Multi-rover coverage method in prior unknown environment

Abstract

The invention discloses a multi-rover coverage method in a priori unknown environment, and relates to the technical field of probability modeling and cooperative control. The method comprises the following steps: deploying and forming a multi-rover network in a target area, virtually distributing and uniformly driving rovers to respective sub-target areas according to Voronoi segmentation; based on a sampling method, generating uniform sampling points in a sub-target area in charge of each rover in a self-adaptive manner, and continuously iterating and updating a continuous round-trip sampling path; according to the sampling path, each rover iterates in an online and distributed manner and updates estimation on unknown priori, and respective estimation mapping on target distribution is formed; based on a multi-source fusion mechanism, through weighted fusion of estimation data of each rover, the overall estimation accuracy and consistency of the system are improved; according to the Zensen-Xiang divergence, calculating change differences between self iterations of the rovers and between the rovers, and taking a double-threshold mechanism as a basis for estimating iteration stop; and iteratively driving each rover to the optimal position based on the control rate of the rover.

Description

Technical Field

[0001] The present invention relates to the field of probabilistic modeling and collaborative control technology, and in particular to a multi-robot coverage method in an a priori unknown environment. Background Art

[0002] In recent years, with the increasing complexity of missions such as deep space exploration, rovers are facing increasingly stringent technical requirements in terms of size, performance, and energy consumption. Multi-rover systems, consisting of multiple rovers, have become a preferred solution for Mars exploration, especially for large-scale monitoring missions, due to their strong adaptability, high processing efficiency, and robustness. Coverage control, a key technology for achieving efficient and comprehensive coverage, is a crucial component of multi-rover system control. Coverage control algorithms have a wide range of applications in various critical missions, such as target monitoring, terrain coverage, positioning services, and communication services, and possess significant engineering value. In coverage missions, a multi-rover system (MRS) can be viewed as a collection of coverage units, and the distribution of coverage targets in the mission space can be represented by their density function. Therefore, the goal of coverage control is to dynamically optimize the MRS deployment strategy based on the spatial target density distribution characteristics, thereby achieving precise coverage and focused monitoring of high-density areas.

[0003] Therefore, the mission of terrain coverage in unknown outer space will drive MRS to optimize its coverage quality to obtain high-value terrain data. Traditional research in the coverage field has focused on optimizing control strategies and adaptive expansion under known density conditions. However, outer space exploration often involves areas never before explored by humans. Furthermore, multiple factors such as cosmic radiation interference, the extreme environment of outer space, and bandwidth limitations of long-distance communications make it impossible to obtain high-precision prior terrain information within the mission area. This completely unknown prior information poses a significant challenge to developing MRS coverage deployment strategies.

[0004] Therefore, the low accuracy, low precision, and low efficiency of multi-robot coverage in a priori unknown environments have become technical problems that need to be solved urgently. Summary of the Invention

[0005] The present invention provides a multi-rover coverage method in an a priori unknown environment, which solves the technical problems of low accuracy, low precision and low efficiency of multi-rover coverage in an a priori unknown environment.

[0006] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0007] A multi-robot coverage method in an a priori unknown environment includes the following steps:

[0008] Step S1: deploy n rovers to form a multi-rovers network at the boundary of a target area that is completely unknown a priori, establish a virtual distribution, and drive the rovers evenly to their respective sub-target areas according to the centroid Voronoi partitioning;

[0009] Step S2: Design a sampling method to adaptively generate uniform sampling points in the sub-target area of ​​each rover and iteratively update the continuous round-trip sampling path;

[0010] Step S3: Based on the sampling path, each rover iterates and updates its estimate of the unknown prior in an online and distributed manner to form its own estimated mapping of the target distribution;

[0011] Step S4: During iterations, the estimation mappings of each rover are fused through a multi-source data fusion mechanism to improve the accuracy and consistency of the system's global estimation;

[0012] Step S5: Based on the Jensen-Shannong divergence, calculate the difference between the iterations of each rover and between each rover, and set a stability threshold as the basis for estimating the end of the iteration;

[0013] Step S6: Estimate and map the target distribution after weighted fusion, design the control rate of the rover, iteratively drive each rover to its own Voronoi centroid, and complete the autonomous planning and control of multi-rover coverage in a priori unknown environment.

[0014] A further technical solution is that: Step S1 specifically includes: in the target area Set the initial deployment area at the boundary of , place n rovers in the initial deployment area, establish a two-dimensional spatial coordinate system for the area, and set its coordinate set as , the spatial coordinates of a single rover are ; Set the target density function to a uniform positive virtual distribution , ; for Position in; by minimizing The cost function shown in the figure uses the centroid Voronoi segmentation method to drive each rover evenly to the Voronoi centroid shown in the following equation (2.1), and allocates the entire target area as a sub-area of ​​each rover. ;

[0015]

[0016] In formula (2.1), For sub-region The area For its centroid.

[0017] A further technical solution is: uniform sampling and reciprocating sampling path design; the sampling method in step S2 is specifically: for the first rover, in its sub-area at the sampling resolution Generate a uniformly sampled grid point set ; Initial resolution The selection of is generally large, which is to quickly form a rough estimate of the unknown target distribution in the early stage of sampling;

[0018] The reciprocating sampling path point set is constructed by flip connection, as shown in formula (3.1):

[0019]

[0020] In formula (3.1), is the set of sampling path points, is the number of columns of the sampling point set, m is the total number of columns of the sampling point set, is the connection function, specifically:

[0021]

[0022] In formula (3.2), is a flip operator; this function can connect sampling points in a reciprocating manner to form an efficient sampling path; in addition, in the process of iteratively generating the path graph, the resolution iteration method is set to:

[0023]

[0024] In formula (3.3), is the sampling resolution at the kth iteration, is the number of path iterations, is the sampling resolution at the k-1th iteration; in this iterative mode, each iteration will make the newly generated sampling path denser and have more sampling points; the parameter The calculation method is:

[0025]

[0026] In formula (3.4), For iterative convergence parameters, appropriate selection is made according to the map size. This design method is to quickly reduce the To enter the fine sampling process; In addition, the iterative path diagram is also used Connect different graphs, namely:

[0027]

[0028] In formula (3.5), The resolution is The sampling path point set at time ;

[0029] Therefore, the above generation algorithm can obtain a continuous and progressive sampling path from coarse to fine. The low resolution in the early stage can ensure the efficiency and uniform coverage of sampling, while the high resolution in the later stage can ensure the stability of sampling accuracy. In addition, the progressive method can reasonably set the resolution iteration convergence parameter. , which can effectively prevent repeated sampling and improve the credibility of the estimated mapping.

[0030] A further technical solution is that the estimation method in step S3 is specifically: setting a Gaussian process prior model for the unknown target density ; where the prior expectation is a constant function, the prior covariance Determined by the following formula:

[0031]

[0032] In formula (4.1), is the radial basis kernel function, For sample points is the prediction point; is the variance of the observation error, yes The kernel function's hyperparameters can be pre-trained with previous datasets to match the target distribution characteristics; thus, each rover can obtain Prior mapping of ;

[0033] According to the Kalman filter update rule, for s new observations The design iteration equation is:

[0034]

[0035]

[0036] In formula (4.2), represents the posterior expectation, is the Kalman gain, which is used to balance the weights of observation and prediction; is the covariance residual and is the observation residual; For one The observation matrix is ​​responsible for mapping the state value to the observation space; is a representation of the observation noise diagonal matrix;

[0037] In formula (4.3), represents the posterior covariance.

[0038] A further technical solution is to design a multi-source fusion mechanism based on the covariance matrix; the fusion mechanism designed in step S4 is specifically as follows:

[0039]

[0040] In formula (5.1), , For the The rover's own a posteriori estimate, For the The posterior expectation of the robots, For the The posterior covariance of the rovers, , For the The robot's adjacent The posterior estimate of the rovers, For the The posterior expectation of the robots, For the The posterior covariance of the rovers, is the total number of adjacent rovers; For the The weight of the robot itself, For the The robot's adjacent The weights of the bots are calculated as follows:

[0041]

[0042]

[0043] In formula (5.2) and formula (5.3), For the The inverse of the determinant of the posterior covariance of the rover itself, For the The robot's adjacent The inverse of the determinant of the posterior covariance of the rovers;

[0044] This method gives greater credibility to the estimated distribution with smaller error, and improves the accuracy and consistency of the overall estimate by assigning a larger weight; in this way, the new estimated distribution set after fusion can be updated and obtained .

[0045] A further technical solution is: a dual threshold design based on Jensen-Shannon divergence; the Jensen-Shannon divergence in step S5 can be expressed as:

[0046]

[0047] In formula (6.1), For distribution and The Jensen-Shannon divergence between and are two different distributions. yes and The mean of represents the Kullback-Leibler divergence, specifically:

[0048]

[0049] In formula (6.2), For distribution and The Kullback-Leibler divergence between them, q is the position of the target region T;

[0050] Therefore, by calculating the Jensen-Shannon divergence of each robot's own iteration, that is, the JS divergence, the degree of change of each robot in its own iteration process can be obtained. , these values ​​form the set , For the The prior expectation of robots, For the The posterior expectation of each robot; in addition, by calculating the JS divergence between robots, the degree of difference between robots can be compared. , these values ​​form the set , For the The posterior expectation of the number of robots;

[0051] According to the sampling density and map characteristics, a bi-stable threshold is designed for the JS and JO quantitative differences. and , the value range of the bistable threshold is (0, 0.001), where is the threshold for the rover to iteratively change itself during the density estimation process, and The reason for designing double thresholds is that due to the existence of observation errors and the fact that the sample data sources used by each rover for estimation are limited to its own sub-area, the differences between rovers are large. The value of will inevitably be greater than its own difference variation ; To avoid errors, additional design times threshold , the system can be judged to enter a stable state if and only if each difference continuously meets the double threshold condition for a set number of times.

[0052] A further technical solution is to design a control law for estimation density weighting; the control law in step S6 is: first, the estimation mapping set of the multi-roamer system is Perform mean fusion processing to obtain the estimated mapping of the target area: ; Assume that the global loss function in the coverage process is:

[0053]

[0054] In formula (7.1), is the global loss function in the coverage process, is the loss term in coverage, which means that the coverage quality loss of the target point in coverage increases with the Euclidean distance from the rover, that is, the unreliability of the measurement increases; the control law of the rover is designed according to the gradient descent,

[0055]

[0056] In formula (7.2), is the rover’s acceleration, and is the gain parameter, is the Voronoi center of mass, is the robot position, is the speed; parameter and The calculation of is as follows:

[0057]

[0058]

[0059] In formula (7.3) or formula (7.4), For robots and centroid The Euclidean distance, is the control law parameter, which is related to the map size and robot performance; is the distance threshold, and the control law switches according to the threshold to achieve the effect of quickly driving the rover to the specified position.

[0060] The beneficial effects of adopting the above technical solution are:

[0061] A multi-rover coverage method in an a priori unknown environment includes steps S1 to S6. Based on a multi-source fusion mechanism, the estimation data of each rover are weightedly fused to improve the overall estimation accuracy and consistency of the system; based on the control rate of the rover, each rover is iteratively driven to the optimal position, and the multi-rover coverage in the a priori unknown environment has high accuracy, high precision and high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of Example 1 of the present application;

[0063] Figure 2-1 This is a functional block diagram of the system in Example 2 of the present application;

[0064] Figure 2-2 This is the data flow diagram of Example 2 of the present application;

[0065] Figure 3 A distribution map showing the deployment and regional division of multiple rover systems;

[0066] Figure 4 A distribution map of sampling trajectory plans for each rover;

[0067] Figure 5 is the target true distribution map in the experiment;

[0068] Figure 6-1 This is the estimated distribution diagram of the online distributed estimation of unknown target distribution by the multi-rovers system when the number of iterations is 10;

[0069] Figure 6-2 This is the estimated distribution diagram of the online distributed estimation of unknown target distribution by the multi-rovers system when the number of iterations is 45;

[0070] Figure 7 is a graph showing the difference between the estimated mapping of each rover and the true value as a function of the number of iterations;

[0071] Figure 8 The distribution diagram of the rover position changes of the multi-rover system under the weight of the estimated distribution;

[0072] Figure 9 The graph shows the changes in the global loss function under the estimated density weighting and without estimated density weighting. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0074] In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0075] Example 1:

[0076] like Figure 1 As shown, the present invention discloses a multi-robot coverage method in a priori unknown environment, comprising the following steps:

[0077] Step S1: Deploy n rovers at the boundary of a target area that is completely unknown a priori to form a multi-rovers network, establish a virtual distribution and use the centroid Voronoi segmentation method to evenly drive the rovers to their respective sub-target areas.

[0078] Specifically, step S1 is: establish a rectangular coordinate system in the task space, deploy The position set of the multi-rover system composed of each rover is , among which The spatial coordinates of the rover are At this time, the prior information of the target distribution is completely unknown, so its virtual density is set to uniform distribution .

[0079] The objective function when setting the region division is:

[0080]

[0081] In formula (1), A sub-region corresponding to each robot. represents the coverage loss term, which represents the target point With robots The larger the Euclidean distance, the greater the exist The more the information obtained, the less reliable it is, or the greater the loss of coverage quality. When the target density is uniformly distributed, this method can drive each rover to divide the entire mission area in a uniform manner. is the set of their respective sub-regions .

[0082] Calculate the rover position from equation (1) The partial derivatives of are:

[0083]

[0084] In formula (2), For sub-region The area Its centroid. Using this centroid Voronoi segmentation, the original target area can be assigned to each rover, reducing its computational burden. Equation (2) is a variation of Equation (2.1).

[0085] Step S2: Design a sampling method to adaptively generate uniform sampling points in the sub-target area that each rover is responsible for and continuously iteratively update the continuous round-trip sampling path.

[0086] Specifically, step S2 is: after the area is divided, in order to obtain the target area The sample data in the need to design a reasonable sampling method to drive each robot In the area you are responsible for The following sampling rules are designed to ensure the uniformity and efficiency of sampling. First, in the convex polygon sub-area that each rover is responsible for, the initial resolution is used. Generate uniform grid sampling points ,The initial resolution is generally large, in order to quickly form a rough estimate of the entire sub-region at the beginning of sampling.

[0087] The sampling path is formed according to the following rules,

[0088]

[0089] In formula (3), is the set of sampling path points, is the number of columns of the sampling point set, m is the total number of columns of the sampling point set, is the connection function, specifically:

[0090]

[0091] In formula (4), is the flip operator. This function can connect the sampling points in a reciprocating manner to form an efficient sampling path.

[0092] In addition, during the iterative generation of the path map, the resolution iteration mode is set as:

[0093]

[0094] In formula (5), is the sampling resolution at the kth iteration, is the number of path iterations, is the sampling resolution at the k-1th iteration. In this iterative method, each iteration will make the newly generated sampling path denser and have more sampling points.

[0095] parameter The calculation method is:

[0096]

[0097] In formula (6), For iterative convergence parameters, appropriate selection is made according to the map size. This design method is to quickly reduce the To enter the fine sampling process.

[0098] In addition, the iterative path diagram is also used Connect different graphs, namely:

[0099]

[0100] In formula (7), The resolution is The sampling path point set at time ;

[0101] Formula (3) is a deformation of formula (3.1), formula (4) is formula (3.2), formula (5) is formula (3.3), formula (6) is formula (3.4), and formula (7) is formula (3.5).

[0102] Therefore, by using the above generation algorithm, a continuous and progressive sampling path from coarse to fine can be obtained. The low resolution in the early stage can ensure the efficiency and uniform coverage of sampling, while the high resolution in the later stage can ensure the stability of sampling accuracy. In addition, this progressive method can reasonably set the resolution iteration convergence parameter. , which can effectively prevent repeated sampling and improve the credibility of the estimated mapping.

[0103] Step S3: Based on the sampling path, each rover iterates and updates its estimate of the unknown prior in an online distributed manner to form its own estimated mapping of the target distribution.

[0104] Specifically, step S3 is: the density distribution of the target area is completely unknown a priori A two-dimensional Gaussian process model prior is established to map the probability and non-parametric estimation for it. Its expression is as follows:

[0105]

[0106] In formula (8), and are the prior expectation and prior covariance of the target distribution, respectively.

[0107] A uniform zero constant is used as the distribution form of the prior expectation, and the prior covariance is derived from the following Gaussian process derivation formula:

[0108]

[0109] In formula (9), is the initial position of the rover after division, is the set of locations that need to be predicted. The error in the observation process is set to Gaussian noise . for The identity matrix of . represents the kernel function, which is used to control the properties and behavior of the model. Equation (9) is the same as Equation (4.1).

[0110] The kernel function uses the radial basis kernel (RBF), which has the following form:

[0111]

[0112] In formula (10), and are two hyperparameters of the kernel function. The kernel function can be pre-trained using previous map data to match the characteristics of the target distribution.

[0113] In addition, during the sampling process, the sample set is set to , due to observation error, its sample value is .in For location The true density distribution at . Therefore, we can obtain The corresponding sample value set According to the designed online distributed Gaussian process regression equation, based on the sampling samples between iterations and , each robot can continuously update the prior expectation and covariance into a posterior model .

[0114] The iterative equation is as follows:

[0115]

[0116]

[0117] In formula (11), represents the posterior expectation, and Equation (11) is Equation (4.2).

[0118] In formula (12), represents the posterior covariance, and Equation (12) is Equation (4.3).

[0119] in Represents the Kalman gain, which is used to balance the weight of the estimate and the state. and represent the covariance residual and the observation residual, respectively. is a representative observation error The covariance of The diagonal matrix is a The observation matrix maps the state value to the observation space. Therefore, through equations (11) and (12), each rover can obtain an estimated mapping of the unknown target distribution, forming a matrix containing A collection of estimated distributions .

[0120] Step S4: During iterations, the estimation mappings of each rover are fused through a multi-source data fusion mechanism to improve the accuracy and consistency of the system's global estimation.

[0121] Specifically, step S4 is: after each iteration, a multi-source data fusion mechanism is designed to gradually improve the accuracy and consistency of the global target distribution estimation. The fusion mechanism used is as follows:

[0122]

[0123] In formula (13), , For the The rover's own a posteriori estimate, For the The posterior expectation of the robots, For the The posterior covariance of the rovers, , For the The robot's adjacent The posterior estimate of the rovers, For the The posterior expectation of the robots, For the The posterior covariance of the rovers, is the total number of adjacent rovers; For the The weight of the robot itself, For the The robot's adjacent The weight of each robot, formula (13) is the same as formula (5.1).

[0124] and are the weight parameters of each rover, and their calculation formulas are as follows:

[0125]

[0126]

[0127] In formula (15), For the The inverse of the determinant of the posterior covariance of the rover itself, For the The robot's adjacent The inverse of the posterior covariance determinant of each rover; this method gives greater credibility to the estimated distribution with smaller error, and improves the accuracy of the overall estimate by assigning a larger weight. In this way, the new estimated distribution set after fusion can be updated and obtained Formula (15) is the same as Formula (5.2), and Formula (14) is the same as Formula (5.3).

[0128] Step S5: Based on the Jensen-Shannong divergence, calculate the difference in changes between each rover's own iterations and between each rover, and design a double threshold method to judge stability, which is used as the basis for estimating the end of iteration.

[0129] Specifically, step S5 is as follows: During the iteration process, the differences between each robot and between robots can be quantitatively represented by the Jensen-Shannon (JS) divergence. The JS divergence is a modified Kullback-Leibler (KL) divergence with symmetry. It can be expressed as:

[0130]

[0131] In formula (16), For distribution and The Jensen-Shannon divergence between and are two different distributions. is their mean distribution, expressed as , formula (16) is formula (6.1).

[0132] represents the KL divergence, which is expressed as:

[0133]

[0134] In formula (17), For distribution and The Kullback-Leibler divergence between q and q is the position in the target region T. Equation (17) is the same as Equation (6.2).

[0135] Therefore, by calculating the Jensen-Shannon divergence of each robot's own iteration, that is, the JS divergence, the degree of change of each robot in its own iteration process can be obtained. , these values ​​form the set , For the The prior expectation of robots, For the In addition, by calculating the JS divergence between robots, the degree of difference between robots can be compared. , these values ​​form the set , For the The posterior expectation of the robot. The range of the normalized JS divergence is [ , the closer it is to 0, the smaller the difference between the two distributions. In areas with unknown target density, the difference from the true value cannot be obtained because the true value is unknown. However, the stability of the system can be determined by calculating the JS divergence between the rover's own iterations and between rovers.

[0136] According to the sampling density and map characteristics, a bi-stable threshold is designed for the JS and JO quantitative differences. and , the value range of the bistable threshold is (0, 0.001), where is the threshold for the rover to iteratively change itself during the density estimation process, and The reason for designing double thresholds is that due to the existence of observation errors and the fact that the sample data source used by each rover for estimation is limited to its own sub-area, the difference between rovers is large. The value of will inevitably be greater than its own difference variation To avoid errors, additional design times threshold , the system can be judged to enter a stable state if and only if each difference continuously meets the double threshold condition for a set number of times.

[0137] Step S6: Estimate the target distribution after weighted fusion and map it. Design the control rate of the rover and use the gradient descent method to iteratively drive each rover to its own Voronoi centroid to complete the autonomous planning and control of multi-rover coverage in an a priori unknown environment.

[0138] Specifically, step S6 is: after iterating through the estimation framework and finally obtaining a stable set of estimation mappings, each estimation mapping is fused by arithmetic mean to obtain the final estimation result. Therefore, by weighting this estimated density, the loss function can be obtained The specific expression is as follows:

[0139]

[0140] The control law of the rover designed for it is:

[0141]

[0142] In formula (19), is the acceleration of the rover, parameter and is the control law gain, For the Weno area The corresponding center of mass, is the robot position, For speed.

[0143] Each rover will move to the optimal position under the control rate to minimize the loss. The calculation formula of the parameters is:

[0144]

[0145]

[0146] In formula (20), Representative robot and centroid The Euclidean distance, are parameter gains, and are distance thresholds, and their values ​​depend on the size of the map.

[0147] In formula (21), is the parameter gain.

[0148] The principle of Equations (20) and (21) is that when the distance is far, the control law based on the distance will quickly drive the rover to the vicinity of the target point, while when the distance is close, the control method will be changed to avoid oscillation, thereby achieving rapid control of the rover to reach the target point.

[0149] Formula (18) is the same as Formula (7.1), Formula (19) is the same as Formula (7.2), Formula (20) is the same as Formula (7.3), and Formula (21) is the same as Formula (7.4).

[0150] Example 1 includes virtual coverage, subdomain division, adaptive iterative sampling path planning, online distributed density estimation, multi-source data fusion, difference calculation and system stop judgment, and estimated density weighted rover control method. Compared with the existing technology, the beneficial effects of this application are as follows.

[0151] This application designs a new estimation method that can model a target space that is completely unknown a priori and estimate and restore its information distribution. Compared with traditional methods, this estimation method has both online and distributed characteristics, with advantages such as real-time updates, higher computational efficiency, and stronger parallel data processing capabilities. In addition, this method allows a multi-rover system to perform coverage tasks in an unknown mission area in a probabilistic and non-parametric manner, and has strong adaptability to unknown environments. The method has a low computational load, and its complexity is positively correlated with the resolution of the raster map. Therefore, its computational load can be adaptively adjusted according to the map size and mission requirements.

[0152] The multi-source fusion method designed in this application can achieve efficient fusion of the estimated distributions of each rover. The weight of each distribution is determined by its degree of dispersion, and the distribution with lower dispersion is used as the component with greater weight. This can effectively improve the accuracy and consistency of the global estimate.

[0153] By using the Voronoi segmentation method of virtual density, this application can evenly divide the target area of ​​a convex polygon into multiple convex polygon sub-areas, drive each rover and allocate its own area, which not only avoids the collision problem of the rover in the subsequent measurement process, but also improves the estimation efficiency of the multi-rover system, and facilitates the sampling allocation and density estimation of each rover in the later stage.

[0154] The sampling method designed in this application enables a progressive estimation process from coarse to fine. Initially, a low-resolution sampling approach is used to quickly sample the rough outline. As iterations progress, the sampling grid resolution is adaptively increased, and precise sampling is performed to further refine the estimated map until the estimated distribution stabilizes. This balances both estimation efficiency and accuracy.

[0155] This application designs a dual difference quantification calculation method for the rover itself and between rovers through the Jensen-Shannong divergence, and sets a dual stability threshold as a stability condition for the estimated iteration, which can effectively quantify the iterative state and terminate the iteration under the condition that the true value of the target distribution is unknown.

[0156] The distributed rover control law designed in this application, combined with the estimated mapping of target density distribution, can effectively achieve local optimal deployment of rovers and minimize coverage loss.

[0157] Example 2:

[0158] The present invention discloses a multi-rover coverage method for an a priori unknown environment. The method comprises three major parts: a pre-estimation region division step, an online distributed density estimation step, and a final estimated density weighted coverage control step. The pre-estimation region division step is the initialization and region division control step, while the estimated density weighted coverage control step is the optimal coverage control under the estimated density weighting.

[0159] like Figure 2-1 As shown, the system includes a region division module, an online distributed density estimation module and an estimated density weighted coverage control module. The region division module is used to implement the region division step, the online distributed density estimation module is used to implement the online distributed density estimation step, and the estimated density weighted coverage control module is used to implement the estimated density weighted coverage control step.

[0160] like Figure 2-2 As shown, the initial deployment area is input into the area division module, and the divided area is obtained by uniform coverage based on virtual uniform density and input into the online distributed density estimation module. The data obtained by sensor sampling is processed for density estimation. In this process, the data is subjected to prior, posteriori, and multiple iterations to obtain JS divergence. The estimated density obtained by multi-source data fusion is input into the weighted coverage control module, i.e., the optimal coverage control module, for coverage control and loss function processing. The specific method steps are detailed as follows.

[0161] First, the region division step includes the following steps.

[0162] Step 1.1: When starting to divide the virtual density area, first set the initialization parameters according to the map size, the accuracy of the sensors on the rover, etc. These parameters include the number of rovers in the multi-rovers system n, the target grid map resolution , region partitioning iteration stable distance condition And the number of conditions .

[0163] Step 1.2: Deploy a multi-robot system. You can select a portion of the target area, such as the lower left corner, as the robot initialization deployment area, or deploy it randomly.

[0164] Step 1.3: Set a virtual uniform density , and perform iterative centroid Voronoi segmentation on the target area based on the virtual density, and use the rover step size As a restriction.

[0165] Step 1.4: Calculate the movement distance of each robot during the iteration process , and continues with the distance threshold Compare, when the conditions are met Reached times When , the iterative process is judged to have reached a steady state and the iteration is terminated.

[0166] like Figure 3 As shown, the moving paths of the first rover 1 to the fifth rover 5 in the area segmentation are shown, the horizontal axis represents the coordinate in the X direction, the unit is meter, the English symbol m, and the vertical axis represents the coordinate in the Y direction, the unit is meter, the English symbol m.

[0167] After the above steps, the unknown target area can be divided into five areas, and each rover corresponds to one area.

[0168] Thereafter, the online distributed density estimation step includes the following steps.

[0169] Step 2.1: Set the initialization parameters for density estimation, including the kernel function hyperparameters and . Sampling initial resolution Resolution iteration parameters . Estimation of the stable number of iterations And self-iterative JS divergence threshold and JS divergence threshold between robots , the sensor's observation error variance .

[0170] Step 2.2: Use Gaussian process to model the target distribution and make its expected function a constant value of zero. Use RBF function as the kernel function, the expression is:

[0171]

[0172] Based on the robot position, hyperparameters and the new predicted position, its covariance matrix is ​​obtained by the following formula.

[0173]

[0174] Step 2.3: At sampling resolution Generates a set of grid sampling points in each rover's sub-area , a round-trip sampling path is formed according to the generation rule of the following formula.

[0175]

[0176] Step 2.4: During the iteration process of the path diagram, design the following formula:

[0177]

[0178] According to the resolution iteration rule, the resolution is adjusted along with the sampling process to form a progressive sampling effect from coarse to fine.

[0179] like Figure 4 As shown in the figure, this sampling process is demonstrated, in which the fourth rover 4 and the fifth rover 5 have just completed the first round of sampling trajectory and the first three rovers have started the second round. The first three rovers include the first rover 1, the second rover 2 and the third rover 3. The horizontal axis represents the coordinate in the X direction, the unit is meter, the English symbol m, and the vertical axis represents the coordinate in the Y direction, the unit is meter, the English symbol m.

[0180] Step 2.5: Based on the new sample data obtained in the sampling, the unknown density is estimated and mapped online and distributed according to the designed iterative equation. The update equation used is:

[0181]

[0182]

[0183] The above iteration method can continuously update the estimation of the unknown distribution of each rover. According to the fusion mechanism, the estimated distribution of each rover is weighted with the estimated distribution of its neighboring rovers. The formula is as follows:

[0184]

[0185] The parameters and The calculation is done using the following formula:

[0186]

[0187]

[0188] Step 2.6: Plot the estimated distribution of each rover according to the expectation function in the iteration, according to its covariance matrix To obtain a 95% confidence interval, use the following formula:

[0189]

[0190] This interval is superimposed on the expected distribution to form an estimated mapping of the unknown distribution by each rover.

[0191] like Figure 5 As shown in the figure, the target distribution during the experiment is shown. The horizontal axis represents the coordinate in the X direction, the unit is meter, the English symbol m, the vertical axis represents the coordinate in the Y direction, the unit is meter, the English symbol m, and the vertical axis represents the true density. .

[0192] like Figure 6-1 As shown, the estimated mapping of each robot is shown when the iteration reaches the 10th time.

[0193] like Figure 6-2 As shown, the estimated mapping of each rover is shown when the iteration reaches the 45th time.

[0194] Step 2.7: In the iteration, calculate the JS divergence of each robot's own iteration , and JS divergence between bots According to the dual-threshold composite judgment method, when the two divergences meet their respective thresholds and The number of times reaches the convergence threshold When , the estimated model is determined to have converged; otherwise, the iteration continues.

[0195] like Figure 7 As shown, the difference between the robot and the true value is shown As the number of iterations changes, the horizontal axis represents the number of iterations and the vertical axis represents the difference .

[0196] After the above steps, the density of the unknown target area can be estimated and the estimated density can be obtained.

[0197] Thereafter, the estimation density weighted coverage control step includes the following steps.

[0198] Step 3.1: Combine the estimates of the unknown density obtained by each rover Perform the average operation to obtain the final estimated distribution .

[0199] Step 3.2: If Figure 8 As shown, the estimated distribution Weighted to the global loss function, according to the following robot control law,

[0200]

[0201] The parameters are calculated as:

[0202]

[0203]

[0204] The parameters Set according to the map size and the robot's own mobility performance.

[0205] like Figure 8 As shown, the horizontal axis represents the coordinate in the X direction, the unit is meter, the English symbol is m, and the vertical axis represents the coordinate in the Y direction, the unit is meter, the English symbol is m.

[0206] Step 3.3: Calculate the rover's movement distance during the control law iteration , set the threshold parameters and the number of parameters , when the robot moves a distance Continuous satisfaction When the number of rovers reaches 0, the rovers are determined to be stable; otherwise, the number of rovers is reset and the iteration continues.

[0207] Step 3.4: If Figure 9 As shown, when performing coverage control, the loss function is calculated synchronously to obtain a loss function change curve.

[0208] like Figure 9 As shown, the horizontal axis represents the number of iterations, and the vertical axis represents the loss function value C. The coverage control curve of the estimated density loss is above the coverage control curve under the estimated density. As the number of iterations increases, the loss function value C of the coverage control curve under the estimated density decreases.

[0209] In summary, this application proposes a multi-rover coverage method in an a priori unknown environment in order to solve the problems of narrow adaptability, low efficiency and complex calculation of existing multi-rover systems in coverage tasks in a priori completely unknown scenarios such as deep space planetary exploration. The method includes: deploying n rovers to form a multi-rovers network at the boundary of a target area that is completely unknown a priori, establishing a virtual distribution and driving the rovers evenly to their respective sub-target areas according to Voronoi partitioning; designing a sampling method to adaptively generate uniform sampling points in the sub-target area responsible for each rover and continuously iteratively update a continuous round-trip sampling path; based on the sampling path, each rover iterates and updates its estimate of the unknown prior in an online and distributed manner to form its own estimated mapping of the target distribution; designing a multi-source fusion mechanism to improve the overall estimation accuracy and consistency of the system by weighted fusion of the estimated data of each rover; based on the Jensen-Shannong divergence, calculating the change differences between each rover's own iterations and between each rovers, and designing a dual threshold mechanism to use this as the basis for stopping the estimation iteration; based on the weighted fusion target distribution estimation mapping, designing the rover control rate, iteratively driving each rover to the optimal position, minimizing the coverage loss, and completing the autonomous planning and control of multi-rovers coverage in an a priori unknown environment.

Claims

1. A multi-robot coverage method in an a priori unknown environment, characterized by: The steps include: Step S1: deploy n rovers to form a multi-rovers network at the boundary of a target area that is completely unknown a priori, establish a virtual distribution, and drive the rovers evenly to each rover's sub-target area based on centroid Voronoi partitioning; Step S2: Design a sampling method to adaptively generate uniform sampling points in each rover's sub-target area and iteratively update the continuous round-trip sampling path; Step S3: Based on the sampling path, each rover iteratively updates its estimate of the unknown prior in an online and distributed manner, forming an estimated mapping of the target distribution for each rover; Step S4: obtaining a multi-source data fusion mechanism, and fusing each rover's estimated mapping through the multi-source data fusion mechanism during iterations; Step S5: Calculate the difference between each rover's own iterations and that of other rovers based on the Jensen-Shannong divergence, and set a stability threshold as the basis for estimating the end of iteration. Step S6: Estimated target distribution mapping after weighted fusion is designed to obtain the control rate of the rover, and each rover is iteratively driven to its own Voronoi centroid to complete the autonomous planning and control of multi-rover coverage in a priori unknown environment.

2. The multi-robot coverage method in an a priori unknown environment according to claim 1, characterized in that: The step S1 specifically includes the following steps: Set the initial deployment area at the boundary of , place n rovers in the initial deployment area, establish a two-dimensional spatial coordinate system for the area, and set the coordinate set as , the spatial coordinates of a single rover are ; Set the target density function to a uniform positive virtual distribution , ; for Position in; by minimizing The cost function shown in the figure uses the centroid Voronoi segmentation method to drive each rover evenly to the Voronoi centroid shown in the following equation (2.1), and allocates the entire target area as a sub-area of ​​each rover. ; In formula (2.1), For sub-region The area For its centroid.

3. The multi-robot coverage method in an a priori unknown environment according to claim 1, characterized in that: The step of obtaining the sampling method in step S2 includes the following steps: rover, in its sub-area at the sampling resolution Generate a uniformly sampled grid point set ; The reciprocating sampling path point set is constructed by flip connection, as shown in formula (3.1): In formula (3.1), is the set of sampling path points, is the number of columns of the sampling point set, m is the total number of columns of the sampling point set, is the connection function, specifically: In formula (3.2), is the flip operator; in the process of iteratively generating the path graph, the resolution iteration mode is set to: In formula (3.3), is the sampling resolution at the kth iteration, is the number of path iterations, is the sampling resolution at the k-1th iteration; parameter The calculation formula is: In formula (3.4), is the iterative convergence parameter; it is also used between the iterative path diagrams Connect different graphs, namely: In formula (3.5), The resolution is The sampling path point set at time ; A continuous and progressive sampling path from coarse to fine is obtained.

4. The multi-robot coverage method in an a priori unknown environment according to claim 1, characterized in that: The estimation step in step S3 includes the following steps: setting a Gaussian process prior model for the unknown target density ; Let the prior expectation is a constant function, the prior covariance Determined by the following formula: In formula (4.1), is the radial basis kernel function, For sample points is the prediction point; is the variance of the observation error, yes The kernel function's hyperparameters are pre-trained with previous datasets to match the target distribution characteristics; each robot obtains Prior mapping of ; According to the Kalman filter update rule, for s new observations The design iteration equation is: In formula (4.2), represents the posterior expectation, is the Kalman gain, which is used to balance the weights of observation and prediction; is the covariance residual, is the observation residual; For one The observation matrix is ​​responsible for mapping the state value to the observation space; is a representation of the observation noise diagonal matrix; In formula (4.3), represents the posterior covariance.

5. The multi-robot coverage method in an a priori unknown environment according to claim 1, characterized in that: The step of obtaining the multi-source data fusion mechanism in step S4 includes the following steps: In formula (5.1), , For the The rover's own a posteriori estimate, For the The posterior expectation of the robots, For the The posterior covariance of the rovers, , For the The robot's adjacent The posterior estimate of the rovers, For the The posterior expectation of the robots, For the The posterior covariance of the rovers, is the total number of adjacent rovers; For the The weight of the robot itself, For the The robot's adjacent The weight of a robot is calculated as follows: In formula (5.2) and formula (5.3), For the The inverse of the determinant of the posterior covariance of the rover itself, For the The robot's adjacent The inverse of the determinant of the posterior covariance of the rovers; Able to update and obtain the new estimated distribution set after fusion .

6. The multi-robot coverage method in an a priori unknown environment according to claim 1, characterized in that: The Jensen-Shannon divergence in step S5 is expressed as, In formula (6.1), For distribution and The Jensen-Shannon divergence between and are two different distributions. yes and The mean of represents the Kullback-Leibler divergence, specifically: In formula (6.2), For distribution and The Kullback-Leibler divergence between them, q is the position of the target region T; By calculating the Jensen-Shannon divergence (JS divergence) of each robot's own iteration, the degree of change of each robot in its own iteration process is obtained. , these values ​​form the set , For the The prior expectation of robots, For the The posterior expectation of each robot; by calculating the JS divergence between robots, the degree of difference between each robot can be compared , these values ​​form the set , For the The posterior expectation of the number of robots; According to the sampling density and map characteristics, a bi-stable threshold is designed for the JS and JO quantitative differences. and , the value range of the bistable threshold is (0, 0.001), is the threshold for the rover’s own iteration change during the density estimation process, The difference threshold between the estimated distribution of the rover and other rovers during the density estimation process; set the number threshold , the system is judged to enter a stable state if and only if each difference continuously meets the double threshold condition for a set number of times.

7. The multi-robot coverage method in an a priori unknown environment according to claim 1, characterized in that: The step of obtaining the control rate of the rover in step S6 includes the following steps: Perform mean fusion processing to obtain the estimated mapping of the target area: ; Assume that the global loss function in the coverage process is: In formula (7.1), is the global loss function in the coverage process, is the loss term in coverage, indicating that the coverage quality loss of the target point in coverage increases with the Euclidean distance from the rover, that is, the increase in the degree of unreliability of the measurement; the control law of the rover is designed according to the gradient descent, In formula (7.2), is the rover’s acceleration, and is the gain parameter, is the Voronoi center of mass, is the robot position, is the speed; parameter and The calculation of is as follows: In formula (7.3) or formula (7.4), For robots and centroid The Euclidean distance, is the control law parameter, which is related to the map size and robot performance; is the distance threshold, and the control law switches according to this threshold.

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