A Cooperative Localization Method and System for Multi-AUV Systems with Transmission Time Delay

Abstract

The present invention proposes a cooperative positioning method and system for a multi-underwater robot system with transmission time delay, including: establishing a measurement model of a monitoring point for a target underwater robot based on the kinematic linearization model of the target underwater robot; reconstructing the measurement model, converting the measurement information with time-varying time delay in the measurement model into measurement information with constant time delay, and the reconstructed measurement model contains the same measurement information as the original measurement model; obtaining a locally optimal pose estimate of the target underwater robot by using the method of geometric projection based on the measurement information in the reconstructed measurement model; obtaining a regionally optimal pose estimate of the target underwater robot by using the method of weighted fusion based on the locally optimal pose estimates of the target underwater robot by different monitoring points. It solves the influence of time-varying communication time delay on distributed cooperative positioning and improves the real-time performance of cooperative positioning.

Description

Technical Field

[0001] The present invention belongs to the technical field related to cooperative positioning of underwater robots, and particularly relates to a cooperative positioning method and system for a multi-underwater robot system under transmission time delay. Background Art

[0002] The statements in this part merely provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] Autonomous Underwater Vehicles (AUVs) are gradually playing a crucial role in the development and utilization of marine resources. Without the restraint of cables, AUVs are very flexible when working underwater. It integrates scientific and technological products such as artificial intelligence, computer software, advanced computing technology, energy storage, and sensors, and has become a research hotspot in the current marine field. Especially since the 21st century, humans have continuously expanded the scope of ocean exploration and strengthened the intensity of marine resource development. As the pioneer of ocean exploration, AUVs have received extensive attention. They have the characteristics of intelligence, concealment, and mobility, can dive underwater for detection operations for a long time, and AUVs can rely on their own power propulsion and can independently conduct detection activities in areas that are difficult for humans to reach easily.

[0004] Among the many positioning methods of AUVs, the distributed cooperative positioning of multiple underwater robots has unique advantages. The so-called distributed cooperative positioning means that in a multi-AUV system, other AUVs or monitoring buoys can only estimate the pose information of the target AUV by using their own measurement information and the measurement information of other AUVs within the communication range, rather than using global measurement information for estimation. In a distributed architecture, there is no information fusion center similar to a centralized one, and there is no primary or secondary distinction among AUVs. They are mutually reference and corrected with each other. It can be understood that the status of each underwater robot is equal, but the configuration is not equal. This configuration method is more flexible, and some underwater robots can choose to be equipped with high-precision navigation equipment and participate in the mutual correction process. The distributed configuration scheme has the advantages of flexibility, robustness, etc., and can improve the locatability, integrity, and cooperation ability of the system. Therefore, it is of great significance to explore the distributed cooperative positioning algorithm of multiple underwater robots. In order to ensure the real-time performance of positioning and the reliability of the results, it is necessary to design a suitable filtering algorithm to solve the influence of the random and uncertain marine environment on positioning. However, in the case of incomplete information, that is, the random and uncertain perturbations of the kinematic model, the random time delay of relative measurement, signal attenuation and loss, etc., the design of the filter is very difficult, especially in the case where the uncertain information has time correlation, which is a challenging problem in multi-AUV cooperative positioning. Summary of the Invention

[0005] To overcome the deficiencies of the above-mentioned existing technologies, the present invention provides a collaborative positioning method and system for a multi-underwater robot system under transmission time delay. By using the kinematic linearization model of the underwater robot, which is easy to solve the time-varying time delay problem by the projection method, the measurement model established for the target underwater robot based on the monitoring points is reconstructed, solving the influence of time-varying communication time delay on distributed collaborative positioning and improving the real-time performance of collaborative positioning.

[0006] To achieve the above object, the first aspect of the present invention provides a collaborative positioning method for a multi-underwater robot system under transmission time delay, including:

[0007] Step 1: Establish a measurement model of the monitoring points for the target underwater robot based on the kinematic linearization model of the target underwater robot;

[0008] Step 2: Reconstruct the measurement model, convert the measurement information with time-varying time delay in the measurement model into measurement information with constant time delay, and the reconstructed measurement model contains the same measurement information as the original measurement model;

[0009] Step 3: Based on the measurement information in the reconstructed measurement model, obtain the local optimal pose estimation of the target underwater robot by using the method of geometric projection;

[0010] Step 4: Based on the local optimal pose estimations of the target underwater robot from different monitoring points, obtain the regional optimal pose estimation of the target underwater robot by using the method of weighted fusion.

[0011] The second aspect of the present invention provides a collaborative positioning system for a multi-underwater robot system under transmission time delay, including:

[0012] Measurement model establishment module: Establish a measurement model of the monitoring points for the target underwater robot based on the kinematic linearization model of the target underwater robot;

[0013] Reconstruction module: Reconstruct the measurement model, convert the measurement information with time-varying time delay in the measurement model into measurement information with constant time delay, and the reconstructed measurement model contains the same measurement information as the original measurement model;

[0014] Local optimal pose estimation module: Based on the measurement information in the reconstructed measurement model, obtain the local optimal pose estimation of the target underwater robot by using the method of geometric projection;

[0015] Regional optimal pose estimation module: Based on the local optimal pose estimations of the target underwater robot from different monitoring points, obtain the regional optimal pose estimation of the target underwater robot by using the method of weighted fusion.

[0016] The third aspect of the present invention provides a computer device, comprising: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device runs, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, a cooperative positioning method for a multi-underwater robot system with transmission time delay is executed.

[0017] The fourth aspect of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, a cooperative positioning method for a multi-underwater robot system with transmission time delay is executed.

[0018] The above one or more technical solutions have the following beneficial effects:

[0019] In the present invention, a kinematic linearization model of an underwater robot is adopted. This model is easy to solve the time-varying time-delay problem by the projection method, and the measurement model established for the target underwater robot based on the monitoring points is reconstructed, solving the influence of time-varying communication time delay on distributed cooperative positioning and improving the real-time performance of cooperative positioning.

[0020] In the present invention, on the basis of reconstruction, the optimal local pose estimation of the target underwater robot for different monitoring points is obtained, and then the optimal regional pose estimation of the target underwater robot is obtained based on the optimal local pose estimation of the target underwater robot for different monitoring points, solving the problem of difficult filter design in the case where uncertain information has time correlation.

[0021] The advantages of the additional aspects of the present invention will be partly given in the following description, partly will become obvious from the following description, or will be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0023] Figure 1 It is a schematic diagram of information interaction of the multi-AUV system in the first embodiment of the present invention;

[0024] Figure 2 It is a schematic diagram of the robot imitating the flying gurnard in the simulation experiment of the first embodiment of the present invention;

[0025] Figure 3 It is a dot matrix diagram of information interaction delay in the simulation experiment of the first embodiment of the present invention;

[0026] Figure 4 It is a three-dimensional space positioning effect diagram in the simulation experiment of the first embodiment of the present invention;

[0027] Figure 5 It is the two-dimensional plane positioning effect diagram in the simulation experiment of Embodiment 1 of the present invention. Specific implementation manner

[0028] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0029] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention.

[0030] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0031] Embodiment 1

[0032] This embodiment discloses a cooperative positioning method for a multi-underwater robot system under transmission time delay, including:

[0033] Step 1: Establish a measurement model of the monitoring point for the target underwater robot based on the kinematic linearization model of the target underwater robot;

[0034] Step 2: Reconstruct the measurement model to convert the measurement information with time-varying time delay in the measurement model into measurement information with constant time delay, and the reconstructed measurement model contains the same measurement information as the original measurement model;

[0035] Step 3: Based on the measurement information in the reconstructed measurement model, use the method of geometric projection to obtain the local optimal pose estimation of the target underwater robot;

[0036] Step 4: Based on the local optimal pose estimations of the target underwater robot by different monitoring points, use the method of weighted fusion to obtain the regional optimal pose estimation of the target underwater robot.

[0037] In Step 1 of this embodiment, first establish the kinematic linearization model of the target underwater robot AUV. Considering the miniaturized target AUV, it cannot directly obtain its speed like a mobile robot using an odometer or an AUV using a DVL. Use a class of discretized nonlinear models to describe the position information s of the target AUV k =[L x , L y , L z T (Range measurement L x , L y , depth measurement L z ) and attitude information (Roll angle φ k , pitch angle θ k and yaw angle ψ k ), and are transformed into a linearized model by the method of linear approximation. The linearization residuals are treated as non - linear terms. The established model is:

[0038] x k+1 = f(x k , u k ) + w k = x k +ΔTJ(x k )u k + w k

[0039] = A k x k + p(x k , u k ) + w k (1)

[0040] Among them, u k is the external control input, ΔT is the sampling time, A k x k is the linear approximation of the non - linear function f(x k , u k ). The state transition matrix A k is obtained by linear approximation methods such as second - order Taylor expansion or matrix partial derivative. w k is the external disturbance, is the linear approximation residual and satisfies:

[0041] E[p(x, u k )|x k = 0,

[0042] E[p(x k , u k )p T (x j , u j )|x k = F k δ kj (2)

[0043] Among them, F k is the known positive - definite matrix, δ kj is the Dirac function. The transformation matrix J(x) is:

[0044]

[0045] Among them,

[0046]

[0047]

[0048] Among them, w k is an external disturbance, and w k is assumed to be Gaussian white noise with a mean of zero and a covariance matrix of Q k .

[0049] Establish a measurement model of monitoring node i (buoy or neighbor underwater robot) with respect to the target AUV, including distance measurement z r , attitude measurement z a and depth measurement z d There are three categories, specifically:

[0050]

[0051] Among them, is Gaussian white noise with zero mean and its variance is R i ; The linear approximation of h(x k ) is obtained through linear approximation methods such as second-order Taylor expansion or matrix partial derivative, that is The measurement information transfer matrix is obtained through linear approximation methods such as second-order Taylor expansion or matrix partial derivative is the linear approximation residual of the measurement of the monitoring node and satisfies:

[0052] E[g i (x)|x k = 0,

[0053]

[0054] Among them, G k is a known positive definite matrix. The subscripts of x j and x k represent different times.

[0055] In step 2 of this embodiment, due to the complex underwater communication environment, there is a time delay that changes with time in the transmission process of the measurement information of the sensor. The measurement information received at the estimator end is:

[0056]

[0057] Among them, is a time-varying time delay, and its value is in the set .

[0058] In order to convert the time-varying time delay into a multi-channel constant time delay, a binary indicator function is defined. The output of the binary indicator function is used as the time stamp of the measurement time delay to mark the magnitude of the transmission time delay, and the measurements regarding the pose information of the target AUV at the same moment are combined to form new measurement information.

[0059] Specifically, the defined binary indicator function is:

[0060]

[0061] where \(t\) represents the value taken in the set .

[0062] Through the above-defined binary indicator function, the measurement information with time-varying time delay can be equivalently converted into the measurement information with multi-channel constant time delay:

[0063]

[0064] In order to design a pose estimator through the method of geometric projection, this embodiment further reconstructs the above multi-channel measurement information so that it contains the same amount of information as the original measurement information. Specifically:

[0065]

[0066]

[0067] where, and represent the reconstructed measurement information in two time intervals, and \(s\) is a time variable.

[0068]

[0069]

[0070]

[0071]

[0072] Through the reconstruction of the above measurement information, for the pose information of the target AUV, the above measurement information no longer contains time delay.

[0073] In step 3 of the embodiment, based on the above-reconstructed measurement information, a local optimal estimator for the pose information of the target AUV is designed by using the method of geometric projection, and an estimator in the following 3-steps form is designed:

[0074] 1-step: When , the local optimal pose estimator is:

[0075]

[0076] Among them,

[0077]

[0078]

[0079] Among them, represents the covariance matrix of the estimation error, are the estimated values at different times, is the binary indicator function. The purpose of the 1-step design is to provide a one-step predicted value of the pose information for the 2-step.

[0080] 2-step: When the local optimal pose estimator is:

[0081]

[0082] Among them,

[0083]

[0084]

[0085] The purpose of the 2-step design is to provide a one-step predicted value of the pose information at time k for the 3-step.

[0086] 3-step: When s = k, the local optimal pose estimator is:

[0087]

[0088] Among them,

[0089]

[0090] In this embodiment, based on the output of the local state estimation of the target AUV by the above monitoring nodes, using weighted information fusion, on the basis of the local state estimator, a regional optimal pose estimator of the target AUV is designed, still in the 3-steps form, specifically:

[0091] 1-step: When the one-step prediction of the regional optimal pose is:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Among them, is the estimated information of the neighbor nodes of the monitoring node i, is the set of neighbor nodes of the monitoring node i, is the fusion weighting coefficient. In the formula represents the inner product of two estimation errors.

[0098] 2-step: When the one-step prediction of the regional optimal pose is:

[0099]

[0100]

[0101] Where is the same as in the calculation of 1-step.

[0102] 3-step: When s = k, the regional optimal pose estimator is:

[0103]

[0104] Where is calculated in the same way as 1-step, is the time stamp at time k.

[0105] The above-mentioned fusion weighting coefficient w ij can be a set value. If it is an unknown parameter to be optimized, it can be obtained by optimization in the following way:

[0106]

[0107] Where

[0108]

[0109]

[0110]

[0111] In formula (34) is the local estimation error of the pose information.

[0112] The fusion weighting coefficient can be obtained through the optimization of the following constraint problem:

[0113]

[0114] The optimization problem of this issue is equivalent to:

[0115]

[0116] where

[0117]

[0118]

[0119] By using the method of completing the square, we can obtain:

[0120]

[0121] Since the solution of the above formula is non-unique, the optimal weight coefficient w is obtained through further optimization as follows ij :

[0122]

[0123] Due to the existence of a large number of cross-term calculations in the design of the above regional optimal pose estimator, the computational complexity and communication complexity of the optimal pose estimator are relatively high. In this embodiment, a sub-optimal estimator design method is proposed by correcting the regional optimal estimator to reduce the computational complexity and thus improve the real-time performance of the algorithm.

[0124] Based on the regional optimal estimator, this embodiment designs a regional sub-optimal pose estimator to improve the real-time performance of the algorithm. The design of the regional sub-optimal pose estimator is specifically as follows:

[0125] 1-step: When , the one-step prediction of the regional sub-optimal pose is:

[0126]

[0127]

[0128] where is the fusion weighting coefficient, and:

[0129]

[0130]

[0131]

[0132] where is the corrected regional estimation covariance matrix.

[0133] 2-step: When the one-step prediction of the region optimal pose is:

[0134]

[0135]

[0136] where

[0137]

[0138]

[0139]

[0140] where is the corrected region estimation covariance matrix.

[0141] 3-step: When s = k, the region sub-optimal pose estimator is:

[0142]

[0143] where is calculated in the same way as in 2-step, is the time stamp at time k.

[0144] Based on the above steps, a cooperative localization method for a multi-AUV system with transmission delay proposed in this embodiment is:

[0145] (1) According to the initial state estimation of the i-th (i = 1,..., N) target AUV and the initial local filtering error matrix and the initial weighting matrix Calculate the region filtering covariance matrix at the initial time according to formula (28) and formula (34)

[0146] (2) According to the calculation methods of formula (32) and formula (35) in step four, online calculate the state interaction covariance matrix

[0147] (3) Based on the results of the local optimal pose estimation in step 3, the region optimal pose estimation in step 4, and the region sub-optimal pose estimation, and based on the optimization method of the region optimal weighting coefficient, obtain the filtering gain and the weighting coefficient W ij , and then obtain the pose information of the target AVU at the current time:

[0148] (4) Let k = k + 1 and recalculate (1) - (3) until the positioning task is completed.

[0149] In underwater acoustic communication networks, some reliable network transmission protocols (such as end-to-end TCP) are not suitable. In underwater information transmission, time delay often varies with time. The existence of time-varying time delay brings many difficulties to the design of positioning algorithms. In existing positioning algorithm research, time-varying time delays in information interaction are often selectively ignored. In order to achieve underwater positioning with high precision and real-time performance, a collaborative positioning method for multiple underwater robot systems under transmission delay proposed in this embodiment solves the impact of time-varying communication delays on distributed collaborative positioning and improves the real-time performance of collaborative positioning.

[0150] The effect of the method of this embodiment can be further illustrated by the following experimental simulation. Figure 2 As shown, a multi-AUV system consisting of four isomorphic leopard bream-like robots is used for simulation experiments. In the present invention, four leopard bream-like robots are considered to form a ring communication topology, and their discretized kinematic model is as follows:

[0151] x k+1 =x k +ΔTJ(x k ) k +w k

[0152]

[0153] in,

[0154]

[0155]

[0156] For the above-mentioned discretized nonlinear model, a linear approximation model is obtained through Matlab linear approximation and data fitting methods, and the estimated gain weighting system is further calculated according to the method proposed in this implementation to achieve distributed collaborative positioning.

[0157] After calculations using the distributed collaborative positioning method proposed in this embodiment, the leopard bream robot uses its own measurement of the target to achieve tracking and positioning. Figure 3 The dot plot of information interaction delay is given. Figure 4 The trajectory of the leopard bream robot in three-dimensional space is clearly shown in the figure. Figure 5 Shows the angled view of the leopard bream-like robot in two-dimensional space.

[0158] Embodiment 2

[0159] The purpose of this embodiment is to provide a cooperative positioning system for a multi-underwater robot system with transmission time delay, including:

[0160] Measurement model establishment module: Based on the kinematic linearization model of the target underwater robot, establish the measurement model of the monitoring point for the target underwater robot;

[0161] Reconstruction module: Reconstruct the measurement model, convert the measurement information with time-varying time delay in the measurement model into measurement information with constant time delay, and the reconstructed measurement model contains the same measurement information as the original measurement model;

[0162] Local optimal pose estimation module: Based on the measurement information in the reconstructed measurement model, use the method of geometric projection to obtain the local optimal pose estimation of the target underwater robot;

[0163] Regional optimal pose estimation module: Based on the local optimal pose estimations of the target underwater robot by different monitoring points, use the method of weighted fusion to obtain the regional optimal pose estimation of the target underwater robot.

[0164] Embodiment III

[0165] The purpose of this embodiment is to provide a computing device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device runs, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, a cooperative positioning method for a multi-underwater robot system with transmission time delay is executed.

[0166] Embodiment IV

[0167] The purpose of this embodiment is to provide a computer-readable storage medium.

[0168] A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium. When the computer program is run by a processor, a cooperative positioning method for a multi-underwater robot system with transmission time delay is executed.

[0169] The steps involved in the devices in Embodiments II, III, and IV above correspond to those in Method Embodiment I. For specific implementation manners, reference may be made to the relevant description part of Embodiment I. The term "computer-readable storage medium" should be understood to include a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0170] Those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0171] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that, based on the technical solutions of the present invention, various modifications or deformations that can be made without creative efforts by those skilled in the art are still within the protection scope of the present invention.

Claims

1. A cooperative positioning method for a multi - underwater robot system with transmission time - delay, characterized in that, it includes: Step 1: Establish a measurement model of the monitoring point for the target underwater robot based on the kinematic linearization model of the target underwater robot; Step 2: Reconstruct the measurement model, convert the measurement information with time - varying time - delay in the measurement model into measurement information with constant time - delay, and the reconstructed measurement model contains the same measurement information as the original measurement model; In step 2, mark the magnitude of the transmission time - delay in the measurement model through the output of the binary indicator function, and convert the measurement information with time - varying time - delay in the measurement model into multi - channel measurement information with constant time - delay; After combining the multi - channel measurement information with constant time - delay of different monitoring points for the target underwater vehicle at the same moment, obtain the reconstructed measurement model; Step 3: Based on the measurement information in the reconstructed measurement model, use the method of geometric projection to obtain the local optimal pose estimation of the target underwater robot; Step 4: Based on the local optimal pose estimations of different monitoring points for the target underwater robot, use the weighted fusion method to obtain the regional optimal pose estimation of the target underwater robot.

2. The cooperative positioning method for a multi - underwater robot system with transmission time - delay according to claim 1, characterized in that, in step 1, according to the distance measurement, depth measurement and attitude measurement of the target underwater robot, establish a discretized non - linear model of the target underwater robot, and convert the discretized non - linear model into a kinematic linearization model through linear approximation; Combined with the kinematic linearization model of the target underwater robot, linearly approximate the outputs of the distance measurement, attitude measurement and depth measurement of the monitoring point for the target underwater robot to establish a measurement model.

3. The cooperative positioning method for a multi - underwater robot system with transmission time - delay according to claim 1, characterized in that, In the step 3, the local optimal pose estimation of the target underwater robot is: when the local optimal pose estimator is: When the local optimal pose estimator is as follows: when s = k, the local optimal pose estimation is: Among them, is the local estimation of the pose information, is a binary indicator function representing the timestamp, is the local filtering gain, is the measurement model of the monitoring point for the target underwater robot, is the measurement information transfer matrix.

4. The cooperative positioning method for a multi - underwater robot system with transmission time - delay according to claim 1, characterized in that, in step 4, the regional optimal pose estimation of the target underwater robot is: When the one-step prediction of the region optimal pose is as follows: When one-step prediction of the region optimal pose is as follows: when s = k: Among them, is the estimated information of the neighbor nodes of the monitoring node i, is the set of neighbor nodes of the monitoring node i, is the fusion weighting coefficient, is the regional estimation of the corrected pose information, is the covariance matrix of the regional estimation error, represents the inner product of two estimation errors.

5. The cooperative positioning method for a multi - underwater robot system with transmission time - delay according to claim 4, characterized in that, The fusion weighting coefficient is optimized to be: Among them, is the weighted factor matrix after dimension expansion.

6. The cooperative positioning method for a multi - underwater robot system with transmission time - delay according to claim 4, characterized in that, it also includes the design of the regional sub - optimal pose estimator, specifically: When the one-step prediction of the regional sub-optimal pose is as follows: Among them is the corrected regional estimated covariance matrix; When the one-step prediction of the region optimal pose is as follows: when s = k, the regional sub - optimal pose estimator is:

7. A cooperative positioning system for a multi - underwater robot system with transmission time - delay, characterized in that, it includes: A measurement model establishment module: Establish a measurement model of the monitoring point for the target underwater robot based on the kinematic linearization model of the target underwater robot; Reconstruction module: Reconstruct the measurement model, convert the measurement information with time-varying time delay in the measurement model into measurement information with constant time delay, and the reconstructed measurement model contains the same measurement information as the original measurement model; Mark the magnitude of the transmission time delay in the measurement model through the output of the binary indicator function, and convert the measurement information with time-varying time delay in the measurement model into multi-channel measurement information with constant time delay; After combining the multi-channel measurement information with constant time delay of different monitoring points for the target underwater vehicle at the same moment, obtain the reconstructed measurement model. Local optimal pose estimation module: Based on the measurement information in the reconstructed measurement model, use the method of geometric projection to obtain the local optimal pose estimation of the target underwater robot. Regional optimal pose estimation module: Based on the local optimal pose estimation of the target underwater robot by different monitoring points, use the method of weighted fusion to obtain the regional optimal pose estimation of the target underwater robot.

8. A computer device, characterized in that, it includes: A processor, a memory and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device runs, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, it executes a cooperative positioning method for a multi-underwater robot system under a transmission time delay as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, and when the computer program is run by a processor, it executes a cooperative positioning method for a multi-underwater robot system under a transmission time delay as described in any one of claims 1 to 6.

Images