CN116382307A - Multi-robot autonomous exploration method and system based on mass centers of unknown connected areas - Google Patents
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Abstract
The invention discloses a multi-robot autonomous exploration method and a system based on an unknown connected region centroid, and relates to the technical field of multi-robot collaborative autonomous exploration, wherein the method comprises the following steps: dividing an unknown area to be explored by using a voronoi diagram, and distributing the voronoi diagram partition responsible for exploration for the robot; selecting a global exploration window and a local exploration window around a robot team and around each robot respectively; extracting unknown connected areas of all the exploration windows; calculating the mass center of the unknown connected region; and determining the exploration area of the robot by using the value of the designed non-parametric utility function. In the multi-robot collaborative autonomous exploration process, the centroid is estimated through the designed non-parametric utility function by utilizing the multi-robot collaborative strategy based on the voronoi diagram and the exploration strategy based on the centroid guidance of the unknown communication area, so that the multi-robot autonomous exploration efficiency is improved.
Description
Technical Field
The invention relates to the technical field of multi-robot collaborative autonomous exploration, in particular to a multi-robot autonomous exploration method and system based on an unknown connected region centroid.
Background
The problem of collaborative autonomous exploration of multiple robots is always a hot spot research problem in the field of robots. The robot autonomous exploration mainly solves the problems that the robot autonomously selects an unknown area and explores a target point, safely and efficiently goes to the target point to conduct map drawing, and the unknown environment exploration is completed with the lowest consumption cost. Meanwhile, in order to improve the exploration efficiency, the autonomous exploration algorithm can be applied to multi-robot collaborative exploration.
The autonomous exploration strategy in the current multi-robot autonomous exploration method mainly comprises two main categories, namely an exploration strategy based on boundary points and an exploration strategy based on viewpoint sampling.
The searching strategy based on the boundary points refers to calculating the boundary between the unknown region and the known free region, evaluating the boundary by considering the area of the unknown region around the boundary and the distance between the robot and the boundary, and selecting the best boundary to guide the robot to search the unknown environment. The method has the problems of low boundary calculation efficiency, slow boundary updating, limitation of boundary evaluation and the like.
The exploration strategy based on viewpoint sampling refers to uniformly or unevenly scattering viewpoints in an exploration space, constructing a road network diagram by the viewpoints, calculating potential exploration values of each path formed in the road network diagram, and finally enabling the robot to execute the path with the highest exploration value. The main consideration of the exploration value is the area of the unknown area around each viewpoint on the path and the path length. The method has the problems that the robot repeatedly turns back between two paths, the exploration environment is incomplete, and the like.
In addition, the multi-robot cooperative strategy in the multi-robot autonomous exploration method mainly includes a cooperative method based on actions, a cooperative method based on market-auction, and a cooperative method based on division areas. The multi-robot collaborative exploration is used, so that the exploration efficiency is improved, and the system has stronger fault tolerance and stability. However, the conventional collaborative method tends to cause a different robot to repeatedly search the same unknown region, and thus the collaborative search efficiency is low.
In the collaborative autonomous exploration of multiple robots, how to solve the problems of low exploration efficiency and low collaborative efficiency of the existing method is a remarkable research content.
Disclosure of Invention
The invention aims to solve the problems of low exploration efficiency and low cooperative efficiency of the existing multi-robot cooperative autonomous exploration technology. Therefore, the invention aims to provide a multi-robot autonomous exploration method and a system based on the barycenter of an unknown connected region, and in multi-robot cooperative autonomous exploration, the multi-robot cooperative autonomous exploration efficiency is improved by evaluating the barycenter through a designed non-parametric utility function by utilizing a multi-robot cooperative strategy based on a Voronoi diagram and an exploration strategy based on barycenter guidance of the unknown connected region.
In order to achieve the above purpose, the invention provides a multi-robot autonomous exploration method based on the mass center of an unknown connected region, which comprises the following steps:
step S1, dividing an unknown region to be explored by using a Veno map to obtain a Veno map partition, and distributing the Veno map partition responsible for exploration to each robot so that each robot explores in the associated Veno map partition;
step S2, selecting global exploration windows around a team consisting of robots, and selecting local exploration windows around each robot;
step S3, if the unknown connected areas exist in the local exploration window, extracting all the unknown connected areas in the local exploration window, and entering a step S4, otherwise, judging whether the unknown connected areas exist in the global exploration window, if so, extracting all the unknown connected areas in the global exploration window, and entering a step S4, and if not, entering a step S5;
step S4, calculating the mass centers of all unknown connected areas determined in the exploration window, calculating the value of the non-parametric utility function of each mass center, determining the unknown connected area explored at this time according to the value of the non-parametric utility function, and returning to the step S1 after the exploration is completed;
and S5, if all robots do not find the unknown communication area, ending the exploration task, otherwise, entering the step S1.
Further, in the step S1, when the unknown area to be searched is divided by using the voronoi diagram, the real-time position of each robot is taken as the base point of the voronoi diagram division, and the voronoi diagram division with the number equal to the number of robots is divided on the unknown area to be searched.
Further, in the step S2, the global search window is a minimum circumscribed rectangle including all robots.
Further, in the step S2, the local search window is a rectangle centered on the real-time position of each robot.
Further, the local search window is created by the following steps: setting a rectangle with a length of a and a width of b as a center by taking the real-time position of each robot as a center, dynamically expanding the length and the width of the rectangle, increasing the length by c and increasing the width by c each time, wherein c is an expansion parameter, stopping expanding when at least one edge is completely positioned in an unknown area or positioned on a map boundary, and the rectangular area at the moment is a local exploration window of the robot.
Further, the centroid of the unknown connected region is obtained through calculation of the contour moment.
Further, the formula of the non-parametric utility function is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
f(c i ,r,p k ) The value of the parametrized function of the ith centroid of the kth robot,
c i as the i-th centroid, the centroid,
p k for the kth robot,
s(c i r) is defined as centroid c i Is the center of the circle, r is the area of the unknown region contained by the radius circle,
d(c i , p k ) Is the centroid c i With robot p k Euclidean distance between them. Further, an unknown connected region corresponding to the largest value in the values of the non-parametric utility function is selected as the unknown connected region explored by the robot.
Further, the centroid of the unknown connected region serves as a search target for the current search of the robot.
A multi-robot autonomous exploration system based on the centroid of an unknown connected region, using the multi-robot autonomous exploration method based on the centroid of the unknown connected region as described in any one of the above, comprising the following modules:
the voronoi diagram partitioning module: dividing an unknown region to be explored by using a voronoi diagram to obtain a voronoi diagram partition, and distributing the voronoi diagram partition responsible for exploration to each robot so that each robot explores in the associated voronoi diagram partition;
window dividing module: the voronoi diagram partitioning module is connected with the voronoi diagram partitioning module and is used for selecting a global exploration window and a local exploration window;
unknown connected region extraction module: the window dividing module is connected with the window dividing module, if an unknown connected region exists in the local exploration window, the unknown connected region of the exploration is determined in the local exploration window, otherwise, whether the unknown connected region exists in the global exploration window is judged, if the unknown connected region exists in the global exploration window, the unknown connected region of the exploration is determined in the global exploration window, and if the unknown connected region does not exist, the exploration is ended;
the parameter-free utility function calculation module: the unknown connected region extraction module is connected with the unknown connected region extraction module and is used for evaluating the mass center of the unknown connected region extracted by the unknown connected region extraction module and calculating the value of the non-parametric utility function of the mass center;
the exploration task determination module: the system comprises a non-parametric utility function calculation module, a non-parametric utility function calculation module and a mass center calculation module, wherein the non-parametric utility function calculation module is connected with the non-parametric utility function calculation module and is used for selecting an unknown connected region for each robot to be explored according to the value of the non-parametric utility function, and the mass center of the unknown connected region is used as an exploration target of the robot.
Compared with the prior art, the invention has the beneficial effects that:
firstly, in the multi-robot collaborative autonomous exploration process, the multi-robot collaborative strategy based on the Veno diagram is utilized, so that the problem that different robots explore the same unknown area at the same time is avoided, and the multi-robot collaborative efficiency is improved;
secondly, by utilizing an exploration strategy based on the centroid guidance of the unknown connected region, the unknown region can be accurately and rapidly positioned, and the autonomous exploration efficiency is improved;
thirdly, the invention designs the non-parametric utility function for acquiring the unknown connected region and the exploration target explored in the next step, and the non-parametric utility function evaluates the potential exploration value of the centroid by using the exploration gain obtained when the robot moves to the centroid by the unit Euclidean distance, and more accurately and conveniently determines the unknown connected region to be explored according to the evaluation result.
In conclusion, compared with the prior art, the multi-robot collaborative autonomous exploration system has the advantage that the exploration efficiency is greatly improved.
Drawings
FIG. 1 is a flow diagram of a multi-robot autonomous exploration method of the present invention;
FIG. 2 is a detailed flow chart of calculating the centroid of an unknown connected region;
fig. 3 is a block diagram of a multi-robot autonomous exploration system according to the present invention.
Detailed Description
In order to make the present application solution better understood by those skilled in the art, the following description will be made in detail and with reference to the accompanying drawings in the embodiments of the present application, it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, shall fall within the scope of the present application. It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other.
As shown in fig. 1, the invention provides a multi-robot autonomous exploration method based on the mass center of an unknown connected region, which comprises the following steps:
and S1, dividing an unknown region to be explored by using a voronoi diagram to obtain a voronoi diagram partition, and distributing the voronoi diagram partition responsible for exploration to each robot so that each robot explores in the associated voronoi diagram partition.
A Voronoi Diagram (Voronoi Diagram) is composed of a set of consecutive polygons consisting of perpendicular bisectors connecting two adjacent point lines. The method has the following characteristics:
(1) Dividing a plane into n polygonal domains by the Veno graph, wherein each polygon is provided with only one generating element, and n is the number of base points;
(2) The distance from a point within each polygon to the generator is shorter than the distance to other generators;
(3) The distances from the point on the polygon boundary to the two generating elements generating the boundary are equal;
(4) The Voronoi polygon boundary of the adjacent graph takes the original adjacent boundary as a subset;
(5) The Voronoi diagram has at most 2*n-5 vertices and 3*n-6 edges;
(6) The generating element in the polygon is the center of an external circle of a triangle formed by three points forming three sides, and all the external circles do not contain any vertex (hollow circle characteristic) except the three points.
The voronoi diagram has very important position in the computational geometry discipline, and has wide application in the fields of geography, meteorology, crystallography, aerospace, nuclear physics, robots and the like due to the characteristic that the distance from a region divided according to a point set to a point is nearest. If in the obstacle point set, the obstacle avoidance searches for the best path.
In the multi-robot collaborative autonomous exploration process, a novel multi-robot collaborative strategy based on a Veno diagram is utilized, the problem that different robots explore the same unknown area simultaneously is avoided, the multi-robot collaborative efficiency is improved, when the Veno diagram is used for dividing the unknown area to be explored, the real-time position of each robot is taken as a base point for the division of the Veno diagram, and the Veno diagram division with the number equal to that of the robots is divided on the unknown area to be explored.
Step S2, selecting a global exploration window around a team consisting of robots, and selecting a local exploration window around each robot.
The global exploration window is a minimum circumscribed rectangle containing all robots, and the local exploration window is a rectangle taking the real-time position of each robot as a center.
The local exploration window is created by the following steps: setting a rectangle with a length of a and a width of b as a center by taking the real-time position of each robot as a center, dynamically expanding the length and the width of the rectangle, increasing the length by c and increasing the width by c each time, wherein c is an expansion parameter, stopping expanding when at least one edge is completely positioned in an unknown area or positioned on a map boundary, and the rectangular area at the moment is a local exploration window of the robot. a. The values of b and c can be set according to the area of the unknown area which is searched in actual need.
Step S3, if the unknown connected areas exist in the local exploration window, extracting all the unknown connected areas in the local exploration window, and entering step S4, otherwise judging whether the unknown connected areas exist in the global exploration window, if so, extracting all the unknown connected areas in the global exploration window, and entering step S4, and if not, entering step S5.
And judging whether the unknown connected region outline exists in the exploration region by using a computer vision outline extraction technology, and if so, extracting the unknown connected region outline in all windows.
Contour feature extraction is a commonly used image processing technique in the field of computer vision, and can be used for identifying and classifying objects by analyzing and extracting the contours of the objects in an image. In practical application, the contour feature extraction technology is widely applied to the fields of image recognition target tracking, robot vision and the like.
The basic principle of contour feature extraction is to obtain contour information of an object by detecting the edge of the object in an image. Common edge detection algorithms include Sobel operators, canny operators, laplacian operators, and the like. After the contour information of the object is obtained, the shape and size of the object can be described by calculating the length, width, area, perimeter and other characteristics of the contour. In addition, the geometry and structure of the object can be described by computing features such as convex hulls, convex defects, shape factors, etc. of the contours.
In practical applications, contour feature extraction techniques may be used for image recognition and classification. For example, in face recognition, face recognition and classification can be achieved by extracting features of the face contours. In target tracking, tracking and positioning of a target can be achieved by extracting features of the target profile. In robot vision, autonomous navigation and obstacle avoidance of a robot can be realized by extracting outline features of objects in the environment.
The invention simultaneously sets the local exploration window and the global exploration window, and aims to ensure that the robot can complete exploration of all unknown areas completely. When the robot is positioned near the boundary of the whole exploration area, whether the unknown communication area exists in the central zone of the whole exploration area or not can also be observed through the global exploration window, and when the unknown communication area does not exist in the local exploration window and the global exploration window at the same time, the exploration is ended, and the arrangement can further ensure the integrity of exploration results.
And S4, calculating the mass centers of all unknown connected areas determined in the exploration window, calculating the value of the non-parametric utility function of each mass center, determining the unknown connected areas explored at this time according to the value of the non-parametric utility function, and returning to the step S1 after the exploration is completed.
And calculating the centroid of the unknown connected region through the contour moment.
The contour moments generally describe the global features of an image and provide a large amount of information about the various types of geometric characteristics of the image, such as size, position, orientation, shape, etc. In pattern recognition, object classification, object recognition, and the like have been widely used.
If m unknown connected regions exist in the exploration window corresponding to the robot A, calculating to obtain values of m non-parametric utility functions, selecting the unknown connected region corresponding to the maximum value in the values of the m non-parametric utility functions as the unknown connected region explored by the robot A at the present time, and taking the mass center of the unknown connected region as an exploration target of the robot A.
The formula of the non-parametric utility function is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
f(c i ,r,p k ) The value of the parametrized function of the ith centroid of the kth robot,
c i as the i-th centroid, the centroid,
p k for the kth robot,
s(c i r) is defined as centroid c i Is the center of the circle, r is the area of the unknown region contained by the radius circle,
d(c i , p k ) Is the centroid c i With robot p k Euclidean distance between them.
Unlike available utility function with weight parameters, the utility function of the present invention has no need of regulating weight parameters based on experience and is endowed with practical physical significance. Because it adopts the concept of per-cost benefit, in particular the value of the non-parametric utility function represents the amount of exploratory benefit that would be obtained by the robot moving a unit Euclidean distance to the centroid.
And selecting an unknown connected region corresponding to the largest value in the values of the non-parametric utility function as the unknown connected region of the current exploration of the robot, wherein the centroid of the unknown connected region is used as an exploration target of the current exploration of the robot.
And S5, if all robots finish the exploration, ending the exploration task, otherwise, entering step S1.
And if the unknown area does not exist in the local window of one robot, calculating the non-parametric utility function between the robot and the centroids of the unknown areas in the global window, and selecting the centroid with the maximum value of the non-parametric utility function to allow the robot to search.
Fig. 2 is a detailed flow chart of a method for extracting the centroid of an unknown connected region by realizing multi-robot cooperation according to the invention.
Specifically, during implementation, the real-time position of the robot is taken as a base point of the Voronoi diagram division, the Voronoi diagram division with the quantity equal to the quantity of the robot number is divided on an unknown area to be explored, and each robot is responsible for exploring the unknown area in the Voronoi diagram division where the robot is located;
secondly, taking the minimum circumscribed rectangle containing all robots as a global exploration window, taking a rectangle with at least one edge completely positioned in an unknown area or a map boundary and taking the real-time position of each robot as the center as a local exploration window;
then judging whether the unknown connected region contours exist in the exploration region by using a computer vision contour extraction technology, and if so, extracting the unknown connected region contours in all windows;
calculating the mass center of the unknown connected region through the contour moment;
and finally, constructing a non-parametric utility function according to the area of an unknown area around the centroid and the Euclidean distance between the centroid and the robot, calculating a utility function value between each centroid and the robot responsible for the Voronoi diagram partition where the centroid is located by using the utility function, and taking the centroid with the highest value as an exploration target of the robot.
The invention provides a multi-robot autonomous exploration system based on the barycenter of an unknown connected region, which guides a robot to explore an unknown environment by using the barycenter of the unknown connected region. Therefore, when multiple robots explore an unknown environment, a centroid-based method only allocates one robot to explore an unknown connected region, and the existing method can have the problem that a plurality of robots explore an unknown connected region at the same time, so that the autonomous exploration efficiency of the existing method can be reduced. In addition, the centroid calculation efficiency of the centroid-based method is higher than that of the existing method. Compared with the prior art, the method based on the Voronoi diagram can avoid the problem that different robots search the same unknown area at the same time. In conclusion, compared with the existing method, the method has higher efficiency of collaborative exploration of the unknown environment.
The invention also provides a multi-robot autonomous exploration system based on the barycenter of the unknown connected region, which uses the multi-robot autonomous exploration method based on the barycenter of the unknown connected region, as shown in figure 3, and comprises the following modules:
the voronoi diagram partitioning module: dividing an unknown region to be explored by using a voronoi diagram to obtain a voronoi diagram partition, and distributing the voronoi diagram partition responsible for exploration to each robot so that each robot explores in the associated voronoi diagram partition;
window dividing module: the voronoi diagram partitioning module is connected with the voronoi diagram partitioning module and is used for selecting a global exploration window and a local exploration window;
unknown connected region extraction module: the window dividing module is connected with the window dividing module, if an unknown connected region exists in the local exploration window, the unknown connected region of the exploration is determined in the local exploration window, otherwise, whether the unknown connected region exists in the global exploration window is judged, if the unknown connected region exists in the global exploration window, the unknown connected region of the exploration is determined in the global exploration window, and if the unknown connected region does not exist, the exploration is ended;
the parameter-free utility function calculation module: the unknown connected region extraction module is connected with the unknown connected region extraction module and is used for evaluating the mass center of the unknown connected region extracted by the unknown connected region extraction module and calculating the value of the non-parametric utility function of the mass center;
the exploration task determination module: the system comprises a non-parametric utility function calculation module, a non-parametric utility function calculation module and a mass center calculation module, wherein the non-parametric utility function calculation module is connected with the non-parametric utility function calculation module and is used for selecting an unknown connected region for each robot to be explored according to the value of the non-parametric utility function, and the mass center of the unknown connected region is used as an exploration target of the robot.
Alternatively, specific examples in this embodiment may refer to examples described in the foregoing embodiments and optional implementations, and this embodiment is not described herein.
The foregoing embodiment numbers of the present application are merely for describing, and do not represent advantages or disadvantages of the embodiments.
In the foregoing embodiments of the present application, the descriptions of the embodiments are emphasized, and for a portion of this disclosure that is not described in detail in this embodiment, reference is made to the related descriptions of other embodiments.
In the several embodiments provided in the present application, it should be understood that the disclosed technology content may be implemented in other manners. The above-described embodiments of the apparatus are merely exemplary, and the division of the units, such as the division of the units, is merely a logical function division, and may be implemented in another manner, for example, multiple units or components may be combined or may be integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be through some interfaces, units or modules, or may be in electrical or other forms.
The foregoing is merely a preferred embodiment of the present application and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present application and are intended to be comprehended within the scope of the present application.
Claims (10)
1. The multi-robot autonomous exploration method based on the barycenter of the unknown connected region is characterized by comprising the following steps:
step S1, dividing an unknown region to be explored by using a Veno map to obtain a Veno map partition, and distributing the Veno map partition responsible for exploration to each robot so that each robot explores in the associated Veno map partition;
step S2, selecting a global exploration window around a team formed by all robots together, and selecting a local exploration window around each robot;
step S3, if the unknown connected areas exist in the local exploration window, extracting all the unknown connected areas in the local exploration window, and entering a step S4, otherwise, judging whether the unknown connected areas exist in the global exploration window, if so, extracting all the unknown connected areas in the global exploration window, and entering a step S4, and if not, entering a step S5;
step S4, calculating the mass centers of all unknown connected areas determined in the exploration window, calculating the value of the non-parametric utility function of each mass center, determining the unknown connected area explored at this time according to the value of the non-parametric utility function, and returning to the step S1 after the exploration is completed;
step S5, if all robots finish the exploration, finishing the exploration task; otherwise, step S1 is entered.
2. The method according to claim 1, wherein in the step S1, when the unknown area to be searched is divided by using the voronoi diagram, the real-time position of each robot is taken as the base point of the voronoi diagram division, and the voronoi diagram division equal to the number of robots is divided on the unknown area to be searched.
3. The method according to claim 1, wherein in the step S2, the global search window is a minimum circumscribed rectangle containing all robots.
4. The method according to claim 1, wherein in the step S2, the local search window is a rectangle centered on the real-time position of each robot.
5. The multi-robot autonomous exploration method based on the barycenter of the unknown connected region of claim 3, wherein the local exploration window is created by the following ways: setting a rectangle with a length of a and a width of b as a center by taking the real-time position of each robot as a center, dynamically expanding the length and the width of the rectangle, increasing the length by c and increasing the width by c each time, wherein c is an expansion parameter, stopping expanding when at least one edge is completely positioned in an unknown area or positioned on a map boundary, and the rectangular area at the moment is a local exploration window of the robot.
6. The multi-robot autonomous exploration method based on the centroid of the unknown connected region according to claim 1, wherein in the step S4, the centroid of the unknown connected region is obtained by calculation of a contour moment.
7. The multi-robot autonomous exploration method based on the centroid of the unknown connected region according to claim 1, wherein in the step S4, the formula of the non-parametric utility function is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
f(c i ,r,p k ) The value of the parametrized function of the ith centroid of the kth robot,
c i as the i-th centroid, the centroid,
p k for the kth robot,
s(c i r) is defined as centroid c i Is the center of the circle, r is the area of the unknown region contained by the radius circle,
d(c i , p k ) Is the centroid c i With robot p k Europe in betweenA formula distance.
8. The method for autonomous exploration by multiple robots based on the centroid of the unknown connected regions according to claim 7, wherein the unknown connected region corresponding to the largest value among the values of the non-parametric utility function is selected as the unknown connected region currently being explored by the robots.
9. The multi-robot autonomous exploration method based on the barycenter of the unknown connected regions according to claim 8, wherein the barycenter of the unknown connected regions is used as an exploration target of the current exploration of the robot.
10. A multi-robot autonomous exploration system based on the centroid of an unknown connected region, using the multi-robot autonomous exploration method based on the centroid of an unknown connected region as claimed in any one of claims 1 to 9, comprising the following modules:
the voronoi diagram partitioning module: dividing an unknown region to be explored by using a voronoi diagram to obtain a voronoi diagram partition, and distributing the voronoi diagram partition responsible for exploration to each robot so that each robot explores in the associated voronoi diagram partition;
window dividing module: the voronoi diagram partitioning module is connected with the voronoi diagram partitioning module and is used for selecting a global exploration window and a local exploration window;
unknown connected region extraction module: the window dividing module is connected with the window dividing module, and if an unknown connected region exists in the local exploration window, the unknown connected region of the exploration is determined in the local exploration window; otherwise, judging whether an unknown connected region exists in the global exploration window, and if so, determining the unknown connected region explored in the global exploration window; if not, ending the exploration;
the parameter-free utility function calculation module: the unknown connected region extraction module is connected with the unknown connected region extraction module and is used for evaluating the mass center of the unknown connected region extracted by the unknown connected region extraction module and calculating the value of the non-parametric utility function of the mass center;
the exploration task determination module: the system comprises a non-parametric utility function calculation module, a non-parametric utility function calculation module and a mass center calculation module, wherein the non-parametric utility function calculation module is connected with the non-parametric utility function calculation module and is used for selecting an unknown connected region for each robot to be explored according to the value of the non-parametric utility function, and the mass center of the unknown connected region is used as an exploration target of the robot.
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