A distributed elastic positioning method and system for underwater multi-robots

Abstract

This invention proposes a distributed elastic localization method and system for underwater multi-robots, relating to the field of underwater robotics. It establishes a kinematic model of the target robot and a measurement model that fuses distance, depth, and attitude information from monitoring nodes. Communication is triggered when the target robot's state change exceeds a preset threshold. A binary indicator function is used to identify the random delay state of the measurement signal. Scenes are divided according to the relationship between the current time and the total task duration, and the random delay information is transformed into a delay-free equivalent sequence. Based on the kinematic model, measurement model, and delay-free equivalent sequence, delay channels are selected in different scenes to perform state prediction and elastic gain correction, obtaining the target robot's state estimate. A tight upper bound is constructed for the localization error covariance matrix, and the optimal localization gain is solved to iteratively optimize the elastic gain. By adapting to time-varying delays and optimizing gain control errors, efficient collaborative localization in complex environments is ensured, providing reliable pose information for underwater tasks.

Description

Technical Field

[0001] This invention relates to the field of underwater robot technology, and in particular to a distributed elastic positioning method and system for multiple underwater robots. Background Technology

[0002] Underwater multi-robot cooperative localization is a technique that uses the interactive information of multiple autonomous underwater vehicles (AUVs) to estimate the pose of a target. Its core lies in improving the accuracy and reliability of localization in complex underwater environments through information fusion. Kalman filtering and its derivative algorithms are commonly used state estimation tools, which recursively update the state estimate and error covariance to handle measurement information affected by noise.

[0003] As the complexity of underwater missions increases, traditional periodic communication modes suffer from resource waste due to data redundancy. Event-triggered mechanisms have emerged to address this, triggering communication only when state changes exceed a threshold, thus reducing transmission costs. However, this mechanism breaks the traditional Kalman filter's assumption of continuous and lag-free measurement information. The triggering error generated by the receiver using historical signals during non-triggered periods, coupled with the inherent random delays in underwater communication, makes it difficult to model the sources of error, affecting filter stability and positioning accuracy.

[0004] While existing technologies simplify calculations by approximating the covariance matrix, they do not fully consider the randomness errors caused by events and lack dynamic adaptability in handling time-varying delays. Therefore, they still suffer from problems of accuracy fluctuations and insufficient real-time performance in multi-robot collaborative scenarios. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a distributed elastic localization method and system for multiple underwater robots. First, a kinematic and measurement model of the target robot is established. Communication is triggered when the state change measured by the monitoring node exceeds a threshold. A binary indicator function is used to characterize the random delay characteristics of the interactive measurement information between the monitoring node and the target node. Based on an information reconstruction method, the delayed information is transformed into a delay-free equivalent information sequence. Based on the reconstructed equivalent information sequence, a partitioned distributed iterative localization algorithm is designed to achieve efficient cooperative pose estimation for multiple AUVs.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides an underwater multi-robot distributed elastic positioning method, comprising:

[0008] Establish a kinematic model of the target robot and a measurement model that integrates distance, depth and attitude information of monitoring nodes;

[0009] Communication is triggered when the monitoring node detects that the state change of the target robot exceeds a preset threshold.

[0010] A binary indicator function is used to identify the random delay state of the measurement signal. Scenarios are divided according to the relationship between the current time and the total duration of the task. Based on different scenarios, the random delay information is transformed into a delay-free equivalent sequence.

[0011] Based on the kinematic model, measurement model and delay-free equivalent sequence, the delay channel is selected to perform state prediction and elastic gain correction in different scenarios to obtain the state estimate of the target robot.

[0012] Construct a tight upper bound for the localization error covariance matrix, solve for the optimal localization gain, iteratively optimize the elastic gain, and finally obtain the pose state of the target robot.

[0013] In a second aspect, the present invention provides an underwater multi-robot distributed elastic positioning system, comprising:

[0014] The system modeling module is configured to establish a kinematic model of the target robot and a measurement model that fuses distance, depth and attitude information of the monitoring nodes.

[0015] The event triggering module is configured to trigger communication when the monitoring node detects that the state change of the target robot exceeds a preset threshold.

[0016] The random delay reconstruction module is configured to use a binary indicator function to identify the random delay state of the measurement signal, divide the scenario according to the relationship between the current time and the total task duration, and convert the random delay information into a delay-free equivalent sequence based on different scenarios.

[0017] The partitioned collaborative localization module is configured to select a delay channel to perform state prediction and elastic gain correction in different scenarios based on the kinematic model, measurement model and delay-free equivalent sequence, so as to obtain the state estimate of the target robot.

[0018] The elastic optimization module is configured to construct a tight upper bound of the positioning error covariance matrix, solve for the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the pose state of the target robot.

[0019] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the underwater multi-robot distributed elastic positioning method described in the first aspect.

[0020] Fourthly, the present invention 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 executes the program to implement the steps of the underwater multi-robot distributed elastic positioning method described in the first aspect.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] (1) This invention establishes a model that integrates multiple information to accurately describe the motion and measurement characteristics of the robot; reduces redundant transmission through an event triggering mechanism; introduces a binary indicator function and scene division to effectively handle random delays; the converted delay-free sequence ensures data validity; and then performs state prediction and elastic gain correction based on the delay-free sequence. Combined with error covariance tight upper bound optimization, it improves positioning accuracy and stability, realizes efficient collaboration of multiple robots, adapts to complex underwater environments, and provides reliable solutions for positioning tasks.

[0023] (2) The present invention dynamically monitors the status information of each robot through an event trigger generator and triggers communication only when the current information changes beyond a preset threshold, thereby adaptively adjusting the information interaction frequency between multiple robots, effectively reducing the load and congestion of the underwater acoustic communication network, and improving communication efficiency and system reliability.

[0024] (3) Under the error conditions introduced by the event-triggered mechanism, this invention rigorously derives the tight upper bound of the positioning error covariance and optimizes the distributed positioning gain of each robot to ensure high-precision positioning and robustness of the system under communication constraints and environmental interference. This method not only significantly reduces unnecessary communication and computational overhead, but also improves the adaptability, flexibility and resource utilization efficiency of underwater multi-robot cooperative positioning, and is suitable for long-term operation needs in complex underwater environments.

[0025] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0027] Figure 1 A main flowchart of an underwater multi-robot distributed elastic positioning method provided in an embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of the MAUV system and information interaction provided in an embodiment of the present invention;

[0029] Figure 3 This is a diagram illustrating the positioning effect of the target AUV in the x-axis direction according to an embodiment of the present invention.

[0030] Figure 4 This is a diagram illustrating the positioning effect of the target AUV in the y-axis direction according to an embodiment of the present invention.

[0031] Figure 5The mean square error diagram of the target AUV in the x-axis direction provided in the embodiments of the present invention;

[0032] Figure 6 The mean square error diagram of the target AUV in the y-axis direction is provided for the embodiments of the present invention. Detailed Implementation

[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0034] Underwater acoustic communication suffers from limited bandwidth, high latency, and high energy consumption. Frequent information exchange exacerbates communication load and energy consumption, limiting the long-term operational capability of the system. While event-triggered mechanisms can alleviate this problem by adjusting the communication frequency through state change thresholds, they break the traditional Kalman filter's assumptions about measurement information. Traditional Kalman filtering relies on measurement information being updated synchronously at fixed periods with known error characteristics. However, under event triggering, the receiver uses historical signals during non-trigger periods. The deviation between the actual state and the used signal forms the triggering error. Its randomness makes it difficult to accurately model the error using traditional formulas, thus affecting error covariance calculation and positioning stability.

[0035] To this end, this invention proposes an underwater multi-robot distributed elastic cooperative positioning method, system, medium, and device based on an event-triggered mechanism. By reducing communication load through dynamic triggering conditions and combining random analysis and matrix theory to handle errors and delays, positioning accuracy and stability are ensured. The details are described below.

[0036] Example 1

[0037] like Figure 1 As shown, this embodiment discloses a distributed elastic localization method for underwater multi-robots, which estimates the pose state of a target AUV, including the following steps:

[0038] S1: Establish the kinematic model of the target robot and the measurement model that integrates distance, depth and attitude information of the monitoring nodes;

[0039] S2: Communication is triggered when the monitoring node detects that the state change of the target robot exceeds a preset threshold.

[0040] S3: Use a binary indicator function to identify the random delay state of the measurement signal, divide the scenario according to the relationship between the current time and the total task duration, and transform the random delay information into a delay-free equivalent sequence based on different scenarios;

[0041] S4: Based on the kinematic model, measurement model and delay-free equivalent sequence, select the delay channel to perform state prediction and elastic gain correction in different scenarios to obtain the state estimate of the target robot;

[0042] S5: Construct the tight upper bound of the localization error covariance matrix, solve for the optimal localization gain, iteratively optimize the elastic gain, and finally obtain the pose state of the target robot.

[0043] Next, combined Figure 1 This embodiment provides a detailed description of a distributed elastic positioning method for underwater multi-robots.

[0044] In S1, linearization techniques such as Taylor expansion are used to process the nonlinear terms in the model, while retaining higher-order terms as nonlinear perturbations to establish a discretized kinematic model with perturbation compensation.

[0045] 1) Establish an AUV kinematic model

[0046] like Figure 2 As shown, the position information is in the global coordinate system. and posture (Roll angle, pitch angle, and yaw angle) serve as the state information of the target AUV. ,in:

[0047]

[0048] In the formula, These represent the positions of the three coordinate axes along the lower edge of the target AUV's fixed coordinate system. These are the Euler angles in the fixed coordinate system. The linear velocity in the fixed coordinate system and the linear velocity in the vehicle coordinate system satisfy the following relationship:

[0049]

[0050] in, Let be the linear velocity of the target AUV in the carrier coordinate system. Here is the transformation matrix used to convert the linear velocity in the carrier coordinate system to the fixed coordinate system:

[0051]

[0052] The angular velocity in the fixed coordinate system and the angular velocity in the vehicle coordinate system satisfy the following relationship:

[0053]

[0054] in, Let be the linear velocity of the target AUV in the carrier coordinate system. Here is the transformation matrix used to convert the angular velocity in the carrier coordinate system to the fixed coordinate system:

[0055]

[0056] In summary, the transformation relationship from the carrier coordinate system to the fixed coordinate system is as follows:

[0057]

[0058] in, The velocity vector in the carrier coordinate system is represented as:

[0059]

[0060] Represented as:

[0061]

[0062] 2) Establish an AUV dynamic model

[0063] According to the Lagrange mechanics method, the dynamic model of the target AUV can be established in the following form:

[0064]

[0065] in, M For the quality matrix, D It is a linear damping matrix. C For Coriolis matrix, To control the input quantity, a system model can be obtained based on the kinematic and dynamic models described above.

[0066] Furthermore, the Euler method is used to discretize the dynamic model, transforming the continuous-time model into a discrete-time kinematic model. Linearization techniques such as Taylor expansion are employed to handle nonlinear terms in the model, while higher-order terms are retained as nonlinear perturbations, thus establishing a discretized kinematic model with perturbation compensation.

[0067]

[0068] in, and Let be the state vectors of the target AUV at discrete times s and s+1, respectively. This is the discretized state transition matrix. The nonlinear disturbance term, which includes external disturbances and linearization errors, can be represented as:

[0069]

[0070] in, Sampling time, This represents the multiplicative nonlinear perturbation and linearization error. This represents the control input at discrete time s. Additive external disturbance. Assuming the noise is Gaussian white noise with zero mean and covariance matrix as follows: .

[0071] 3) Establish a measurement signal model for the target AUV.

[0072] Other underwater robots within the communication range of the target underwater robot are called monitoring nodes, or monitoring AUVs. The monitoring AUVs monitor the status information of the target AUV. Measurement information can be defined as:

[0073]

[0074] in, For measurement functions, It is zero-mean Gaussian white noise with variance of ; For distance measurement information, The target AUV broadcasts its IMU measurement information (its own attitude data) to the monitoring AUV, where T represents the transpose. This involves depth measurement information of the interaction between the target AUV and the monitoring AUV. Linearization techniques such as Taylor expansion are used to process nonlinear terms in the model, while retaining higher-order terms as nonlinear perturbations, thus establishing a discretized measurement model with perturbation compensation.

[0075]

[0076] in, To reduce the attenuation of interactive information, It is zero-mean Gaussian white noise with variance of ; To linearize the measurement matrix, This includes nonlinear disturbance terms, nonlinear errors, etc. It is zero-mean Gaussian white noise.

[0077] To address the limitation of miniaturized AUVs in directly acquiring velocity information, this embodiment proposes a discrete dynamics model that uses three-dimensional position and attitude angles as state vectors, combined with process noise interference, to fully describe its motion state. A discrete measurement model integrates distance, depth, and attitude information, taking into account underwater acoustic delay characteristics, to provide a basis for information reconstruction. Thus, by establishing the AUV discrete dynamics model and discrete measurement model, a basic framework is provided for underwater multi-robot cooperative localization.

[0078] In S2, an adaptive trigger is designed based on the event-triggered mechanism.

[0079] The monitoring AUV determines whether data interaction needs to be triggered by sensing and judging. It acquires information related to the target AUV (such as distance, relative position, etc.) through its own sensors, and then decides whether to send a data request to the target AUV or receive information sent by the target AUV according to the set triggering rules.

[0080] Order No. i The times when each monitored AUV triggers data interaction are arranged in chronological order as follows: ,Right now The following triggering conditions are designed to determine the next triggering moment: taking the previous triggering moment as the starting point, the difference between the current measurement value and the historical transmission value is monitored. Once the difference exceeds a threshold, the moment when the difference condition is first met is set as the next triggering moment. This controls when the AUV should transmit new measurement data, balancing data validity and transmission cost.

[0081]

[0082] in, It is a pre-assigned threshold. and These represent the current and most recently transmitted measurement values, respectively. Between two consecutive event triggers, the most recently transmitted signal... The sampling time is held in the estimator by a zero-order hold. For ease of description, this embodiment will use the sampling time... s The latest trigger signal at time is defined as Among them, those with superscript The signal indicates a trigger signal, marked with a superscript. The signal indicates the transmitted signal; This indicates that the measured signal has no delay, and the triggering condition is met immediately upon acquisition, so it is directly used as the latest signal; It reflects the delay relationship and identifies signals that were not transmitted in time due to delay but were retained by a zero-order hold; This indicates the maximum delay indicator, representing the maximum number of delay steps allowed by the system. Exceeding this limit... Delayed signals will be treated as invalid or discarded to ensure system stability.

[0083] By using reasonable triggering rules, unnecessary data transmission can be reduced and resources avoided while ensuring the accuracy of location estimation. When the triggering conditions are met, the two systems exchange the latest information. The monitoring AUV can then combine this information to calculate the target AUV's location more accurately, making positioning both efficient and precise.

[0084] In S3, random delay information is processed and the interaction information is reconstructed.

[0085] Measurement information It is time-related. Because underwater communication relies on underwater acoustic signal transmission, and this transmission can be affected by underwater environmental interference, a time delay between the monitoring AUV and the target AUV is unavoidable. Furthermore, the time delay is usually time-varying, and the time-varying observation delay takes on a finite set. The value, which means that in The delayed transmission of measurement information will be received within each time step. Then monitor the AUV in time s The possible observation values ​​received at this location are:

[0086]

[0087] in, For bivariate characteristic functions:

[0088]

[0089] This binary indicator function is used to identify measurement signals. At any moment s Reception status ( It is relative to the current moment. s (This refers to a historical moment), clearly defining the measurement reception status corresponding to different delay offsets in complex time-varying delay scenarios. Among these... Indicates in Receive measurement signals at all times .

[0090] Because each measurement can only be received once, The following relationship must be satisfied:

[0091]

[0092] Formula (17) represents at time t. s Corresponding different delay offsets and ( Under these circumstances, the reception of measurement signals is mutually exclusive. That is, for the same reference time... s It is impossible to be at the same time Receive corresponding delay at all times The measurement, and in Receive the corresponding delay at any time The measurement ensures the uniqueness of the measurement reception across different delay channels.

[0093] Formula (18) represents the expression for time. s In the delay offset from 0 to Of all possible scenarios, there must be one and only one binary indicator function corresponding to the delay channel that takes a value of 1. That is, the measurement signal... At any moment s It will definitely be received through a specific delay channel, covering all possible delay reception scenarios and ensuring the completeness of measurement reception.

[0094] Considering the random delays in underwater communication and the varying remaining time before the preset total duration at different times—this difference stems from the progress of the mission, with the remaining time naturally decreasing as it approaches the preset total duration from the initial moment. The preset total duration is the upper limit of the entire mission cycle pre-set for the underwater AUV collaborative positioning mission, used to define the complete time range from the start to the end of the mission. To ensure data timeliness, this embodiment transforms the random delays in actual communication into a multi-channel fixed delay mode: (a) in case (a), the remaining time covers the maximum delay; (b) in case (b), it only covers a portion of the delay; and (c) in case (c), there is no remaining time, thus achieving standardized processing of delay characteristics. Specifically:

[0095] (a) when hour,

[0096]

[0097] "Time" indicates the current moment. Total time remaining until mission Far enough that the remaining time is sufficient to cover the maximum latency. That is, from From the moment the measurement information experiences the maximum delay It can also be used in the total duration Data is fully received and processed, and delayed data is not discarded due to insufficient time.

[0098] At this point, equation (19) is expressed in vector form as follows: All delay channels that may be received at any given time (from 0 to ...) The measurement information is integrated. Each element corresponds to a "delay". "Whether the step measurement is received." The entire set of measurements received in parallel through multiple delay channels at that moment is constructed to provide an input format for subsequent unified processing of measurement data with different delays.

[0099] Due to the binary characteristic function Since each measurement can only be received by one delay channel, and the integration rules follow the linearized measurement model framework, there is an equivalent delay-free measurement sequence. It can be expressed as equation (20):

[0100]

[0101] in:

[0102]

[0103] Equation (21) represents the linearization of the measurement matrix by a binary indicator function. Perform multi-channel weighting; Equation (22) represents the measurement noise. Multi-channel reconstruction; Equation (23) represents the nonlinear perturbation term Multi-channel adaptation.

[0104] (b) When hour,

[0105]

[0106] "Time" indicates the current moment. Total time remaining until mission In the near term, the remaining time is insufficient to cover the maximum latency. At this point, the delay exceeds... Even if the measurement is sent, it cannot be completed within the total duration. The delay is processed internally, so only a delay of 0 to 1 needs to be considered. An effective channel to cut off the possibility of delays exceeding the time window.

[0107] At this point, equation (24) is integrated using vector form. The actual measurement information that may be received at any given moment. Compared to scenario (a), the channel limit is increased from... Compress to This is a delay channel pruning under time window constraints, ensuring that measurement processing matches the remaining time and avoiding redundant calculations of invalid delay channels.

[0108] Obviously, satisfy:

[0109]

[0110] in:

[0111]

[0112] Equation (26) represents the expression based on the remaining time. For linearized measurement matrices Channel clipping and weighting are performed; Equation (27) represents the measurement noise. The short-delay window reconstruction, Equation (28) represents the reconstruction of the nonlinear perturbation term. Short delay window adaptation.

[0113] (c) When hour,

[0114]

[0115] "Time" indicates the current moment. This marks the end of the total task duration, with 0 time remaining. At this point, only the latency-free (real-time) measurement channel needs to be considered. Any latency measurement not performed within this timeframe... If the data is received before the specified time, it will be unable to participate in the state calculation of this task. Therefore, the focus is on the reception and processing of real-time measurements. At this time, equation (29) only retains the measurement channel corresponding to delay 0 and directly extracts the data. Real-time measurement information at any moment This is a simplified process under extreme time constraints, compressing multi-channel latency into single-channel real-time measurement, adapting to measurement termination scenarios at the end of the task.

[0116] Obviously, satisfy:

[0117]

[0118] in:

[0119]

[0120] Equation (31) represents the linearized measurement matrix. Real-time channel adaptation; Equation (32) represents the measurement noise Real-time channel extraction; Equation (33) represents the extraction of nonlinear disturbance terms. Real-time channel adaptation.

[0121] In this embodiment, by dividing the delay channels and using binary indicator functions to mark the receiving state, complex random delays are transformed into a processable fixed pattern, ensuring the integrity of measurement information; and unifying the model form of measurement information. This ensures consistent data processing across different latency scenarios, enhancing algorithm applicability; it accurately incorporates disturbances and noise, increasing model realism and providing reliable data support for positioning, thereby reducing invalid data processing while maintaining accuracy and improving the efficiency and reliability of underwater AUV collaborative work.

[0122] In S4, a distributed cooperative localization algorithm is constructed to solve for the pose information of the target AUV.

[0123] The three scenarios (a), (b), and (c) in S4, which are divided based on the relationship between the current time and the total task duration, have a one-to-one correspondence with the scenarios (a), (b), and (c) defined in S3 based on the same classification criteria. Furthermore, the equivalent measurement sequences involved in this section... The delay-free equivalent sequence obtained by reconstructing with random delay in S3 They belong to the same sequence.

[0124] Based on the reconstructed equivalent information sequence, a partitioned distributed iterative localization algorithm is designed to achieve efficient collaborative pose estimation for multiple AUVs.

[0125] (a) When hour,

[0126]

[0127] in, Defined as an innovation sequence, it is the difference between actual and theoretical measurements. Initial value. , and These are the AUV state vectors. The first step is prediction and filtering. Indicates monitoring with his neighbors Weighting coefficients for information exchange between them.

[0128] There is ample time remaining in this phase to cover the maximum latency. During positioning, the motion model is used first. The filtered state from the previous time step Predict the current state in one step ; and then integrate the new information from the neighboring AUV By positioning gain and elastic gain The weighted correction of the prediction state yields the current filtering state. By making full use of the remaining time, incorporating measurements across the entire delay channel, and leveraging neighbor collaboration and gain adaptation, the state can be accurately corrected in the early stages of the task, laying a solid foundation for subsequent positioning and improving overall estimation accuracy.

[0129] (b) when hour,

[0130]

[0131] in, This is a new information sequence. Initial value. , and These are the AUV state vectors. The first step is prediction and filtering.

[0132] At this point, the remaining time is shortened, and it can only cover part of the delay. The positioning logic continues the "predict first, correct later" approach, but adapts to the remaining time, focusing on effective delay channels. It first uses a motion model... predict Then use the new information of the neighbor's corresponding delayed channel. The predicted state is obtained after gain adjustment and correction. By dynamically trimming delay channels based on the remaining time, invalid calculations are avoided, maintaining the continuity of cooperative positioning in the middle of the mission, balancing computational efficiency and state estimation accuracy, and ensuring that the state remains accurate near the end of the mission.

[0133] (c) when hour,

[0134]

[0135] in, The new sequence is initialized to a value. .

[0136] This stage is the final phase of the task, with zero remaining time, and only handles real-time measurements without delay. First, a motion model is used... predict Then use the neighbors' real-time updates. Corrected At the mission endpoint, final state calibration is completed based on real-time measurements. Utilizing information accumulated through prior collaboration and combined with a gain mechanism, the positioning results are ensured to converge to high accuracy, providing accurate pose for mission completion and guaranteeing a complete closed loop for multi-AUV collaborative missions.

[0137] In the above-mentioned partitioning iterative positioning algorithm, To determine the positioning gain, For elastic gain, satisfying ,in This is the default value.

[0138] The distributed cooperative localization algorithm in this embodiment, based on the reconstructed equivalent information sequence, achieves efficient cooperative pose estimation for multiple AUVs through partitioned distributed iteration. At different stages, the delay channels are dynamically adjusted according to the remaining time. Combined with the innovation sequence, localization gain, and elastic gain correction state, this ensures that the full-delay channel measurement is utilized in the early stages to improve accuracy, balances efficiency and accuracy through mid-stage channel pruning, and completes final calibration at the end of the task. S3 transforms random delays into a fixed mode, ensuring measurement integrity and processing consistency. S4 builds upon S3 to design an adaptation algorithm; the combination of these two approaches seamlessly integrates delay processing and cooperative estimation, improving cooperative efficiency while ensuring data reliability, and enhancing the stability and accuracy of underwater multi-robot localization.

[0139] In S5, elastic optimization and error control are performed. The positioning gain is optimized and fed back to S4 to obtain the final pose information of the target AUV.

[0140] Due to gain The existence of these factors makes it difficult to recursively solve for the prediction error covariance and the estimation error covariance, and even more difficult to design the optimal positioning gain parameters. Therefore, this embodiment introduces a minimum upper bound for the positioning error covariance:

[0141]

[0142] in, As a preset factor,

[0143]

[0144] The optimal gain can be obtained using the matrix maxima principle:

[0145]

[0146] because , Therefore from It can obtain the optimal positioning gain.

[0147] in, This represents the minimum upper bound of the one-step prediction covariance matrix representing the positioning error. This represents the minimum upper bound of the positioning error covariance; Represents the Hadamard product; Represents an n-dimensional column vector whose elements are all 1s; It is a positive scalar; , It represents the Kronecker product.

[0148] make Recalculate S1-S5 until the location task is completed.

[0149] The specific implementation process is achieved using the simulation tool Matlab. The effectiveness of this embodiment can be further illustrated by the following experimental simulation. In this embodiment, the target AUV is a moving target in three-dimensional space, and its pose information is acquired using a multi-source information fusion strategy. High-precision real-time pose calculation is achieved through distributed elastic state estimation and adaptive weighted fusion algorithm.

[0150] In this embodiment, a ring topology communication network consisting of four isomorphic AUVs is constructed. This topology has the following characteristics: each AUV adopts the same dynamic structure and sensor configuration; and ring information exchange is achieved through bidirectional communication links.

[0151] In this embodiment, a ring topology of four AUVs is considered. It is assumed that the four underwater robots have the same structure, and their parameters are set as follows: , This embodiment only considers the planar motion of the target AUV, so heave motion is ignored. Considering the good static stability of the AUV, it will only generate very small pitch and roll angles during motion, therefore roll and pitch angles are ignored and set to zero. The nonlinear disturbance term satisfies:

[0152]

[0153] Furthermore, the second moments of the additive external disturbance are set to have covariances of... and The initial point on the plane where the target AUV is projected is set to (3). m ,3 m ).

[0154] Based on the calculations performed using the distributed elastic positioning method proposed in this embodiment, the multi-AUV system, utilizing its own measurements of the target, in Figure 3 The image clearly shows the real-time positioning effect of the AUV in the x-axis direction. Figure 4 The real-time positioning effect of the AUV in the y-axis direction is shown. The estimated position curve and the actual position curve almost coincide in the two figures, proving that the algorithm can accurately track the real-time pose of the target AUV with small positioning error.

[0155] Figure 5 and Figure 6 The mean squared error of distributed resilient positioning is shown to change over time. The mean squared error curves in both figures decrease rapidly from the initial moment and stabilize below 0.2 within a short period of time (about 20 seconds later), without significant fluctuations throughout the process. This indicates that the algorithm can quickly converge to a low-error state and is not significantly affected by underwater communication delays or noise interference.

[0156] Simulation results show that the distributed elastic positioning algorithm proposed in this invention has high positioning accuracy and robustness.

[0157] This embodiment establishes a kinematic model and pose measurement model of the MAUV system in a global coordinate system; pre-assigns dynamic thresholds to each AUV and constructs an event trigger generator to trigger communication only when the state change exceeds the threshold; uses a binary indicator function to characterize the random delay characteristics of the interactive measurement information between the monitoring node and the target node, and transforms the delayed information into a delay-free equivalent information sequence based on an information reconstruction method; based on the reconstructed equivalent information sequence, designs a partitioned distributed iterative localization algorithm to achieve efficient collaborative pose estimation of multiple AUVs; constructs a tight upper bound for the localization error covariance matrix, and uses an optimization method to solve for the optimal localization gain, effectively overcoming the non-convex optimization problem caused by factors such as linearization error, pose perturbation, and elastic gain.

[0158] Existing technologies for underwater multi-robot localization suffer from discontinuous measurement information, time delays, and uncertainties, which traditional Kalman filters struggle to address, resulting in insufficient positioning accuracy and real-time performance. This embodiment reduces invalid transmissions through an event-triggered mechanism, handles random delays using a binary indicator function and scene segmentation, and transforms delay-free sequences to meet filtering requirements. It constructs a tight upper bound for error covariance to optimize gain, solving the error modeling challenges of traditional methods, improving positioning accuracy and robustness, enhancing multi-robot collaborative efficiency, effectively overcoming the shortcomings of existing technologies, and promoting the development of underwater positioning technology.

[0159] Example 2

[0160] This embodiment provides an underwater multi-robot distributed elastic positioning system, including:

[0161] The system modeling module is configured to establish a kinematic model of the target robot and a measurement model that fuses distance, depth and attitude information of the monitoring nodes.

[0162] The event triggering module is configured to trigger communication when the monitoring node detects that the state change of the target robot exceeds a preset threshold.

[0163] The random delay reconstruction module is configured to use a binary indicator function to identify the random delay state of the measurement signal, divide the scenario according to the relationship between the current time and the total task duration, and convert the random delay information into a delay-free equivalent sequence based on different scenarios.

[0164] The partitioned collaborative localization module is configured to select a delay channel to perform state prediction and elastic gain correction in different scenarios based on the kinematic model, measurement model and delay-free equivalent sequence, so as to obtain the state estimate of the target robot.

[0165] The elastic optimization module is configured to construct a tight upper bound of the positioning error covariance matrix, solve for the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the pose state of the target robot.

[0166] Example 3

[0167] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the underwater multi-robot distributed elastic positioning method as described in Embodiment 1 above.

[0168] Example 4

[0169] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the underwater multi-robot distributed elastic positioning method described in Embodiment 1 above.

[0170] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0171] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A distributed elastic positioning method for underwater multi-robot systems, characterized in that, include: Establish a kinematic model of the target robot and a measurement model that integrates distance, depth and attitude information of monitoring nodes; Communication is triggered when the monitoring node detects that the state change of the target robot exceeds a preset threshold. A binary indicator function is used to identify the random delay state of the measurement signal. Scenarios are divided according to the relationship between the current time and the total duration of the task. Based on different scenarios, the random delay information is transformed into a delay-free equivalent sequence. Based on the kinematic model, measurement model and delay-free equivalent sequence, the delay channel is selected to perform state prediction and elastic gain correction in different scenarios to obtain the state estimate of the target robot. Construct a tight upper bound for the localization error covariance matrix, solve for the optimal localization gain, iteratively optimize the elastic gain, and finally obtain the pose state of the target robot.

2. The underwater multi-robot distributed elastic positioning method as described in claim 1, characterized in that, The construction of the kinematic model includes: Establish the target robot's position coordinates and attitude angles as a state vector in the global coordinate system; By transforming the matrix, the linear velocity and angular velocity in the carrier coordinate system are converted to the fixed coordinate system, and the kinematic relationship is established. The dynamic equations are derived using Lagrange mechanics based on kinematic relationships; The continuous dynamic equations are discretized, and nonlinear perturbation terms are introduced to characterize linearization errors and external disturbances, resulting in a kinematic model. The construction of the measurement model includes: fusing distance, depth and attitude information collected by monitoring nodes, and establishing a discrete measurement model containing noise and nonlinear disturbances through linearization processing.

3. The underwater multi-robot distributed elastic positioning method as described in claim 1, characterized in that, The triggering conditions for the communication include: based on the previous triggering time, when the difference between the current measurement value and the historical transmission value of the monitoring node exceeds a preset threshold for the first time, the next communication is triggered; It also includes maintaining the historical signal output through a zero-order hold during non-trigger periods.

4. The underwater multi-robot distributed elastic positioning method as described in claim 1, characterized in that, The method of using a binary indicator function to identify the random delay state of the measurement signal specifically includes: using a binary indicator function to mark the reception state of the measurement signal at a specific time, and taking the constraint that the same measurement signal can only be received through one delay channel.

5. The underwater multi-robot distributed elastic positioning method as described in claim 1, characterized in that, The scenarios are divided according to the relationship between the current time and the total task duration, and the scenarios include: In the first scenario, if there is sufficient remaining time before the task ends, and this remaining time is enough to cover the maximum latency, then the full latency channel measurement is integrated. In the second scenario, if the current time is insufficient to cover the maximum delay, then the effective delay channel corresponding to the remaining time is selected. The third scenario, at the end of the task, only handles real-time measurements with no delay.

6. The underwater multi-robot distributed elastic positioning method as described in claim 5, characterized in that, The process of selecting a delay channel to perform state prediction and elastic gain correction under different scenarios based on the kinematic model, measurement model, and delay-free equivalent sequence to obtain the state estimate of the target robot specifically includes: selecting the corresponding delay channel according to different scenarios, predicting the current state through the kinematic model, then fusing the delay-free equivalent sequence and neighbor node information, and correcting the predicted value through weighted adjustment of positioning gain and elastic gain to obtain the state estimate.

7. The underwater multi-robot distributed elastic positioning method as described in claim 1, characterized in that, The process of constructing a tight upper bound for the localization error covariance matrix and solving for the optimal localization gain specifically includes: constructing a minimum upper bound for the localization error covariance matrix, solving for the optimal localization gain based on the principle of matrix maxima, iteratively optimizing the elastic gain to reduce the error, and finally obtaining the pose state of the target robot.

8. An underwater multi-robot distributed elastic positioning system, characterized in that, include: The system modeling module is configured to establish a kinematic model of the target robot and a measurement model that fuses distance, depth and attitude information of the monitoring nodes. The event triggering module is configured to trigger communication when the monitoring node detects that the state change of the target robot exceeds a preset threshold. The random delay reconstruction module is configured to use a binary indicator function to identify the random delay state of the measurement signal, divide the scenario according to the relationship between the current time and the total task duration, and convert the random delay information into a delay-free equivalent sequence based on different scenarios. The partitioned collaborative localization module is configured to select a delay channel to perform state prediction and elastic gain correction in different scenarios based on the kinematic model, measurement model and delay-free equivalent sequence, so as to obtain the state estimate of the target robot. The elastic optimization module is configured to construct a tight upper bound of the positioning error covariance matrix, solve for the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the pose state of the target robot.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the underwater multi-robot distributed elastic positioning method as described in any one of claims 1-7.

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 program, it implements the steps of the underwater multi-robot distributed elastic positioning method as described in any one of claims 1-7.

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