Underwater multi-robot distributed elastic positioning method and system

Abstract

The invention provides an underwater multi-robot distributed elastic positioning method and system, and relates to the field of underwater robots. Establishing a kinematic model of the target robot and a measurement model of monitoring node fusion distance, depth and attitude information; when the state variation of the target robot exceeds a preset threshold value, communication is triggered; identifying a random delay state of a measurement signal by adopting a binary indicative function, dividing a scene according to a relationship between the current moment and the total time length of a task, and converting random delay information into a non-delay equivalent sequence; on the basis of the kinematic model, the measurement model and the non-delay equivalent sequence, delay channels are selected in different scenes to execute state prediction and elastic gain correction, and a state estimation value of the target robot is obtained; wherein the tight upper bound of the positioning error covariance matrix is constructed, and the optimal positioning gain is solved to iteratively optimize the elastic gain. By adapting time-varying delay and optimizing gain control errors, efficient cooperative positioning in a complex environment is ensured, and reliable pose information is provided for underwater tasks.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater robots, and in particular to a distributed elastic positioning method and system for multiple underwater robots. Background Art

[0002] Underwater multi-robot collaborative localization utilizes the interactive information of multiple autonomous underwater vehicles (AUVs) to estimate target pose. Its core goal is to improve positioning accuracy and reliability in complex underwater environments through information fusion. Kalman filtering and its derivatives are commonly used state estimation tools. They recursively update state estimates and error covariances to handle measurement information affected by noise.

[0003] As underwater missions become more complex, traditional periodic communication models waste resources due to data redundancy. Event-triggered mechanisms have emerged to reduce transmission costs by triggering communication only when a state change exceeds a threshold. However, this mechanism breaks the traditional Kalman filter's assumption of continuous and lag-free measurement information. The triggering errors caused by the receiver using historical signals during non-trigger periods, combined with the inherent random delays of underwater communications, make it difficult to model the source of these errors, impacting filter stability and positioning accuracy.

[0004] Although existing technologies simplify operations by approximating the covariance matrix, they do not fully consider the random errors caused by event triggering, and lack the ability to dynamically adapt to time-varying delays. In multi-robot collaborative scenarios, there are still problems with accuracy fluctuations and insufficient real-time performance. Summary of the Invention

[0005] In order to solve the above problems, the present invention proposes a distributed elastic positioning method and system for underwater multi-robots. First, the kinematic and measurement models of the target robot are established. Communication is triggered when the state change measured by the monitoring node exceeds the 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 the information reconstruction method, the delayed information is converted into an equivalent information sequence without delay. Based on the reconstructed equivalent information sequence, a partitioned distributed iterative positioning algorithm is designed to achieve efficient collaborative pose estimation of multiple AUVs.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a distributed elastic positioning method for underwater multi-robots, comprising: Establish the kinematic model of the target robot and the measurement model of the monitoring node integrating distance, depth and posture information; When the monitoring node detects that the state change of the target robot exceeds the preset threshold, communication is triggered; A binary characteristic function is used to identify the random delay state of the measurement signal. The scenarios are divided according to the relationship between the current moment and the total duration of the task. Based on different scenarios, the random delay information is converted into a delay-free equivalent sequence. Based on the kinematic model, measurement model and delay-free equivalent sequence, a delay channel is selected in different scenarios to perform state prediction and elastic gain correction to obtain the state estimation value of the target robot; A tight upper bound of the positioning error covariance matrix is ​​constructed, the optimal positioning gain is solved, the elastic gain is iteratively optimized, and finally the position and posture state of the target robot is obtained.

[0007] In a second aspect, the present invention provides an underwater multi-robot distributed elastic positioning system, comprising: The system modeling module is configured to establish a kinematic model of the target robot and a measurement model for monitoring nodes that integrates distance, depth, and posture information; An event triggering module is configured to trigger communication when the monitoring node measures that the state change of the target robot exceeds a preset threshold; The random delay reconstruction module is configured to use a binary characteristic function to identify the random delay state of the measurement signal, divide the scenarios 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; A partitioned collaborative localization module is configured to select a delayed channel to perform state prediction and elastic gain correction in different scenarios based on the kinematic model, the measurement model, and the delay-free equivalent sequence to obtain a 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 the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the posture state of the target robot.

[0008] In a third aspect, 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.

[0009] In a fourth aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the underwater multi-robot distributed elastic positioning method described in the first aspect are implemented.

[0010] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention accurately describes the robot's motion and measurement characteristics by establishing a model that integrates multiple information; reduces redundant transmission through an event trigger mechanism, introduces binary characteristic functions and scene division to effectively handle random delays, and converts the delay-free sequence to ensure data validity. State prediction and elastic gain correction are then performed based on the delay-free sequence. Combined with the optimization of the tight upper bound of the error covariance, the positioning accuracy and stability are improved, and efficient multi-robot collaboration is achieved. It adapts to complex underwater environments and provides reliable solutions for positioning tasks.

[0011] (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 exceed a preset threshold, thereby adaptively adjusting the frequency of information interaction between multiple robots, effectively reducing the load and congestion of the underwater acoustic communication network, and improving communication efficiency and system reliability.

[0012] (3) This method rigorously derives a tight upper bound on the positioning error covariance under the error conditions introduced by the event triggering mechanism and optimizes the distributed positioning gain of each robot to ensure high-precision positioning and robustness under limited communication 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 collaborative positioning, making it suitable for long-term operations in complex underwater environments.

[0013] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their description are used to explain the present invention but do not constitute a limitation of the present invention.

[0015] Figure 1 A main flow chart of a distributed elastic positioning method for multiple underwater robots provided by an embodiment of the present invention; Figure 2 A schematic diagram of the MAUV system and information interaction provided by an embodiment of the present invention; Figure 3 This is a positioning effect diagram of the target AUV in the x-axis direction provided by an embodiment of the present invention; Figure 4 This is a positioning effect diagram of the target AUV in the y-axis direction provided by an embodiment of the present invention; Figure 5 A graph showing the mean square error of the positioning of the target AUV in the x-axis direction provided by an embodiment of the present invention; Figure 6 This is a graph showing the mean square error of the positioning of the target AUV in the y-axis direction provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0017] Underwater acoustic communications have limited bandwidth, high latency, and high energy consumption. Frequent information exchange increases communication load and energy consumption, restricting the system's long-term operational capability. While event-triggered mechanisms can mitigate this problem by adjusting the communication frequency through state change thresholds, they break the traditional Kalman filter's assumptions about measurement information. Specifically, traditional Kalman filters rely on measurement information being synchronously updated at a fixed period with known error characteristics. However, under event triggering, the receiver continues to use historical signals during non-trigger periods. The deviation between the actual state and the used signal creates trigger error, a random error that is difficult to accurately model using traditional formulas, thus affecting error covariance calculation and positioning stability.

[0018] To this end, the present invention proposes a distributed elastic collaborative positioning method, system, medium and equipment for underwater multi-robots based on an event-triggered mechanism, reduces the communication load through dynamic trigger conditions, combines random analysis and matrix theory to process errors and delays, and ensures positioning accuracy and stability, which is described in detail below.

[0019] Example 1 like Figure 1 As shown, this embodiment discloses a distributed elastic positioning method for underwater multi-robots, which estimates the pose state of the target AUV, including the following steps: S1: Establish the kinematic model of the target robot and the measurement model of the monitoring node integrating distance, depth and posture information; S2: When the monitoring node detects that the state change of the target robot exceeds the preset threshold, communication is triggered; S3: Use a binary characteristic function to identify the random delay state of the measurement signal, divide the scenarios 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; 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 estimation value of the target robot; S5: Construct a tight upper bound of the positioning error covariance matrix, solve the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the position and posture state of the target robot.

[0020] Next, combine Figure 1 , a distributed elastic positioning method for underwater multi-robots disclosed in this embodiment is described in detail.

[0021] In S1, linearization techniques such as Taylor expansion are used to process the nonlinear terms in the model, while retaining high-order terms as nonlinear disturbances to establish a discretized kinematic model with disturbance compensation.

[0022] 1) Establishing AUV kinematic model like Figure 2 As shown, the position information in the global coordinate system and posture (roll angle, pitch angle and yaw angle) as the status information of the target AUV ,in:

[0023] Where, are the positions of the target AUV along the three coordinate axes in the fixed coordinate system, are the Euler angles in the fixed coordinate system. The linear velocity in the fixed coordinate system and the linear velocity in the carrier coordinate system satisfy the following relationship:

[0024] in, is the linear velocity of the target AUV in the carrier coordinate system, is the transformation matrix used to convert the linear velocity in the carrier coordinate system to the fixed coordinate system:

[0025] The angular velocity in the fixed coordinate system and the angular velocity in the carrier coordinate system satisfy the following relationship:

[0026] in, is the linear velocity of the target AUV in the carrier coordinate system, is the transformation matrix used to convert the angular velocity in the carrier coordinate system to the fixed coordinate system:

[0027] In summary, the conversion relationship from the carrier coordinate to the fixed coordinate system is:

[0028] in, The velocity vector in the carrier coordinate system is expressed as:

[0029] Expressed as:

[0030] 2) Establishing AUV dynamics model According to the Lagrangian mechanics method, the dynamic model of the target AUV can be established as follows:

[0031] in, M is the mass matrix, D is the linear damping matrix, C is the Coriolis matrix, is the control input. According to the above kinematic model and dynamic model, the system model can be obtained.

[0032] The Euler method is further used to discretize the dynamic model, converting the continuous-time model into a discrete-time kinematic model. The nonlinear terms in the model are processed through linearization techniques such as Taylor expansion, while retaining high-order terms as nonlinear disturbances to establish a discretized kinematic model with disturbance compensation:

[0033] in, and are the state vectors of the target AUV at discrete time s and s+1 respectively, is the discretized state transfer matrix, Represents the nonlinear disturbance term, including external disturbance, linearization error, etc., which can be expressed as:

[0034] in, is the sampling time, represents the multiplicative nonlinear perturbation and linearization error, Represents the control input at discrete time s. Additive external disturbance Assume Gaussian white noise with zero mean and covariance matrix is .

[0035] 3) Establish a measurement signal model for the target AUV Other underwater robots within the communication range of the target underwater robot are called monitoring nodes, that is, monitoring AUVs. Monitoring AUVs have status information about the target AUV. The measurement information can be defined as:

[0036] in, is the measurement function, is zero-mean Gaussian white noise with variance ; is the distance measurement information, The target AUV broadcasts the IMU measurement information (its own attitude data) to the monitoring AUV through the attitude information exchanged. T represents transposition. The depth measurement information of the interaction between the target AUV and the monitoring AUV is obtained by processing the nonlinear terms in the model through linearization techniques such as Taylor expansion, while retaining the high-order terms as nonlinear perturbations, and establishing a discrete measurement model with disturbance compensation:

[0037] in, is the attenuation of the mutual information, is zero-mean Gaussian white noise with variance ; is the linearized measurement matrix, is the nonlinear disturbance term, nonlinear error, etc. is zero-mean Gaussian white noise.

[0038] In view of the fact that miniaturized AUVs cannot directly obtain velocity information, this embodiment proposes a discrete dynamic model that uses three-dimensional position and attitude angle as state vectors, combined with process noise interference to fully describe its motion state; a discrete measurement model integrates distance, depth and attitude information, and considers the underwater acoustic delay characteristics to provide a basis for information reconstruction; thus, by establishing the AUV discrete dynamic model and discrete measurement model, a basic framework is provided for the collaborative positioning of underwater multi-robots.

[0039] In S2, an adaptive trigger is designed based on the event trigger mechanism.

[0040] The monitoring AUV determines whether data interaction needs to be triggered through perception and judgment. It obtains 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 whether to receive information sent by the target AUV based on the set trigger rules.

[0041] Order i The time sequence of each monitoring AUV triggering data interaction is as follows: ,Right now The next trigger moment is determined by designing the following trigger conditions. That is, the difference between the current measurement value and the historical transmission value is monitored. Once the difference exceeds the threshold, the moment when the difference condition is first met is set as the next trigger moment. This controls when the AUV transmits new measurement data and balances data validity and transmission cost:

[0042] in, is a pre-allocation threshold, and Represents the current and most recently transmitted measurement values. Between two consecutive event triggers, the most recently transmitted signal is retained by a zero-order holder on the estimator. For the convenience of expression, this embodiment will be the sampling time s The latest trigger signal at a certain moment is defined as ; Among them, with superscript The signal with a superscript indicates a trigger signal. The signal represents the transmission signal; Indicates that the measured signal has no delay and meets the trigger condition as soon as it is acquired, and is directly used as the latest signal; Reflects the delay relationship and identifies the signal that is not transmitted in time due to delay but is retained by the zero-order holder; Indicates the maximum delay mark, which represents the maximum delay steps allowed by the system. Delayed signals will be considered invalid or discarded to ensure system stability.

[0043] By implementing appropriate triggering rules, unnecessary data transmission can be reduced, thus avoiding wasted resources while ensuring accurate position estimation. When the trigger conditions are met, the two systems exchange the latest information, which the monitoring AUV can then use to more accurately calculate the target AUV's position, ensuring both efficient and precise positioning.

[0044] In S3, the random delay information is processed and the interaction information is reconstructed.

[0045] Measurement information It is time-related. Since underwater communication relies on underwater acoustic signal transmission and the signal transmission process may be interfered by the underwater environment, the time delay between the monitoring AUV and the target AUV is inevitable. In addition, the time delay is usually time-varying, and the time-varying observation delay takes a finite set This means that in The delayed measurement information will be received within the time step , then the monitoring AUV is at time s The possible observations received at are:

[0046] in, is a binary characteristic function:

[0047] The binary characteristic function is used to identify the measurement signal At the moment s The receiving status ( Is relative to the current moment s The historical moment of the time), clearly defines the measurement reception situation corresponding to different delay offsets in complex time-varying delay scenarios. Among them, Indicates Receive measurement signals at all times .

[0048] Because each measurement can only be received once, The following relationships must be met:

[0049] Formula (17) means that at time s Corresponding different delay offsets and ( ) In this case, 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 The corresponding delay is received at the moment The measurement, and The corresponding delay is received at the moment The measurement ensures the uniqueness of the measurement received on different delay channels.

[0050] Formula (18) represents the time s , the delay offset is from 0 to In all possible cases, there must be only one delay channel corresponding to the binary characteristic function with the value of 1. That is, the measurement signal At the moment s , it will definitely be received through a specific delay channel, covering all possible delayed reception situations and ensuring the completeness of measurement reception.

[0051] Taking into account the random delays in underwater communications and the differences in the remaining time from the preset total time at different times - this difference is due to the advancement of the task process. As time approaches the preset total time from the initial moment, the remaining time will naturally decrease. The preset total time is the upper limit of the entire task cycle preset for the underwater AUV collaborative positioning task, which is used to define the complete time range from the start to the end of the task. To ensure the timeliness of the data, this embodiment converts the random delays in actual communications into a multi-channel fixed delay mode. In case (a), the remaining time can cover the maximum delay, in case (b), only part of the delay can be covered, and in case (c), there is no remaining time, thereby realizing the normalization of the delay characteristics. Specifically: (a) when hour,

[0052] Time, indicating the current time Total time to complete the task Far enough that the remaining time is enough to cover the maximum delay . That is, from Starting from the moment, even if the measurement information experiences the maximum delay , and also in the total time The data is completely received and processed within 1 second, and delayed data will not be discarded due to insufficient time.

[0053] At this time, Equation (19) is transformed into vector form. All delay channels that may be received at the moment (from 0 to ) measurement information. Each element corresponds to the “delay The whole process constructs the measurement set received in parallel by multiple delay channels at that moment, providing input for the subsequent unified processing of measurement data with different delays.

[0054] Since the binary characteristic function It is defined that each measurement can only be received by one delay channel, and the integration rule follows the linearized measurement model framework, so the equivalent delay-free measurement sequence It can be expressed as formula (20):

[0055] in:

[0056] Wherein, Equation (21) represents the linearized measurement matrix through the binary characteristic function Multi-channel weighting is performed; Equation (22) represents the measurement noise Multi-channel reconstruction; Equation (23) represents the nonlinear perturbation term Multi-channel adaptation.

[0057] (b) When hour,

[0058] Time, indicating the current time Total time to complete the task Close, the remaining time is not enough to cover the maximum delay At this point, the delay exceeds Even if the measurement is issued, it cannot be is processed, so only delays from 0 to The effective channel cuts off the possibility of delay exceeding the time window. At this time, Equation (24) is integrated in the form of vector The actual measurement information that can be received at any moment. Compared with scenario (a), the channel upper limit is Compress to ,For delay channel pruning under the time window constraint, it ensures that the measurement processing matches the remaining time and avoids the redundant computation of invalid delay channels.

[0059] Obviously, satisfy:

[0060] in:

[0061] Among them, formula (26) represents the remaining time , for the linearized measurement matrix Channel pruning and weighting are performed; Equation (27) represents the measurement noise The short delay window reconstruction of , Equation (28) represents the nonlinear disturbance term Short delay window adaptation.

[0062] (c) When hour,

[0063] Time, indicating the current time The total duration of the task ends at 0, and the remaining time is 0. At this time, only the measurement channel without delay (real-time) needs to be considered. If it is received before the time, it will not be able to participate in the state solution of this task, so we focus 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 Real-time measurement information at all times This is a simplified process under extreme time constraints, compressing multi-channel delays into single-channel real-time measurement, adapting to the measurement closure scenario at the end of the task.

[0064] Obviously, satisfy:

[0065] in:

[0066] Wherein, 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 nonlinear perturbation term Real-time channel adaptation.

[0067] In this embodiment, by dividing the delay channel and using the binary characteristic function to mark the receiving state, the complex random delay is converted into a processable fixed pattern to ensure the integrity of the measurement information; the unified model form measurement information Make data processing consistent under different delay scenarios to improve algorithm applicability; accurately incorporate disturbances and noise to enhance model authenticity, provide reliable data support for positioning, etc., while ensuring accuracy, reduce invalid data processing, and improve the efficiency and reliability of underwater AUV collaborative work.

[0068] In S4, a distributed collaborative localization algorithm is constructed to solve the pose information of the target AUV.

[0069] The three scenarios (a), (b), and (c) in S4, which are divided based on the relationship between the current moment and the total duration of the task, have a one-to-one correspondence with the scenarios (a), (b), and (c) defined based on the same division criteria in S3, and the equivalent measurement sequences involved in this section are , and the delay-free equivalent sequence obtained by random delay reconstruction in S3 The same sequence.

[0070] Based on the reconstructed equivalent information sequence, a partitioned distributed iterative localization algorithm is designed to achieve efficient collaborative pose estimation of multiple AUVs.

[0071] (a) When hour,

[0072] in, Defined as an innovation sequence, it is the difference between the actual measurement and the theoretical measurement. , and They are the AUV state vectors One-step prediction and filtering. Indicates monitoring With its neighbors The weight coefficient of information interaction between them.

[0073] There is enough time left in this stage to cover the maximum delay When positioning, first use the motion model , the state after filtering at the previous moment , one-step prediction of the current state ; Then integrate the new information of neighboring AUV , by positioning gain and elasticity gain Weighted correction prediction state to obtain the current filtering state By making full use of the remaining time, incorporating full-delay channel measurements, and leveraging neighbor collaboration and gain adaptation, the state can be accurately corrected in the early stages of the mission, laying a solid foundation for subsequent positioning and improving overall estimation accuracy.

[0074] (b) When hour,

[0075] in, is the new information sequence. Initial value , and They are the AUV state vectors One-step prediction and filtering.

[0076] At this point the remaining time is shortened and only part of the delay can be covered The positioning logic continues to predict first and then correct, but adapts to the remaining time and focuses on the effective delay channel. predict ; Then use the new information of the neighbor corresponding to the delayed channel , the predicted state is corrected by gain adjustment to obtain By dynamically trimming the delay channel according to the remaining time, invalid calculations are avoided, the continuity of collaborative positioning is maintained in the middle of the mission, and the computational efficiency and state estimation accuracy are balanced to ensure that the state remains accurate near the end of the mission.

[0077] (c) When hour,

[0078] in, is the new information sequence, the initial value is .

[0079] This stage is the end of the task, the remaining time is 0, and only real-time measurement without delay is processed. predict ; Then use the neighbors' real-time updates Corrected At the mission endpoint, final state calibration is completed based on real-time measurements. The information accumulated during the previous collaboration is utilized, combined with a gain mechanism, to ensure that the positioning results converge to high precision, providing accurate poses for mission completion and ensuring a complete closed-loop multi-AUV collaborative mission.

[0080] In the above partition iterative positioning algorithm, is the positioning gain to be designed, is elastic gain, satisfying ,in is the default value.

[0081] The distributed collaborative positioning algorithm in this embodiment is based on the reconstructed equivalent information sequence and realizes efficient collaborative pose estimation of multiple AUVs through partitioned distributed iteration. The delay channel is dynamically adjusted according to the remaining time at different stages, and the state of the new information sequence, positioning gain and elastic gain correction is combined to ensure the utilization of the full delay channel measurement in the early stage to improve accuracy, balance efficiency and accuracy through mid-term channel clipping, and complete the final calibration at the end of the mission. S3 converts random delays into fixed patterns to ensure measurement integrity and processing consistency; S4 inherits the design of the adaptation algorithm of S3. The combination of the two enables seamless connection between delay processing and collaborative estimation, improves collaborative efficiency while ensuring data reliability, and enhances the stability and accuracy of underwater multi-robot positioning.

[0082] In S5, elastic optimization and error control are performed to optimize the positioning gain and feed it back to S4 to obtain the final target AUV pose information.

[0083] Due to the gain The existence of makes it difficult to recursively solve the prediction error covariance and the estimation error covariance, and even more difficult to design the optimal positioning gain parameters. To this end, this embodiment introduces the minimum upper bound of the positioning error covariance:

[0084] in, is the preset factor,

[0085] Through the matrix maximum principle, the optimal gain can be obtained:

[0086] because , , so from The optimal positioning gain can be obtained.

[0087] in, represents the minimum upper bound of the one-step prediction covariance matrix of the positioning error, represents the minimum upper bound of the positioning error covariance; represents the Hadamard product; represents an n-dimensional column vector whose elements are all 1; is a positive scalar; , represents the Kronecker product.

[0088] make , recalculate S1-S5 until the positioning task is completed.

[0089] The specific implementation process was achieved using the simulation tool Matlab. The effectiveness of this embodiment can be further illustrated through the following experimental simulation. In this embodiment, the target AUV, acting as a mobile target in three-dimensional space, acquires its pose information using a multi-source information fusion strategy. Through distributed elastic state estimation and an adaptive weighted fusion algorithm, high-precision real-time pose calculation is achieved.

[0090] In this example, a ring-topology communication network consisting of four homogeneous AUVs was constructed. This topology has the following characteristics: each AUV uses the same dynamic structure and sensor configuration; and ring-shaped information exchange is achieved through a bidirectional communication link.

[0091] 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: , In this embodiment, only the planar motion of the target AUV is considered, so the heave motion is ignored. Considering that the AUV has good static stability, it will only produce very small pitch and roll angles during the motion, so the roll and pitch angles are ignored and set to zero. The nonlinear perturbation term satisfies:

[0092] And the second-order moments of the additive external disturbances are set as covariances and are and The initial point position of the target AUV projected onto the plane is set to (3 m ,3 m ).

[0093] After the calculation of the distributed elastic positioning method proposed in this embodiment, the multi-AUV system uses its own measurement of the target to Figure 3 The figure clearly shows the real-time positioning effect of the AUV in the x-axis direction. Figure 4 The figure shows the real-time positioning of the AUV in the y-axis direction. The estimated position curves in both figures almost coincide with the actual position curves, proving that the algorithm can accurately track the real-time position of the target AUV with a small positioning error.

[0094] Figure 5 and Figure 6 The time-varying mean squared error of distributed elastic positioning is shown. The mean squared error curves in both figures decrease rapidly from the initial moment and stabilize within 0.2 within a short period of time (about 20 seconds), without significant fluctuations throughout the entire process. This demonstrates that the algorithm can quickly converge to a low-error state and is not significantly affected by underwater communication delays or noise interference.

[0095] Simulation results show that the distributed elastic positioning algorithm proposed in this invention has high positioning accuracy and robustness.

[0096] This embodiment establishes a kinematic model and a pose measurement model of the MAUV system in a global coordinate system. A dynamic threshold is pre-assigned to each AUV, and an event trigger generator is constructed to trigger communication only when the state change exceeds the 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, and the delayed information is converted into a delay-free equivalent information sequence based on the information reconstruction method. Based on the reconstructed equivalent information sequence, a partitioned distributed iterative positioning algorithm is designed to achieve efficient collaborative pose estimation of multiple AUVs. A tight upper bound of the positioning error covariance matrix is ​​constructed, and an optimization method is used to solve the optimal positioning gain, effectively overcoming the non-convex optimization problem caused by factors such as linearization error, pose disturbance, and elastic gain.

[0097] Existing technologies for underwater multi-robot positioning suffer from measurement discontinuity, time lag, and uncertainty interference, making traditional Kalman filtering difficult to address, resulting in insufficient positioning accuracy and real-time performance. This embodiment reduces invalid transmissions through an event-triggered mechanism, uses binary characteristic functions and scene partitioning to address random delays, and transforms the requirements for delay-free sequence adaptive filtering. By constructing a tight upper bound on the error covariance to optimize the gain, it addresses the error modeling challenges of traditional methods, improves positioning accuracy and robustness, and enhances the efficiency of multi-robot collaboration, effectively overcoming the shortcomings of existing technologies and promoting the development of underwater positioning technology.

[0098] Example 2 This embodiment provides a distributed elastic positioning system for multiple underwater robots, including: The system modeling module is configured to establish a kinematic model of the target robot and a measurement model for monitoring nodes that integrates distance, depth, and posture information; An event triggering module is configured to trigger communication when the monitoring node measures that the state change of the target robot exceeds a preset threshold; The random delay reconstruction module is configured to use a binary characteristic function to identify the random delay state of the measurement signal, divide the scenarios 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; A partitioned collaborative localization module is configured to select a delayed channel to perform state prediction and elastic gain correction in different scenarios based on the kinematic model, the measurement model, and the delay-free equivalent sequence to obtain a 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 the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the posture state of the target robot.

[0099] Example 3 This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the distributed elastic positioning method for underwater multi-robots as described in the first embodiment above are implemented.

[0100] Example 4 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, the steps of the distributed elastic positioning method for underwater multi-robots as described in the first embodiment above are implemented.

[0101] The steps or modules involved in Examples 2 to 4 above correspond to those in Example 1. For detailed implementations, please refer to the relevant description of Example 1. The term "computer-readable storage medium" should be understood to mean a single medium or multiple media that includes 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 cause the processor to perform any method of the present invention.

[0102] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A distributed elastic positioning method for underwater multi-robots, characterized in that: include: Establish the kinematic model of the target robot and the measurement model of the monitoring node integrating distance, depth and posture information; When the monitoring node detects that the state change of the target robot exceeds the preset threshold, communication is triggered; A binary characteristic function is used to identify the random delay state of the measurement signal. The scenarios are divided according to the relationship between the current moment and the total duration of the task. Based on different scenarios, the random delay information is converted into a delay-free equivalent sequence. Based on the kinematic model, measurement model and delay-free equivalent sequence, a delay channel is selected in different scenarios to perform state prediction and elastic gain correction to obtain the state estimation value of the target robot; A tight upper bound of the positioning error covariance matrix is ​​constructed, the optimal positioning gain is solved, the elastic gain is iteratively optimized, and finally the position and posture state of the target robot is obtained.

2. The distributed elastic positioning method for underwater multi-robots according to claim 1, characterized in that: The construction of the kinematic model includes: Establish the position coordinates and attitude angles of the target robot as the state vector in the global coordinate system; Through the transformation matrix, the linear velocity and angular velocity in the carrier coordinate system are converted to the fixed coordinate system to establish the kinematic relationship; The dynamic equations are derived using Lagrangian mechanics based on kinematic relations; The continuous dynamic equations are discretized, and nonlinear disturbance terms are introduced to represent linearization errors and external disturbances to obtain the kinematic model. The construction of the measurement model includes: fusing the distance, depth and posture information collected by the monitoring nodes, and establishing a discrete measurement model containing noise and nonlinear disturbances through linearization processing.

3. The distributed elastic positioning method for underwater multi-robots according to claim 1, characterized in that: The triggering condition for triggering communication includes: taking the last triggering moment as a reference, when the difference between the current measurement value of the monitoring node and the historical transmission value exceeds a preset threshold for the first time, triggering the next communication; It also includes maintaining the historical signal output through a zero-order holder during the non-trigger period.

4. The method for distributed elastic positioning of multiple underwater robots according to claim 1, wherein: The use of a binary characteristic function to identify the random delay state of the measurement signal specifically includes: using a binary characteristic function to mark the receiving state of the measurement signal at a specific moment, and setting a constraint condition that the same measurement signal can only be received through one delay channel.

5. The distributed elastic positioning method for underwater multi-robots according to claim 1, characterized in that: The scenarios are divided according to the relationship between the current time and the total duration of the task, including: In the first scenario, if there is sufficient remaining time from the current moment to the end of the task, and the remaining time is sufficient to cover the maximum delay, then all delay channel measurements are integrated; In the second scenario, if the current time is insufficient to cover the task completion time and the remaining time is insufficient to cover the maximum delay, the valid delay channel corresponding to the remaining time is intercepted; The third scenario is the task endpoint, where only real-time measurements without delay are processed.

6. The distributed elastic positioning method for underwater multi-robots according to claim 5, characterized in that: Based on the kinematic model, measurement model and delay-free equivalent sequence, the delay channel is selected in different scenarios to perform state prediction and elastic gain correction to obtain the state estimation value of the target robot. Specifically, the method includes: selecting the corresponding delay channel according to different scenarios, predicting the current state through the kinematic model, fusing the delay-free equivalent sequence and neighbor node information, and weightedly correcting the predicted value through positioning gain and elastic gain to obtain the state estimation value.

7. The distributed elastic positioning method for underwater multi-robots according to claim 1, characterized in that: The method of constructing a tight upper bound of the positioning error covariance matrix and solving the optimal positioning gain specifically includes: constructing a minimum upper bound of the positioning error covariance matrix, solving the optimal positioning gain based on the matrix maximum principle, reducing the error by iteratively optimizing the elastic gain, and finally obtaining the position 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 for monitoring nodes that integrates distance, depth, and posture information; An event triggering module is configured to trigger communication when the monitoring node measures that the state change of the target robot exceeds a preset threshold; The random delay reconstruction module is configured to use a binary characteristic function to identify the random delay state of the measurement signal, divide the scenarios 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; A partitioned collaborative localization module is configured to select a delayed channel to perform state prediction and elastic gain correction in different scenarios based on the kinematic model, the measurement model, and the delay-free equivalent sequence to obtain a 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 the optimal positioning gain, iteratively optimize the elastic gain, and finally obtain the posture 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 a processor, the steps of the distributed elastic positioning method for underwater multi-robots according to any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the underwater multi-robot distributed elastic positioning method according to any one of claims 1 to 7 are implemented.

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