Multi-rover cooperative exploration method for positioning uncertainty and unknown demand

Abstract

This invention relates to the field of multi-detector cooperative control technology, and more particularly to a multi-robot cooperative exploration method for addressing positioning uncertainty and unknown requirements. The method linearizes sampled data containing nonlinear disturbances by designing an observation function and incorporates positioning errors into the covariance matrix of an extended Kalman filter, thereby correcting estimation errors caused by positioning uncertainty online. In the control phase, an alternative density function is constructed by calculating adaptive transition parameters, enabling the rover to automatically and smoothly switch from large-scale exploration to area coverage as environmental uncertainty decreases. Furthermore, precise coverage parameters are superimposed, and low-level control commands are generated by combining the rover's own nonholonomic kinematic constraints. Implementation results show that this invention can effectively improve estimation accuracy, coverage efficiency, and system stability in unknown environments with low computational overhead.

Description

Technical Field

[0001] This invention relates to the field of multi-detector cooperative control technology, and in particular to a multi-robot cooperative exploration method for addressing positioning uncertainties and unknown requirements. Background Technology

[0002] With the increasing importance attached to aerospace missions such as deep space exploration and planetary exploration, more stringent technical requirements have been placed on rovers in terms of autonomous decision-making capabilities, environmental adaptability, long-term stable operation capabilities, and multi-body collaborative capabilities. Compared to a single rover completing a mission independently, a multi-rovers system consisting of multiple rovers has significant advantages in system robustness, mission fault tolerance, space coverage efficiency, and mission execution flexibility, and has therefore gradually become the mainstream solution in planetary exploration missions. Furthermore, planetary exploration missions typically require the rational scheduling of the spatial distribution of each rover to achieve effective exploration and continuous monitoring of the target area, and to construct information on the target density field in the environment, such as the distribution of mineral resources, areas rich in organic matter, geological structural characteristics, and potential areas of scientific interest, thereby providing support for subsequent missions.

[0003] Coverage control, as a method to achieve efficient coverage of the task area by optimizing the spatial distribution of multiple rovers, is an important technical means to realize collaborative exploration and coverage by multiple rovers. Furthermore, coverage control algorithms have wide applications in various fields, such as target monitoring, environmental perception, area inspection, and disaster assessment. In coverage tasks, the spatial distribution characteristics of the target area are usually abstracted as a density field in the task space. Therefore, the main objective of coverage control is to dynamically optimize the spatial distribution of each rovers by continuously adjusting their positions, thereby achieving optimal coverage of non-uniform target density fields.

[0004] Previous research in coverage control has largely focused on optimizing control strategies and extending functionality under known target density field conditions. However, in missions such as planetary exploration, the target region is often an unknown environment unexplored by humans. Due to factors such as cosmic rays, extreme space environments, and limitations in long-distance communication, prior information about the target density field in the mission space is often difficult to obtain, necessitating that such coverage missions typically be conducted in environments with unknown prior information. Furthermore, under the combined influence of these various interference factors, the rover's position information is difficult to obtain accurately, often exhibiting a certain degree of positioning error, further increasing the difficulty of coordinated control and coverage optimization. Moreover, existing coverage control methods for unknown environments often employ a phased strategy of exploration followed by coverage, lacking effective coordination between exploration and coverage, and thus coverage efficiency still needs improvement. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a multi-robot collaborative exploration method for addressing positioning uncertainties and unknown requirements, thereby resolving the problems mentioned in the background section.

[0006] To address the aforementioned technical problems, this invention provides the following technical solution: a multi-robot cooperative exploration method for addressing positioning uncertainty and unknown requirements, comprising a multi-robot system consisting of multiple robots deployed at the boundary of a target area in an unknown environment, the method comprising: A synchronous online distributed density estimation framework to resist positioning uncertainty interference, and an exploration-coverage control strategy with a high-value area precision coverage mechanism, are used to control the rover's exploration-coverage behavior in density estimation; In the online distributed density estimation framework, the Vino partitioning method is used for task space allocation, and a local data sharing mechanism is constructed based on the Vino adjacency relationship. The sampling data containing nonlinear perturbations is linearized through a nonlinear observation function. The positioning error is transformed into a perturbation of the measurement value and incorporated into the covariance matrix of the measurement residual of the extended Kalman filter model. The estimation error caused by positioning uncertainty is directly compensated and corrected through online distributed iteration. During the exploration-coverage control strategy phase, an adaptive transition parameter based on the rate of change of environmental uncertainty is calculated, and an alternative density function is constructed accordingly, so that the behavior objective of the rover smoothly transitions from environmental exploration to area coverage as environmental uncertainty decreases. A precision coverage parameter triggered by an uncertainty threshold is introduced into the alternative density function and updated accordingly. The target pose of each rover in the current iteration step is calculated to guide the rover to prioritize fine coverage of high-value regions. The target pose is combined with the nonholonomic kinematic constraints of the rover body to generate low-level control commands including linear velocity and angular velocity. After the movement is completed, the commands are iterated in a loop until the target pose of each rover coincides with the current position.

[0007] Furthermore, the linearization process includes: Based on the initial poses of each rover, the target region is divided using the Vino segmentation method, and a corresponding sub-region is assigned to each rover. The expression is: ; in, Indicates the first The location of the roamer; Indicates roamer In its subregion Middle Adjacent Roamer A set; Representing the task space Any position in; The observation error experienced by the multi-robot system during the sampling process and positioning error Both are modeled as Gaussian white noise, and are expressed as follows: and ,in and These are observation errors. and positioning error The variance; Each rovers perform sampling at their current position and compare it with the set. Intra-adjacent roamers To conduct communication and data exchange, and obtain information including itself and neighboring rovers. Sampling location set with positioning interference and sampled value set ; Addressing positioning errors caused by positioning uncertainty The resulting nonlinear observation bias is addressed by constructing the nonlinear observation function as follows: ; in, For an unknown density field; For the sampling location set The corresponding real location; With the known prior mean and sampling location set Using this point as the expansion point, a first-order Taylor expansion is used to analyze the nonlinear observation function. Linearization is performed to obtain the linearized sample value set. for: ; in, Let be the Jacobian matrix of the observation function with respect to the density field; Let be the Jacobian matrix of the observation function with respect to the true position; It is the prior mean The set of prior estimates constituted; This represents the observation error.

[0008] Furthermore, the compensation correction includes: Calculate the observation residuals between the sampled value set and the prior estimate set. The calculation formula is: ; in, This is the linearized set of sampled values; It is the prior mean The set of prior estimates constituted; Positioning error variance As an independent perturbation term, it is explicitly included in the covariance matrix of the extended Kalman filter model. The expression is: ; in, For the prior kernel function; and These are observation errors. and positioning error The variance; It is the identity matrix; is the Jacobian matrix of the nonlinear observation function with respect to the density field; Let be the Jacobian matrix of the nonlinear observation function with respect to the true position; Based on including positioning error Covariance matrix of compensation term Calculate Kalman gain The calculation formula is: ; in, This represents the transpose of the Jacobian matrix; Denotes the inverse of the covariance matrix; Based on the observed residuals and Kalman gain Update the posterior mean of the density field of the unknown target and posterior kernel function Its expression is: ; ; in, It is the identity matrix; The prior mean; For the prior kernel function; posterior mean and posterior kernel function The prior estimation model is updated to obtain the posterior estimation model, which will serve as the prior in the next iteration. By continuously iterating, we obtain the posterior estimate set of the density field of the unknown target at the current time. ; in, For the first Posterior estimates for each roamer.

[0009] Furthermore, the construction of the alternative density function includes: Extract the location from the target density field estimation results. The posterior mean and the standard deviation of the estimated uncertainty at the given location. ; Calculate the first The trace of the posterior kernel function at each iteration is used to quantify the total uncertainty of the current unknown target density field. ; The initial total uncertainty of the unknown target density field during the initial deployment of the multi-robot system Calculate the short-term rate of change of uncertainty between iterations. and long-term cumulative rate of change ; Based on the short-term rate of change of uncertainty and long-term cumulative rate of change Constructing comprehensive indicators The expression is: ; According to comprehensive indicators Calculate the adaptive transition parameters for dynamically allocating exploration and coverage weights in the current iteration step. The calculation formula is: ; in, and These are preset smoothing adjustment parameters; Based on adaptive transition parameters Construct an alternative density function that allows the rover to smoothly transition from environment exploration to area coverage. The expression is: ; In the formula, Characterization location The standard deviation of the estimated results; For position The posterior mean at the location.

[0010] Furthermore, the short-term rate of change The calculation formula is: ; Used to indicate the first Second and third The short-term rate of change of uncertainty between iterations.

[0011] Further, the target pose of each rover in the current iteration step is calculated, including: Calculate precise cover parameters for dynamically adjusting the proportion of high-value regions in the density function. The calculation formula is as follows: ; in, These are preset weight parameters; and These are preset constant parameters for controlling the speed at which precision coverage is entered and exited; The start time parameter for precise coverage; For the duration parameter of precision coverage; This represents the number of iterations. Alternate density function Introducing precise coverage parameters based on this The updated alternative density function is obtained. The expression is: ; In the formula, Characterization location The standard deviation of the estimated results; For position The posterior mean at the location; For adaptive transition parameters; Based on the updated alternative density function Construct a new coverage quality loss function The expression is: ; Where n is the number of rovers; Indicates the first The location of the roamer; The resulting sub-regions; Based on the coverage quality loss function set of rovers Calculate the partial derivatives to obtain the corresponding sub-regions for each rovers. The weighted centroid is expressed as: ; in, Based on the alternative density function Defined subregion Weighted quality; sub-region The weighted centroid; Weighted centroid Set as the target pose for the current iteration step of the rovers.

[0012] Furthermore, the formula for calculating the weighted centroid is: ; in, For adaptive transition parameters and precision coverage parameters The updated alternative density function.

[0013] Furthermore, generating low-level control commands includes: The weighted centroid corresponding to the sub-region As a roaming device Target waypoint, calculate the rover Direction vector from current position to target waypoint and its Euclidean distance The calculation formula is: ; ; The direction vector Decoupling into two-dimensional coordinate form And calculate the roamer The expected velocity vector ,Right now: ; in, The preset controller gravity coefficient; Get the current orientation angle of the rovers The desired motion velocity vector Projected onto the rover's own heading coordinate system to satisfy the nonholonomic kinematic constraints of the actual rover; By transforming coordinate projection, the actual executable linear velocity at the underlying level is calculated. and angular velocity The control law for the rovers is calculated using the following formula: ; ; in, Direction vectors exist The component along the axial direction.

[0014] By employing the above technical solution, the present invention provides a multi-robot collaborative exploration method for addressing positioning uncertainties and unknown requirements, which has at least the following beneficial effects: This invention effectively reduces the interference of positioning uncertainty on the estimation of unknown environments. It linearizes the sampled data containing nonlinear positioning uncertainty using a first-order Taylor expansion and converts the positioning error into a perturbation of the measured values, explicitly incorporating it into the covariance matrix of the measurement residuals of the extended Kalman filter model. This approach directly compensates for and corrects estimation errors caused by positioning uncertainty during online distributed iterative computation, significantly improving the accuracy of target density field estimation in environments with prior unknowns and positioning interference.

[0015] This invention improves collaborative exploration and computational efficiency while ensuring real-time performance. It utilizes the Vino partitioning method for task space allocation and constructs a local data sharing mechanism based on Vino adjacency relationships. This approach allows each rover to communicate and interact only with its direct neighbors and update local covariance, effectively reducing the communication network burden and single-machine computational overhead of the multi-rover system, thus ensuring the convergence speed and real-time performance of global target density field estimation.

[0016] This invention achieves an adaptive and smooth transition between exploration and coverage without human intervention. By calculating adaptive transition parameters based on the rate of change of environmental uncertainty and constructing an alternative density function accordingly, it couples reducing environmental uncertainty (exploration) and reducing coverage quality loss (coverage) into the same objective function. This mechanism allows the rover to autonomously and smoothly switch from large-scale exploration tasks to regional coverage tasks as the degree of environmental uncertainty decreases, avoiding the task fragmentation and time loss caused by traditional phased strategies (exploration first, then coverage).

[0017] This invention optimizes system resource allocation and achieves refined coverage of high-value areas. It further introduces a precise coverage parameter triggered by an uncertainty threshold into the alternative density function. When the overall uncertainty of the unknown environment decreases to a safe threshold, the activation of this parameter dynamically increases the weight of high-mean regions in the weighted centroid calculation. This mechanism guides the rover to automatically allocate physical and computational resources to high-value areas (such as resource-rich areas), significantly improving the precision and quality of coverage in key areas without increasing overall system overhead.

[0018] This invention ensures the smoothness and physical feasibility of the rover's underlying motion. It combines the target pose generated based on a weighted centroid with the nonholonomic kinematic constraints of the rover body. By projecting the direction vector onto the heading coordinate system, the ideal particle motion model is transformed into practically executable linear and angular velocity control inputs. This control method eliminates jitter caused by drastic jumps in the target point, ensuring the smoothness of multi-rovers movement and the stability of system operation in complex terrain environments. Attached Figure Description

[0019] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the multi-robot cooperative exploration method in this invention; Figure 2 This is a schematic diagram of the actual target density field during the implementation of this invention; Figure 3This is a graph showing the change of the target density field estimation mapping of each rover in this invention at the number of iterations of 10; Figure 4 This is a graph showing the change of the target density field estimation mapping of each rover in this invention at the number of iterations of 50. Figure 5 This is a graph showing the change of the estimated mapping of the target density field by each rover in this invention at the number of iterations 120; Figure 6 This is a schematic diagram illustrating the change of the root mean square error between the estimated mapping and the true value of each rovers in this invention over time. Figure 7 This is a schematic diagram of the estimation and position change of each rover under the exploration-coverage strategy control during the 10th iteration in this invention; Figure 8 This is a schematic diagram of the estimation and position change of each rover under the exploration-coverage strategy control during the 92nd iteration in this invention; Figure 9 This is a schematic diagram of the estimation and position change of each rover under the exploration-coverage strategy control during the 120th iteration in this invention; Figure 10 This is a graph showing the change of the coverage quality loss function as a function of iteration throughout the entire coverage process in this invention. Detailed Implementation

[0020] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0021] Example 1: This embodiment proposes a multi-robot cooperative exploration method for addressing positioning uncertainty and unknown requirements. It linearizes sampled data containing nonlinear disturbances by designing an observation function and incorporates positioning errors into the covariance matrix of an extended Kalman filter, thereby correcting estimation errors caused by positioning uncertainty online. In the control phase, an alternative density function is constructed by calculating adaptive transition parameters, enabling the rover to automatically and smoothly switch from large-scale exploration to area coverage as environmental uncertainty decreases. Therefore, with low computational overhead, it effectively improves estimation accuracy, coverage efficiency, and system stability in unknown environments. Figure 1 As shown, the method includes the following steps: S1. Multi-robot system initialization and environment modeling. Deployment at the target area boundary in an unknown environment. A multi-robot system is constructed by several rovers. A spatial rectangular coordinate system is established and the initial pose of each rovers is obtained. A Gaussian process probability model is established to describe the prior distribution and uncertainty of the density field of the unknown target. Based on the Gaussian process probability model, the coverage control quantification index is determined, and an initial prior estimation model is constructed for each rovers.

[0022] In this embodiment, let This represents the task space (i.e., the target region) where the prior distribution of the target is unknown. The boundary locations in the middle are randomly deployed by A multi-robot system consisting of individual robots. In the task space. Establish a spatial rectangular coordinate system to obtain the position set of each rovers. and the set of orientation angles This constitutes the initial pose set. Where the first... The position of each roamer is denoted as Orientation angle is .

[0023] For unknown target density field A Gaussian process is used to probabilistically model it, simultaneously describing its prior distribution and its uncertainty. The expression for the Gaussian process probability model is as follows: ; in, Representing the task space Any position in; Representing the task space Middle position The adjacent position; Represents the density field of an unknown target The expected distribution (i.e., prior mean); This is the kernel function of a Gaussian process probability model, used to characterize the correlation and uncertainty between different locations. Specifically, the kernel function can be expressed as: ; in, Hyperparameters, hyperparameter set The kernel function can be pre-trained using historical map data and derived by matching it to the current map size.

[0024] Based on the aforementioned unknown target density field The model establishes the coverage control quantitative index as follows: ; in, To cover the quality loss function, used to measure the entire task space. The coverage effect; To cover the loss term, its meaning is: when the position With roaming device The greater the Euclidean distance between them, the more the performance of the rovers' sensors will affect the rovers. Position The greater the loss of coverage quality during the coverage process, the better. This indicates the task space of each rovers. The division results, each sub-region Each is handled by a corresponding roamer to achieve reasonable allocation of the target area and avoid duplicate coverage or omissions.

[0025] Based on the Gaussian process probability model described above, prior estimates for each rover are constructed using its initial deployment location. In the absence of any initial deployment sampling data, the prior mean of each rover is set to zero, i.e., The prior kernel function is initialized using the following formula: ; in, Indicates the initial deployment location of the rovers; Indicates the target location that needs to be calculated; for A dimensional identity matrix. Thus, each rover can obtain a priori estimation model of the unknown environment as follows: .

[0026] S2. Perform spatial allocation and collaborative sampling based on Vino segmentation. Based on the initial pose of each rover, the target region is divided using the Vino segmentation method, and a corresponding sub-region is assigned to each rover. Each rover performs environmental sampling at its current position and shares the sampling data with neighboring rover through Vino adjacency relationships, obtaining a sampling dataset containing information about itself and its neighboring points. To address the nonlinearity caused by sensor observation errors and positioning uncertainties, each rover uses a designed nonlinear observation function to linearize the sampling dataset using a first-order Taylor expansion, generating a linearized set of sampled values.

[0027] Specifically, in the distributed coverage process, for the roamer ,set up Indicates that it is in its subregion Middle Adjacent Roamer A set. Through the task space After performing the Vino partitioning, obtain the rovers based on the adjacency relationships of the Vino graph. The direct neighbors are obtained. After the above Vino partitioning, the roamer... Sub-regions under responsibility Represented as: ; After the system is divided, each rover samples at its current position. During the sampling process, the multi-robot system is mainly affected by two types of error interference: one is the observation error introduced by sensor measurements. Another type is the positioning error introduced by positioning uncertainty. Both types of errors mentioned above are Gaussian white noise, denoted as follows: and ,in and These are observation errors. and positioning error The variance. Based on this, a sampling observation function considering error is established. For sampled data The data is converted to the following format: ; During sampling, each rover performs sampling at its current position and combines it with its set. Intra-adjacent roamers To conduct communication and data exchange, and obtain information including itself and neighboring rovers. Sampling location set with positioning interference and sampled value set Among them The data includes a sample of the roaming itself and neighboring points. One sampled data.

[0028] Addressing positioning errors caused by positioning uncertainty The resulting nonlinear observation bias is addressed by constructing the nonlinear observation function as follows: ; in, For an unknown density field; For the sampling location set The corresponding actual location.

[0029] To handle positioning errors caused by positioning uncertainty The resulting nonlinear observation problem is addressed by each rover using a first-order Taylor expansion of the aforementioned nonlinear observation function. Perform linearization. Using the known prior mean... and sampling location set Using this point as the expansion point, higher-order terms are truncated. get: ; in, It is a set of sampling locations The corresponding real location; It is the prior mean The set of prior estimates constituted. The nonlinear observation function for the unknown density field. Jacobian matrix And the actual location Jacobian matrix They are represented as follows: ; ; in, This represents the dimension of the discrete expansion of the density field; Represents a nonlinear observation function; Indicates the actual location Coordinate components; Indicates the actual location Coordinate components; Indicates the first sampling locations The prior mean at that location.

[0030] Finally, each rovers calculates the linearized set of sampled values ​​as follows: ; in, Let be the Jacobian matrix of the observation function with respect to the density field; Let be the Jacobian matrix of the observation function with respect to the true position; This represents the dimension of the discrete expansion of the density field; This represents the observation error.

[0031] The linearized sample value set This will serve as the input basis for online distributed density estimation in subsequent steps.

[0032] This expansion will reduce the positioning error. Linearization is mapped to the measurement disturbance term in the observation model. By transforming the nonlinear position deviation into a linearly compensable measurement residual, the nonlinear comprehensive impact of positioning uncertainty on the observation position is transferred to the observation value. This eliminates the nonlinear interference of positioning uncertainty on the subsequent distributed estimation and control process and reduces the computational complexity of the system.

[0033] S3. Iterative online distributed density estimation of the unknown target density field. Each rover uses the linearized sample value set. The posterior estimate of the density field of the unknown target is updated in an online distributed iterative manner. During the iterative calculation, the positioning error due to positioning uncertainty is considered. Measurement perturbations are explicitly incorporated into the covariance matrix of the extended Kalman filter model for compensation, correcting estimation errors caused by positioning uncertainty and thus reducing the interference of positioning errors on density estimation. Finally, a posterior estimate set of the unknown target density field for each rover at the current time is generated.

[0034] Specifically, each rovers are based on the linearized sample value set generated in step S2. An extended Kalman filter method is used to recursively estimate the density field of the unknown target. In each iteration, the rover calculates and updates the posterior mean of the density field of the unknown target. and posterior kernel function .

[0035] First, the rovers calculate the observation residuals between the sampled set and the prior estimate set. and Kalman gain Observation residuals The calculation formula is: ; Based on including positioning error Covariance matrix of compensation term Calculate Kalman gain This mechanism dynamically adjusts the update weights of the current observation data based on the magnitude of positioning uncertainty. The calculation formula is: ; in, For the prior kernel function; This is the transpose of the observation matrix (Jacobi matrix); is the inverse of the covariance matrix.

[0036] To compensate for positioning errors The resulting estimation bias affects the construction of the observation residuals. covariance matrix At that time, the positioning error is explicitly stated. variance It is included as an independent perturbation term to pass through the Kalman gain. The formula for effectively mitigating the impact of positioning uncertainty on density estimation is as follows: ; in, and These are observation errors. and positioning error The variance; It is the identity matrix; is the Jacobian matrix of the nonlinear observation function with respect to the density field; Let be the Jacobian matrix of the nonlinear observation function with respect to the true position.

[0037] Secondly, the observation residuals obtained through calculation are used and Kalman gain The roamer in the aforementioned prior estimation model Based on this, update the posterior mean of the unknown target density field. and posterior kernel function Its expression is: ; ; in, It is the identity matrix; The prior mean; This is the a priori kernel function.

[0038] Therefore, through Kalman gain The change reflects the current positioning error The influence of this allows the rover to adaptively adjust the weight of the current observation data in the state update during iterative estimation. At the same time, it absorbs the positioning error by converting it into the posterior uncertainty of the model to compensate for the impact of positioning uncertainty.

[0039] Using this calculation method, each rover will estimate the prior model in one iteration. Update to posterior estimation model The a priori estimated model is then used as the prior estimate for the next iteration.

[0040] In each iteration, each rover transforms the localization uncertainty into model uncertainty through the above steps, using a posterior kernel function. By absorbing and reducing the interference of positioning errors on density estimation, they ultimately constitute the posterior estimate set of the density field of the unknown target at the current moment. .in, For the first Posterior estimates for each roamer.

[0041] S4. Uncertainty-Based Exploration-Coverage Smooth Transition Control. Based on the target density field estimation results (i.e., the posterior estimation set) obtained in step S3 and the rate of change of its uncertainty, adaptive transition parameters are calculated. An alternative density function is constructed using these adaptive transition parameters, allowing the rover's behavioral objective to smoothly transition from environmental exploration to area coverage as environmental uncertainty decreases.

[0042] In this embodiment, to achieve adaptive switching between the rover's exploration of unknown environments and target area coverage tasks, each rover uses the posterior estimation set output in step S3. Construct alternative density functions Its expression is: ; In the formula, Characterization location The uncertainty (i.e., standard deviation) of the estimated results; For position The posterior mean at the location; An adaptive transition parameter is used to control the exploration and coverage weights.

[0043] To enable the rover to automatically adjust based on the current exploration progress, avoiding task fragmentation caused by a phased strategy of exploring first and then covering, an adaptive transition parameter is calculated for dynamically allocating exploration and covering weights in the current iteration step. The calculation formula is as follows: ; in, and These are preset smoothing adjustment parameters; It is a comprehensive indicator constructed from the short-term rate of change and the long-term cumulative rate of change of uncertainty; Preset constant parameters and Used to adjust the smoothness of the roamer's transition from exploration to coverage behavior. Parameter As a comprehensive index combining the rate of change of uncertainty and the absolute value, its expression is: ; in, , indicating the first The trace of the posterior kernel function at each iteration is used to quantify the total uncertainty of the current unknown target density field; , which represents the initial total uncertainty of the density field during the initial deployment of the multi-robot system. For the first Second and third The short-term rate of change of uncertainty between iterations; Indicates the first The ratio of uncertainty to initial uncertainty at each iteration is the long-term cumulative rate of change of uncertainty.

[0044] Furthermore, comprehensive indicators The design principle is: The rate of change of environmental uncertainty in the short term With long-term cumulative rate of change This is combined with other methods. The multi-robot system determines whether to transition from exploration to coverage based on comprehensive changes in the environment, and calculates adaptive transition parameters accordingly. In the early stages of a mission or when there is significant overall environmental uncertainty, the calculated comprehensive index... Smaller values ​​result in adaptive transition parameters Approaching 1, the environmental standard deviation is given a higher weight, guiding the rover to prioritize exploration. When the long-term cumulative rate of change... It declined to a lower level and then stabilized (i.e., the short-term rate of change) When the value is relatively small, the calculated comprehensive index is... The larger the adaptive transition parameter, the better. Approaching 0, thus smoothly transferring behavioral control to the overlay component in subsequent control. Therefore, through adaptive transition parameters... Compared with comprehensive indicators This enables adaptive and smooth transitions in the behavior of multi-robot systems.

[0045] The substitution density function constructed in this embodiment using the above calculation method It is able to achieve this when the initial total uncertainty is large or decreases sharply (i.e., ), making The rovers are guided to prioritize exploration in areas of high uncertainty; when the total uncertainty decreases to a low level and tends to stabilize (i.e., ), making This guides the rover to high-density areas to perform coverage, thus enabling a smooth exploration-coverage transition without human intervention.

[0046] S5. Generation of the rover target pose with precise coverage of high-value regions. Precise coverage parameters are further superimposed on the substitution density function in step S4. When the total accumulated uncertainty of the multi-robot system decreases to a preset threshold, precise coverage calculation is enabled. The weighted centroid of the corresponding sub-region for each rover is calculated based on the updated substitution density function, and this weighted centroid is used as the target pose for the current iteration step of the rover, guiding the rover to prioritize fine coverage of high-value regions.

[0047] In this embodiment, to achieve focused observation of high-value areas in the later stages of exploration, the multi-robot system obtains a new substitution density function in step S4. Based on this, precise coverage parameters are introduced. The updated alternative density function is then performed. for: ; Among them, precision coverage parameters The formula for dynamically adjusting the proportion of high-value regions (i.e., high-mean regions) in the density function is as follows: ; in, The preset weight parameters control the degree of precision coverage; and These are preset constant parameters for controlling the speed at which precision coverage is entered and exited; The start time parameter for precise coverage; This is the duration parameter for precise coverage.

[0048] Continuously monitor the cumulative total uncertainty of the multi-robot system, when the long-term cumulative rate of change... When the value drops to a preset threshold (e.g., 0.2), the precision coverage logic begins, and the number of iterations at this point is recorded. Assign a value to the start time parameter of the precision coverage (Right now This allows the parameter adjustment logic to be activated once environmental uncertainty has been sufficiently reduced.

[0049] Subsequently, based on the updated alternative density function Construct a new coverage quality loss function for: ; To calculate the rover's moving target point, based on the aforementioned coverage quality loss function... set of rovers Calculate the partial derivatives to obtain the corresponding sub-regions for each rovers. The weighted centroid is expressed as: ; in, Based on the alternative density function Defined subregion Weighted quality; sub-region The weighted centroid.

[0050] The multi-roaming system directly sets the target pose of the current iteration step of the roamer to the weighted centroid. This allows the rover to move toward the target pose through subsequent control.

[0051] By introducing precise coverage parameters and in the new alternative density function By increasing the weight of high-value regions, the resulting centroid will be biased towards those regions. This weighted centroid will then be shifted. The target pose of the rovers is set to guide the rovers to move to high-value areas first to perform fine-grained coverage after the environmental uncertainty is reduced.

[0052] S6. Rover Motion Control Based on Nonholonomic Constraints. Based on the target pose generated in step S5, the desired motion velocity and direction vector of the rover are calculated. Combining the nonholonomic kinematic constraints of the rover body, the direction vector is projected onto the heading coordinate system and converted into actual linear and angular velocities as control inputs, thereby driving the rover's movement. After completing the movement, the process returns to step S2. Each rover re-executes environmental sampling and data sharing at the new position, and steps S2 to S6 are repeated until the target pose of each rover coincides with its current position, and the multi-rover system reaches its final stable state.

[0053] In this embodiment, the system calculates the underlying control commands based on a nonholonomic constrained kinematic model with heading projection to drive the rover to move to the target position along a smooth trajectory.

[0054] First, extract the weighted centroids of the sub-regions in step S5. As a roaming device The target waypoint. During each iteration of control, the rover calculates... Direction vector from current position to target waypoint and its Euclidean distance The calculation formula is: ; ; Based on the particle motion model, the direction vector Decoupling into two-dimensional coordinate form And calculate the roamer The expected velocity vector ,Right now: ; in, The preset controller gravity coefficient affects the control speed.

[0055] Furthermore, in order to adapt the ideal particle motion model to a non-holonomic real-world physics chassis, the current orientation angle of the rover is obtained. The desired motion velocity vector The coordinates are projected onto the rover's own heading coordinate system to satisfy the nonholonomic kinematic constraints of the actual rover.

[0056] By transforming coordinate projection, the actual executable linear velocity at the underlying level is calculated. and angular velocity The control law for the rovers is calculated using the following formula: ; ; in, Direction vectors exist The component along the axial direction.

[0057] The control law drives the rovers to move, and each rovers move towards the target position in a smooth trajectory. There will be no S-shaped jitter during the movement, and the motion jitter caused by the jump of the target point can also be eliminated.

[0058] Using the calculated linear velocity and angular velocity Eliminate motion jitter caused by target point jumps and ensure the smoothness of the rover's movement trajectory. As iterations progress, target uncertainty continuously decreases, and the rover gradually transitions from exploration to precise coverage, until finally calculating the target pose and the rover's position. The current positions coincide (i.e., the Euclidean distance between the direction vectors) The multi-robot system eventually reaches a stable state.

[0059] Example 2: Based on Example 1, this example implements the above method using a known real target density field as an example, and iteratively verifies the exploration-coverage behavior of the rover in density estimation according to the present invention.

[0060] S1. Multi-robot system initialization and environment modeling, the implementation process is as follows: 1.1. Set the location set for rovers deployment Initialize the robot parameters, including the number of robots. Orientation angle Velocity and angular velocity and Iteration time step Set the speed limit according to the actual performance of the roaming device. as well as .

[0061] Initialize map parameters, including: density field discrete dimension. Number of iterations Initialize system parameters, including smoothing parameters for the transient process. and Weight parameters of precision coverage mechanism for high-value areas Speed ​​parameters for entering and exiting precision coverage and The actual target density field distribution used in this implementation process is set as follows: Figure 2 As shown.

[0062] 1.2. To prepare for establishing the density field model, in the task space A spatial rectangular coordinate system is established, and the radial basis function shown in the following formula is selected as the kernel function; ; Among them, hyperparameters and Selection is achieved by matching a pre-trained kernel function with historical map data.

[0063] 1.3. Task Space The density field of the unknown target is modeled as a Gaussian process, and the initial density is set to a zero-mean function for its parameters. The prior kernel function for its initial uncertainty distribution is established by the following formula: ; Finally, the prior estimation model for the density field of the unknown target is: .

[0064] 1.4. Based on the prior estimation model, the quantitative coverage index is established as follows: ; in, To cover the quality loss function, used to measure the entire task space. The coverage effect; To cover the loss items; This refers to the sub-region that the corresponding roamer is responsible for.

[0065] After the above steps, a preliminary model of the target density field can be established, and the exploration and coverage process can begin.

[0066] S2. Perform spatial allocation and collaborative sampling based on Vino segmentation. The implementation process is as follows: 2.1 Initialize the set of Vino adjacency rovers Establish a dataset for communication between various rovers, including a set of sampling locations. and sampled value set .

[0067] 2.2 The responsibilities of each rovers are divided, with each rovers only responsible for its own sub-region. The division method is as follows: .

[0068] 2.3. Set up a linear observation function to transform the sampled data. The format is as follows: .

[0069] 2.4. Adjacent rovers interact with each other, and each rovers generate its own sampled data for each iteration step, including a set of sampled locations. and sampled value set The above steps yield the dataset sampled from each rovers and then transformed.

[0070] 2.5. Further perform a Taylor first-order linear expansion on the transformed dataset to explicitly transfer the influence of positioning uncertainty. The expansion formula is as follows: ; Among them, positioning uncertainty is mainly classified into In this section, the final expression for the new set of sampled values ​​is: .

[0071] S3. Iterative online distributed density estimation of the unknown target density field. The implementation process is as follows: 3.1 Calculate the observation residuals and their covariance. The formulas are as follows: ; ; 3.2 Based on including positioning error Covariance matrix of compensation term The Kalman gain is calculated using the following formula: ; 3.3. Based on the above intermediate parameters and the intermediate parameters of each iteration, calculate the posterior estimation model between iterations, i.e., its posterior mean and posterior kernel function. The calculation formula is as follows: ; ; Using the above method, the estimated mapping of the target density field for each rover can be iteratively calculated online and in a distributed manner. This estimated mapping will successively approximate the true distribution over time, as illustrated in the diagram below. Figures 3-5 As shown, the opaque curved surface represents the estimated mean, while the blue semi-transparent portion represents the estimation uncertainty. Furthermore, the root mean square error (RMSE) is used to compare the estimated mapping with the true distribution; its calculation formula is as follows: ; The diagram illustrating the change of root mean square error with the number of iterations is shown below. Figure 6 As shown in the figure, it is clearly visible that the difference between the estimated value and the true value decreases rapidly with the number of iterations.

[0072] S4. Uncertainty-based Exploratory-Covered Smooth Transition Control. The implementation process is as follows: 4.1 From the posterior estimation model in each estimation iteration The mean and kernel function are selected for data transformation and intermediate calculations. The calculation method is as follows: , .

[0073] 4.2 Calculate and save the initial total uncertainty of the density field during initial deployment. Calculate the total uncertainty of the current density field. Calculate the short-term rate of change of uncertainty between iterations. Calculate the long-term cumulative rate of change of uncertainty. .

[0074] 4.3 Calculate the adaptive transition parameters The calculation formula is as follows: ; Where parameters The calculation formula is: .

[0075] S5. Generation of rover target pose with precise coverage of high-value areas. The implementation process is as follows: 5.1 Set the start time parameter for entering the precision coverage mechanism in high-value areas according to the target density field requirements. and duration parameters ; 5.2 Calculate the precision coverage parameters The calculation formula is as follows: ; 5.3. Based on the adaptive transition parameter and precision coverage parameters The exploration-coverage control strategy with a precision coverage mechanism for high-value areas is set up, and the corresponding alternative density function is modified as follows: ; 5.4 Substitute the new alternative density function into the original coverage quality loss function, and also substitute the loss term. This yields a new coverage quality loss function. for: ; 5.5 Calculate the weighted centroid of the corresponding sub-region for each rovers. The calculation formula is as follows: ; in, For adaptive transition parameters and precision coverage parameters The updated alternative density function.

[0076] S6. Rover motion control based on nonholonomic constraints. The implementation process is as follows: 6.1. Take the weighted centroid from step S5. Location of each rovers Calculate the direction vector The direction vector is obtained through decoupling. and its Euclidean distance .

[0077] 6.2. Obtain the orientation angle of each rovers. Calculate its trigonometric functions as well as .

[0078] 6.3 Calculate the target control parameters of each rover to form the control law. The calculation formula is as follows: ; ; Finally, speed limiting is applied: as well as It then transmits the data to the roamer and controls its movement.

[0079] The above methods can control the explore-cover behavior of the rover in density estimation, and its movement at 10, 92, and 120 iterations is shown below. Figures 7-9 As shown, this represents three different key time points. Different colors represent different rovers; small circles represent the rovers' starting positions, large circles represent their current positions, and dashed lines represent their paths. The black straight line represents the spatial division of the target area, and the background heatmap shows the current density estimation. Furthermore, the coverage quality loss function changes with the iteration process throughout the entire coverage process, as shown below. Figure 10 As shown.

[0080] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0081] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0082] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A multi-robot cooperative exploration method for addressing positioning uncertainty and unknown requirements, comprising a multi-robot system consisting of multiple robots deployed at the boundary of a target area in an unknown environment, characterized in that, The method includes: A synchronous online distributed density estimation framework to resist positioning uncertainty interference, and an exploration-coverage control strategy with a high-value area precision coverage mechanism, are used to control the rover's exploration-coverage behavior in density estimation; In the online distributed density estimation framework, the Vino partitioning method is used for task space allocation, and a local data sharing mechanism is constructed based on the Vino adjacency relationship. The sampling data containing nonlinear perturbations is linearized through a nonlinear observation function. The positioning error is transformed into a perturbation of the measurement value and incorporated into the covariance matrix of the measurement residual of the extended Kalman filter model. The estimation error caused by positioning uncertainty is directly compensated and corrected through online distributed iteration. During the exploration-coverage control strategy phase, an adaptive transition parameter based on the rate of change of environmental uncertainty is calculated, and an alternative density function is constructed accordingly, so that the behavior objective of the rover smoothly transitions from environmental exploration to area coverage as environmental uncertainty decreases. A precision coverage parameter triggered by an uncertainty threshold is introduced into the alternative density function and updated accordingly. The target pose of each rover in the current iteration step is calculated to guide the rover to prioritize fine coverage of high-value regions. The target pose is combined with the nonholonomic kinematic constraints of the rover body to generate low-level control commands including linear velocity and angular velocity. After the movement is completed, the commands are iterated in a loop until the target pose of each rover coincides with the current position.

2. The multi-robot cooperative exploration method according to claim 1, characterized in that, The linearization process includes: Based on the initial poses of each rover, the target region is divided using the Vino segmentation method, and a corresponding sub-region is assigned to each rover. The expression is: ； in, Indicates the first The location of the roamer; Indicates roamer In its subregion Middle Adjacent Roamer A set; Representing the task space Any position in; The observation error experienced by the multi-robot system during the sampling process and positioning error Both are modeled as Gaussian white noise, and are expressed as follows: and ,in and These are observation errors. and positioning error The variance; Each rovers perform sampling at their current position and compare it with the set. Intra-adjacent roamers To conduct communication and data exchange, and obtain information including itself and neighboring rovers. Sampling location set with positioning interference and sampled value set ; Addressing positioning errors caused by positioning uncertainty The resulting nonlinear observation bias is addressed by constructing the nonlinear observation function as follows: ； in, For an unknown density field; For the sampling location set The corresponding real location; With the known prior mean and sampling location set Using this point as the expansion point, a first-order Taylor expansion is used to analyze the nonlinear observation function. Linearization is performed to obtain the linearized sample value set. for: ； in, Let be the Jacobian matrix of the observation function with respect to the density field; Let be the Jacobian matrix of the observation function with respect to the true position; It is the prior mean The set of prior estimates constituted; This represents the observation error.

3. The multi-robot cooperative exploration method according to claim 1, characterized in that, The compensation correction includes: Calculate the observation residuals between the sampled value set and the prior estimate set. The calculation formula is: ； in, This is the linearized set of sampled values; It is the prior mean The set of prior estimates constituted; Positioning error variance As an independent perturbation term, it is explicitly included in the covariance matrix of the extended Kalman filter model. The expression is: ； in, For the prior kernel function; and These are observation errors. and positioning error The variance; It is the identity matrix; is the Jacobian matrix of the nonlinear observation function with respect to the density field; Let be the Jacobian matrix of the nonlinear observation function with respect to the true position; Based on including positioning error Covariance matrix of compensation term Calculate Kalman gain The calculation formula is: ； in, This represents the transpose of the Jacobian matrix; Denotes the inverse of the covariance matrix; Based on the observed residuals and Kalman gain Update the posterior mean of the density field of the unknown target and posterior kernel function Its expression is: ； ； in, It is the identity matrix; The prior mean; For the prior kernel function; posterior mean and posterior kernel function The prior estimation model is updated to obtain the posterior estimation model, which will serve as the prior in the next iteration. By continuously iterating, we obtain the posterior estimate set of the density field of the unknown target at the current time. ; in, For the first Posterior estimates for each roamer.

4. The multi-robot cooperative exploration method according to claim 1, characterized in that, The construction of the alternative density function includes: Extract the location from the target density field estimation results. The posterior mean and the standard deviation of the estimated uncertainty at the given location. ; Calculate the first The trace of the posterior kernel function at each iteration is used to quantify the total uncertainty of the current unknown target density field. ; The initial total uncertainty of the unknown target density field during the initial deployment of the multi-robot system Calculate the short-term rate of change of uncertainty between iterations. and long-term cumulative rate of change ; Based on the short-term rate of change of uncertainty and long-term cumulative rate of change Constructing comprehensive indicators The expression is: ； According to comprehensive indicators Calculate the adaptive transition parameters for dynamically allocating exploration and coverage weights in the current iteration step. The calculation formula is: ； in, and These are preset smoothing adjustment parameters; Based on adaptive transition parameters Construct an alternative density function that allows the rover to smoothly transition from environment exploration to area coverage. The expression is: ； In the formula, Characterization location The standard deviation of the estimated results; For position The posterior mean at the location.

5. The multi-robot cooperative exploration method according to claim 4, characterized in that, The short-term rate of change The calculation formula is: ； Used to indicate the first Second and third The short-term rate of change of uncertainty between iterations.

6. The multi-robot cooperative exploration method according to claim 1, characterized in that, Calculate the target pose of each rover in the current iteration step, including: Calculate precise cover parameters for dynamically adjusting the proportion of high-value regions in the density function. The calculation formula is as follows: ； in, These are preset weight parameters; and These are preset constant parameters for controlling the speed at which precision coverage is entered and exited; The start time parameter for precise coverage; For the duration parameter of precision coverage; This represents the number of iterations. Alternate density function Introducing precise coverage parameters based on this The updated alternative density function is obtained. The expression is: ； In the formula, Characterization location The standard deviation of the estimated results; For position The posterior mean at point ; For adaptive transition parameters; Based on the updated alternative density function Construct a new coverage quality loss function The expression is: ； Where n is the number of rovers; Indicates the first The location of the roamer; The resulting sub-regions; Based on the coverage quality loss function set of rovers Calculate the partial derivatives to obtain the corresponding sub-regions for each rovers. The weighted centroid is expressed as: ； in, Based on the alternative density function Defined subregion Weighted quality; sub-region The weighted centroid; Weighted centroid Set as the target pose for the current iteration step of the rovers.

7. The multi-robot cooperative exploration method according to claim 6, characterized in that, The formula for calculating the weighted centroid is: ； in, For adaptive transition parameters and precision coverage parameters The updated alternative density function.

8. The multi-robot cooperative exploration method according to claim 1, characterized in that, The generation of low-level control commands includes: The weighted centroid corresponding to the sub-region As a roaming device Target waypoint, calculate the rover Direction vector from current position to target waypoint and its Euclidean distance The calculation formula is: ； ； The direction vector Decoupling into two-dimensional coordinate form And calculate the roamer The expected velocity vector ,Right now: ； in, The preset controller gravity coefficient; Get the current orientation angle of the rovers The desired motion velocity vector Projected onto the rover's own heading coordinate system to satisfy the nonholonomic kinematic constraints of the actual rover; By transforming coordinate projection, the actual executable linear velocity at the underlying level is calculated. and angular velocity The control law for the rovers is calculated using the following formula: ； ； in, Direction vectors exist The component along the axial direction.

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