and the most recent local state estimate transmitted to the fusion center, an event-triggered mechanism for the channel between the remote estimator and the fusion center is established, including: The robot's state estimate is reduced in dimensionality using a dimensionality reduction matrix, which is expressed as follows: .in, It is a binary variable indicating whether to select the first state estimate. One portion, Indicates the number of elements transmitted. n Let be the total dimension of the state vector, satisfying ; Define a channel-triggered decision variable between the remote estimator and the fusion center to determine whether the dimensionality-reduced data should be transmitted to the fusion center, expressed as: Among them, the triggering area Defined as: , It is a predefined trigger threshold. Indicates at time The most recent local state estimate transmitted to the fusion center before the current time; Based on the triggering decision variable and the current state estimate, the local state estimate that needs to be transmitted is determined, expressed as: ,in, To determine the local state estimates that need to be transmitted.

7. The method according to claim 6, characterized in that, The complete local compensation estimate is obtained using the following compensation formula: ， in, For the compressed information received by the fusion center, , The predicted state value at the current moment. For a dimension reduction matrix, It is an identity matrix.

8. The method according to claim 1, characterized in that, Based on all local compensation estimates, a quadratic optimization problem is constructed with the objective of minimizing the global estimation error covariance. The optimal weighting matrix is ​​calculated to achieve distributed fusion and output the global state estimate, including: Define the global fusion estimate as follows: ;in, To optimize the weighting matrix weights of the i-th sensor node, The weight matrix must satisfy the following constraints for the compensated local state estimate of the i-th sensor node at time k: , where I is the identity matrix and N is the total number of sensor nodes; Define the estimation error evolution function after compensation; Based on the compensated estimation error evolution function, the cross covariance matrix function relationship between the compensated local state estimates of any two sensor nodes is constructed. Based on the aforementioned cross-covariance matrix function relationship, a quadratic optimization problem is constructed with the goal of minimizing the global estimation error, and the optimal weighting matrix weights are obtained by solving the problem. Based on the optimal weighted matrix obtained by solving, the global state estimate is output.

9. A multi-agent cooperative localization system based on a dual-channel event triggering mechanism, characterized in that, The system is a multi-agent system composed of multiple mobile robots, and the system includes: The nonlinear state-space model building module is used to build a discrete-time nonlinear state-space model for each robot, and each robot includes multiple sensor nodes. The first event triggering mechanism establishment module is used to establish an event triggering mechanism for the channel between the sensor node and the remote estimator based on the state evolution relationship of each robot and the pre-constructed test statistic that follows the chi-square distribution. The gain module is used to perform local filtering updates based on Kalman gain to obtain local state estimates when the channel between the sensor node and the remote estimator is triggered for transmission. The second event triggering mechanism establishment module establishes an event triggering mechanism for the channel between the remote estimator and the fusion center based on the current local state estimate and the local state estimate most recently transmitted to the fusion center. The compensation module is used by the fusion center to receive all the local state estimates transmitted by the robot and to perform predictive compensation on the local state estimates to obtain complete local compensation estimates. The global optimal output module is used to construct a quadratic optimization problem with the goal of minimizing the global estimation error covariance based on all local compensation estimates, calculate the optimal weighting matrix, realize distributed fusion, and output the global state estimate.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 8.

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