A multi-agent system distributed positioning method based on covariance intersection

Abstract

The application relates to a multi-agent system distributed positioning method based on covariance intersection, which comprises the following steps: for any agent in a multi-agent system without common orientation, a first pose estimation value and a first error covariance of the agent are determined based on a state equation and a covariance propagation method; a global relative orientation angle is determined based on local relative orientation angle measurement; a second pose estimation value and a second error covariance of the agent are determined based on the global relative orientation angle and relative distance; the two pose estimation values are fused by using a covariance intersection method to obtain a final pose estimation; the above steps are performed on each agent in the multi-agent system to complete the multi-agent system distributed positioning. Compared with the prior art, the application has wider applicability, the estimation value fusion can be performed under the condition that mutual covariance is unknown through the covariance intersection method, the complexity of the algorithm is reduced, and the consistency of the pose estimation is ensured.

Description

Technical Field

[0001] This invention relates to the field of multi-agent system technology, and in particular to a distributed localization method for multi-agent systems based on covariance cross-validation. Background Technology

[0002] With the rapid development of sensor networks, robotic systems, and other related technologies, multi-agent systems (MAS) have become widely used due to their advantages such as high fault tolerance, strong robustness, and low computational and communication costs. They play a vital role in various fields, from disaster relief and transportation to data collection. Achieving accurate positioning in MAS is fundamental to completing various tasks. Traditional centralized positioning technologies place extremely high demands on the communication and computational capabilities of computing centers, and a failure of the computing center can paralyze the entire system. Distributed positioning technology, on the other hand, offers advantages such as low communication costs, high fault tolerance, and strong robustness, making it a crucial means of achieving MAS positioning.

[0003] In indoor, tunnel, and underwater environments, traditional GPS and SLAM positioning technologies are difficult to apply to dynamic multi-agent systems due to factors such as the lack of GPS signals and high hardware costs. Therefore, research on distributed positioning algorithms based on relative measurement information has significant application value. Considering the characteristics of inconsistent orientation and real-time pose changes among dynamic multi-agent systems, further research is needed on distributed positioning algorithms for dynamic multi-agent systems. Moreover, in practical positioning, the uncertainty of the initial state and the presence of measurement noise are unavoidable. Therefore, distributed positioning algorithms with random noise, studied from the perspective of stochastic systems, have broad application scenarios.

[0004] Various methods exist for distributed localization in multi-agent systems. Multi-agent distributed localization algorithms based on relative measurements can obtain global pose using local information, showing broad application prospects. However, relative measurements involve the states of at least two agents, leading to cross-correlation between state estimates of different agents. If traditional Kalman filtering is used to calculate and maintain the cross-covariance matrix, non-zero cross-covariance will result between each pair of agents. Each measurement requires updating all covariances, placing extremely high demands on the system's computational, communication, and storage capabilities. Since different agents have different orientations, relative measurements are generally performed in their own coordinate systems. For global position updates, the agent's orientation needs to be estimated. Furthermore, agents typically measure relative distance and relative azimuth, rather than the x-axis and y-axis measurements found in previous studies. Summary of the Invention

[0005] The purpose of this invention is to provide a distributed localization method for multi-agent systems based on covariance cross-validation, which can achieve pose estimation by measuring relative distance and relative azimuth angle, and requires little computation.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A distributed localization method for multi-agent systems based on covariance crossover includes the following steps:

[0008] S1: For any agent in a multi-agent system without common orientation, determine the agent's first pose estimate and first error covariance based on the state equation and covariance propagation method;

[0009] S2: Determine the global relative orientation angle based on local relative azimuth angle measurements;

[0010] S3: Determine the agent's second pose estimate and second error covariance based on the global relative orientation angle and relative distance;

[0011] S4: Use the covariance cross method to fuse the two pose estimates to obtain the final pose estimate;

[0012] S5: Execute S1-S4 for each agent in the multi-agent system to complete the distributed positioning of the multi-agent system.

[0013] The first pose estimate is:

[0014]

[0015] In the formula, This represents the first estimate of agent i's own value at time k+1. Represents the measured velocity and angular velocity of agent i at time k+1, where, This represents the measurement error, which is assumed to be independent Gaussian white noise, with a covariance matrix of...

[0016] Due to pose estimation and measurement Since they are independent of each other, the covariance propagation method based on nonlinear functions decouples the covariance calculation according to the independence of measurements, and obtains the first error covariance:

[0017]

[0018] In the formula, Indicates the estimated value The error covariance, and These represent the linearization of the state equations, respectively. This represents the final error covariance at time k.

[0019] The S2 determines the global relative orientation angle only through local relative azimuth angle measurement and is not limited by the initial relative azimuth angle.

[0020] The method for determining the global relative orientation angle based on local relative azimuth angle measurement is as follows:

[0021] θ ji =δ ji -δ ij +π

[0022] Where, θ ji Indicates the global relative orientation angle, δ ji This represents the azimuth angle of agent i in its own coordinate system.

[0023] All angles in the method for determining the global relative orientation angle are normalized to the range [0, 2π).

[0024] The second pose estimate is:

[0025]

[0026] in Let represent the second pose estimate of agent i at time k+1. This indicates that agent j estimates the orientation angle based on the first estimate. The obtained rotation matrix, Indicates the relative distance measured. Corresponding to the global relative orientation angle, and Let the relative distance and relative azimuth be the measurement noises, respectively, assumed to be zero-mean Gaussian white noise, and the corresponding covariance matrix be...

[0027] estimated value Since the relative measurements are relatively independent, the second error covariance is determined using the covariance propagation method as follows:

[0028]

[0029] in, Indicates the estimated value The error covariance, and These represent the partial derivatives obtained with respect to the estimated and measured values, respectively.

[0030] The method of fusing the two pose estimates using covariance cross-validation yields the final pose estimate and the final error covariance as follows:

[0031]

[0032]

[0033] in, Let i represent the first, second, and final pose estimates of agent i at time k+1, respectively. Let α and β represent the first, second, and final error covariances, respectively, with coefficients α ∈ [0, 1].

[0034] The value of the coefficient α is:

[0035]

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] (1) This invention considers the distributed localization of multi-agent systems based on the covariance cross method. By fusing unknown estimates through the covariance cross method, the complexity of the algorithm in terms of computation, storage and communication is reduced, and the consistency of pose estimation is guaranteed.

[0038] (2) This invention considers the distributed positioning of multi-agent systems without common orientation and designs a new method for obtaining global relative orientation based on local relative azimuth angle, which can achieve angle estimation simply and quickly.

[0039] (3) This invention considers distributed positioning of multi-agent systems based on relative distance measurement and relative azimuth angle measurement, rather than the relative distance measurement based on the x and y directions in existing research, and has a wider range of applications. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention;

[0041] Figure 2 This is a diagram showing the angular relationships between the agents in one embodiment;

[0042] Figure 3 This is a topological relationship diagram between agents in one embodiment;

[0043] Figure 4 This is a trajectory diagram of each agent in one embodiment;

[0044] Figure 5 This is a position estimation error map of each agent in one embodiment. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0046] A distributed localization method for multi-agent systems based on covariance crossover, such as Figure 1 As shown, it includes the following steps:

[0047] S1: For any agent in a multi-agent system without a common orientation, determine the agent's first pose estimate and first error covariance based on the state equation and covariance propagation method.

[0048] By linearizing the agent's state equation, the first pose estimate is obtained as follows:

[0049]

[0050] In the formula, This represents the first estimate of agent i at time k+1, and the difference between the estimate and the measured value at the previous time step. Independent of each other Represents the measured velocity and angular velocity of agent i at time k+1, where, This represents the measurement error, which is assumed to be independent Gaussian white noise, with a covariance matrix of...

[0051] Due to pose estimation and measurement Since they are independent of each other, the covariance propagation method based on nonlinear functions decouples the covariance calculation according to the independence of measurements, and obtains the first error covariance:

[0052]

[0053] In the formula, Indicates the estimated value The error covariance, and These represent the linearization of the state equations, respectively. This represents the final error covariance at time k.

[0054] S2: Determine the global relative orientation angle based on local relative azimuth angle measurement.

[0055] The global relative orientation angle is determined solely by local relative azimuth measurements, without being limited by the initial relative azimuth angle. The resulting global relative orientation angle is:

[0056] θ ji =δ ji -δij +π

[0057] Where, θ ji Indicates the global relative orientation angle, δ ji This represents the azimuth angle of agent i in its own coordinate system.

[0058] In this embodiment, all angles in the method for determining the global relative orientation angle are normalized to the range [0, 2π).

[0059] S3: Determine the agent's second pose estimate and second error covariance based on the global relative orientation angle and relative distance.

[0060] The second pose estimate is:

[0061]

[0062] in Let represent the second pose estimate of agent i at time k+1. This indicates that agent j estimates the orientation angle based on the first estimate. The obtained rotation matrix, Indicates the relative distance measured. Corresponding to the global relative orientation angle, and Let the relative distance and relative azimuth be the measurement noises, respectively, assumed to be zero-mean Gaussian white noise, and the corresponding covariance matrix be...

[0063] estimated value Since the relative measurements are relatively independent, the second error covariance is determined using the covariance propagation method as follows:

[0064]

[0065] in, Indicates the estimated value The error covariance, and These represent the partial derivatives obtained with respect to the estimated and measured values, respectively.

[0066] S4: The covariance cross method is used to fuse the two pose estimates to obtain the final pose estimate.

[0067] Since the correlation (i.e., the cross-covariance matrix) between the first and second estimates is unknown, the two estimates can be fused using the covariance cross method. This yields the optimal solution, including all possible solutions, resulting in the final pose estimate and the final error covariance:

[0068]

[0069]

[0070] in, Let i represent the first, second, and final pose estimates of agent i at time k+1, respectively. Let represent the first, second, and final error covariances, respectively, with coefficient α ∈ [0, 1]. In this embodiment, the value of coefficient α is:

[0071]

[0072] S5: Execute S1-S4 for each agent in the multi-agent system to complete the distributed positioning of the multi-agent system.

[0073] Simulation experiments were conducted on the distributed localization method based on covariance crossover for the aforementioned multi-agent system. Figure 2 This is an illustration of the relative angular relationships in a multi-agent system without a common orientation. Figure 3 This is the topological relationship diagram between the six entities in the simulation experiment. Using the distributed positioning method described in this embodiment, the following was obtained: Figure 4 and Figure 5 The simulation results for the five followers are shown below. Figure 4 The figure shows the agent's actual trajectory, the position estimation curve when only velocity measurement is used, and the position estimation curve after fusing relative measurements using the covariance cross method. It can be seen from the figure that the fused position estimate is closer to the actual trajectory. Figure 5 The figure demonstrates the use of the covariance cross method to fuse the relative positional errors before and after the fusion. As can be seen from the figure, the overall estimation error after fusion is smaller. Therefore, the simulation results verify the effectiveness of the distributed positioning method proposed in this invention.

[0074] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A distributed localization method for a multi-agent system based on covariance crossover, characterized in that, Includes the following steps: S1: For any agent in a multi-agent system without common orientation, determine the agent's first pose estimate and first error covariance based on the state equation and covariance propagation method; S2: Determine the global relative orientation angle based on local relative azimuth angle measurements; S3: Determine the agent's second pose estimate and second error covariance based on the global relative orientation angle and relative distance; S4: Use the covariance cross method to fuse the two pose estimates to obtain the final pose estimate; S5: Execute S1-S4 for each agent in the multi-agent system to complete the distributed positioning of the multi-agent system; The first pose estimate is: In the formula, Represents intelligent agents exist The first estimate of itself at any given moment. Represents intelligent agents exist The velocity and angular velocity measurements at time t, where, This represents the measurement error, which is assumed to be independent Gaussian white noise, with the covariance matrix being... ; For intelligent agents i exist k The final pose estimate at time step; Due to pose estimation and measurement Since they are independent of each other, the covariance propagation method based on nonlinear functions decouples the covariance calculation according to the independence of measurements, and obtains the first error covariance: In the formula, Indicates the estimated value The error covariance, and These represent the linearization of the state equations, respectively. express The final error covariance at time; The method for determining the global relative orientation angle based on local relative azimuth angle measurement is as follows: in, Indicates the global relative orientation angle. Represents intelligent agents In its own coordinate system The azimuth angle; The second pose estimate is: in Represents intelligent agents i exist k The second pose estimate at time +1. Represents intelligent agents Estimate based on the orientation angle in the first estimate The obtained rotation matrix, Indicates the relative distance measured. Corresponding to the global relative orientation angle, , and Let the relative distance and relative azimuth be the measurement noise, respectively, assumed to be zero-mean Gaussian white noise, and the corresponding covariance matrix be... ; estimated value Since the relative measurements are relatively independent, the second error covariance is determined using the covariance propagation method as follows: in, Indicates the estimated value The error covariance, and These represent the partial derivatives obtained with respect to the estimated and measured values, respectively. The method of fusing the two pose estimates using covariance cross-validation yields the final pose estimate and the final error covariance as follows: in, , , Representing intelligent agents respectively i exist k The first pose estimate, the second pose estimate, and the final pose estimate at time +1. , , Let represent the first error covariance, the second error covariance, and the final error covariance, respectively, with coefficients... .

2. The distributed localization method for a multi-agent system based on covariance crossover as described in claim 1, characterized in that, The S2 determines the global relative orientation angle only through local relative azimuth angle measurement and is not limited by the initial relative azimuth angle.

3. The distributed localization method for a multi-agent system based on covariance crossover as described in claim 1, characterized in that, All angles in the method for determining the global relative orientation angle are standardized within... Within the range.

4. The distributed localization method for a multi-agent system based on covariance crossover as described in claim 1, characterized in that, The coefficient The value can be: 。

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