CN105825301A - Multi-vehicle cooperative exploration method and device via environment segmentation - Google Patents
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Abstract
The invention relates to a multi-vehicle cooperative exploration method and device via environment segmentation. The method comprises the followings steps that segmentation areas in a map are identified, and an edge point set of each segmentation area in the map is determined; the corresponding cost for reaching each segmentation area of each vehicle is calculated; and the corresponding cost are substituted into a cost value matrix to calculate an optimal distribution manner, and the vehicles are assigned to target areas according to the optimal distribution manner. Different from the prior art, a lattice point occupied map is identified and segmented into a node skeleton type map (a Voronoi diagram), repetition in map segmentation is reduced, the Voronoi diagram is used to calculate the moving costs of the vehicles, response cost exists when each vehicle moves to each node of the Voronoi diagram, the vehicles and the costs are substituted into a Hungary method, and a method enabling minimal total movement cost is obtained. The efficiency of a multi-vehicle environment exploration method is improved. Problems when multiple vehicles collaborate to explore the unknown environment are sovled.
Description
Technical field
The present invention relates to unmanned vehicle design field, particularly relate to a kind of many vehicles utilizing environment to split and work in coordination with heuristic approach and device.
Background technology
It it is the most all a underlying issue in automatic driving vehicle field to the exploration of environment.In order to build relatively completely the most careful environmental map, environment have to be explored by vehicle efficiently.Introduce herein is a kind of use multi rack vehicle cooperative cooperating, the method exploring environment.Compared with using single Vehicular system, using multi rack vehicle to carry out environment exploration has following four benefit.First, compared with single rack vehicle, many false vehicle cooperative cooperating is potential completes the once exploration task to environment faster.Second, self, whenever in energy perception mutually when, by exchanging the information about respective position, thus efficiently can be positioned by multi rack vehicle.3rd, use multiple relatively cheap motor vehicle-detecting system can bring redundancy, therefore we can obtain than the more preferable fault-tolerant ability of motor vehicle-detecting system using an only powerful costliness.4th, by merging overlapping sensor information, it is uncertain that we can offset a part of sensor.
But, when multi rack vehicle carries out collaborative exploration, the risk interfered with each other between vehicle can be introduced.For giving an example, if vehicle uses active sensor, such as ultrasonic sensor, then the crosstalk between sensor is it is possible to the overall performance of system can be reduced.System uses the most vehicles, and each unwheeling, in order to avoid producing the interference phenomenons such as crosstalk with other vehicles in system, is necessary for around farther road to avoid producing with other vehicles conflicting.
Summary of the invention
For this reason, it may be necessary to provide a kind of many vehicles utilizing environment to split to work in coordination with heuristic approach so that many vehicles are to the exploration of environment more effectively.
For achieving the above object, inventor provide a kind of many vehicles utilizing environment to split and work in coordination with heuristic approach, comprise the steps,
Identify the cut zone in map, determine the edge point set of each cut zone in map；
Calculate each vehicle and arrive the corresponding cost of each cut zone；
Corresponding cost is substituted into cost value matrix calculus optimum allocation mode, according to optimum allocation mode by vehicle sending to target area；
Specifically, described step " calculates each vehicle and arrives the corresponding cost of each cut zone " and also includes, if vehicle is the most in an area, then the cost that vehicle arrives this region devalues.
Specifically, also include step, vehicle is sent to the marginal point of target area.
Further, described step " identifies the cut zone in map " and specifically includes step, and individual point occupies formula map skeletonizing, generates Voronoi diagram.
Preferably, also including step, by the node in vehicle sending to Voronoi diagram, described node is the point that distance is local minimum of nearest obstacle with figure.
Exploration device worked in coordination with by a kind of many vehicles utilizing environment to split, and including map segmentation module, cost calculation module, plans as a whole to send module,
Described map segmentation module, for identifying the cut zone in map, determines the edge point set of each cut zone in map；
Described cost calculation module arrives the corresponding cost of each cut zone for calculating each vehicle；
Described pool send module for by corresponding cost substitute into cost value matrix calculus optimum allocation mode, according to optimum allocation mode by vehicle sending to target area；
Further, described cost calculation module be additionally operable to when vehicle the most in an area, then vehicle is arrived this region cost devalue.
Further, described pool module is additionally operable to, and vehicle is sent to the marginal point of target area.
Specifically, described map segmentation module is additionally operable to, and individual point occupies formula map skeletonizing, generates Voronoi diagram.
Preferably, described pool sends module to be additionally operable to the node in vehicle sending to Voronoi diagram, and described node is the point that distance is local minimum of nearest obstacle with figure.
It is different from prior art, technique scheme is divided into the skeleton map of node (Voronoi diagram) by lattice point occupies formula Map recognition, advantageously reduce the repeatability of map segmentation, Voronoi diagram is used to calculate the mobile cost of vehicle therewith, the node each car being moved to each Voronoi diagram has response cost, vehicle is substituted into hungarian method with cost, tries to achieve the method moving integrally cost minimization.Reach the raising many vehicles purpose to environment heuristic approach efficiency.Solve many vehicles and work in coordination with the problem exploring circumstances not known.
Accompanying drawing explanation
Fig. 1 is the many vehicles heuristic approach flow chart utilizing environment to split described in the specific embodiment of the invention；
Fig. 2 is that the Voronoi diagram described in the specific embodiment of the invention generates schematic diagram；
Fig. 3 is that carrying out environment division described in the specific embodiment of the invention splits schematic diagram；
Fig. 4 is the many vehicles exploration device module map utilizing environment to split described in the specific embodiment of the invention.
Description of reference numerals:
400, map segmentation module；
402, cost calculation module；
404, plan as a whole to send module.
Detailed description of the invention
By describing the technology contents of technical scheme, structural feature in detail, being realized purpose and effect, below in conjunction with specific embodiment and coordinate accompanying drawing to be explained in detail.
1, general introduction
Present invention contemplates that and how to utilize many Vehicular systems that environment carries out efficient exploration, thus minimized and explored the time thinking required.The environment of many vehicle map explores task can be roughly classified into two subtasks.First, system to be capable of identify that potential goal seeking.Then, system wants the target bearing that can be calculated by each independent vehicle sending to back.
B.Yamauchi it is proposed that a more universal potential goal seeking recognition methods, which use the concept of an edge cells lattice (frontiercells), these edge cells lattice are exactly potential goal seeking orientation.One edge cells lattice is known per se, the cell detected, and it must be the adjacent unit lattice of unknown (detection) cell simultaneously.But in the environment of many Vehicular systems, when vehicle is coordinated, it is necessary to the repetition operation minimizing between vehicle will be considered how and interfere with each other.In many additive methods, determine that the value equation in vehicle target orientation is a balance between mobile cost relevant to Set cell and expected utility.What these coordination strategies considered is all the cut zone in independent target bearing rather than environment.
2, implement
The method that invention is to be introduced, is that strategy is explored in a kind of new many Vehicular systems on-line coordination.Refer to Fig. 1, work in coordination with heuristic approach flow chart for the many vehicles utilizing environment to split of the present invention.This method starts from step S100, identifies the cut zone in map, and S102 determines the edge point set of each cut zone in map；One map dividing method based on figure of concrete mode the 2.2nd introduction below illustrates.
S104 calculates each vehicle and arrives the corresponding cost of each cut zone；
Corresponding cost is substituted into cost value matrix calculus optimum allocation mode by S106, according to optimum allocation mode by vehicle sending to target area；How 2.1st introduction below is utilized hungarian method to carry out in Target Assignment by the process of known cost calculation optimum allocation mode is introduced.2.3rd part also describes coordination mode and the algorithm of entirety.
Explore the segmentation in environment by utilizing, vehicle sending has been gone different cut zone rather than directly they are sent to edge destination cell.Based on such a Target Segmentation, vehicle more effectively dispersed and distributed in the environment, thus can obtain minimizing and repeats operation and the purpose interfered with each other between vehicle.So, the time used by whole exploration task just significantly reduces.Reach the many vehicles of optimization and utilize the collaborative effect explored of environment segmentation.
2.1 utilize hungarian method to carry out Target Assignment
Kuhn 1955 it is proposed that mistake, when a given fixing cost value matrix, to the general described hungarian method of the conventional method of a series of machine assignment a series of activities-namely.Considering given n × n cost value matrix, the work that n machine assignment n to be given is different, this matrix illustrates all costs to particular machine distribution particular job.Hungarian method can find the optimum allocation mode at this matrix, the namely method of salary distribution of cost minimization.The method is realized by general below three steps:
1) item each in matrix is deducted the value of the item of this middle minimum of being expert at, be calculated the Cost matrix of a reduction.Item each in matrix is deducted the value of item minimum in this column the most again.
2) finding can all of 0 minimal number of horizontal line and vertical line in set covering theory.If our minimum needs lucky n bar line could cover all of 0, then just covered by this n bar line 0 is given the optimal method of salary distribution.Otherwise, step 3 is entered.
3) find the minimum non-zero item not covered by the horizontal line in step 2 or vertical line, then this value is deducted from each item of matrix.Then, this value is added back in condensation matrix the item covered by horizontal line or vertical line.Proceed step 2.
The difficult point calculated is how to find the minimum lines quantity that can cover all 0, namely step 2.The time complexity of total algorithm is O (n3).Algorithm above is used directly for distributing a series of different target bearings to a series of vehicles.Here, the cost item of cost value matrix can be the path length of corresponding vehicle corresponding entry to be driven to target bearing.
Owing to the realization of above-mentioned hungarian method requires that the quantity of vehicle is identical with the quantity in potential target orientation, we need somewhat to adjust, and cost value matrix that thus method calculates-we are by using " virtual vehicle " (existence of virtual vehicle can generate some target bearings not having vehicle to go) and replicating existing target bearing and expand our cost value matrix, and then use hungarian method calculates the optimal objective method of salary distribution under this cost value matrix.
The segmentation of 2.2 maps
In some concrete embodiment, described step " identifies the cut zone in map " and specifically includes step, and individual point occupies formula map skeletonizing, generates Voronoi diagram.
Many scholars had studied map segmentation problem based on node diagram subregion the most.One of them the most universal expression based on figure is Voronoi diagram (VoronoiGraphs).A given map m, we first have to build her node diagram figure G (m)=(V, E) of the voronoi about m, and V is the set of Voronoi diagram interior joint here, and E is the set on limit.
Firstly, for each some p in the free space C of map m, it is contemplated that a set O containing the nearest barrier point of all range points pp(m).So gather OpM in (), those have the point of barrier point that at least two has identical minimum range just to constitute our her node diagram G (m)=(V, E) of voronoi:
V={p ∈ C | | Op(m)≥2|}
E={ (p, q) | p, q ∈ V, p and q are neighbor point in m }
To every a pair node in G (m), (p, q), if they are neighbor points in map m, we are just upper for increasing a limit between p and q at G (m).Voronoi diagram can be generated by the characteristic map of environment, such as lattice point occupies formula map (occupancygridmap)-in reality performs, and we can convert by lattice point occupies formula map application Euclidean distance effectively, thus generate her node diagram of voronoi.Each lattice point cell in the distance map obtained by Euclidean transformation saves this lattice point range information to nearest obstacle.By this distance map skeletonizing (skeletonization), we just can construct her node diagram of a voronoi.Fig. 2 illustrates the process occupying formula map generation her node diagram of voronoi from a sample lattice point, and Zuo Tu: lattice point occupies formula map specimen.Middle figure: map and range conversion (the most black obstacle just representing it closest of the color of point is the most remote).Right figure: her node diagram (conversion carries out skeletonizing by adjusting the distance) of the voronoi of map and generation.
After generation has obtained her node diagram of voronoi, our present concern has reformed into and how this node diagram has been divided into k disjoint setAnd meet following condition:
Make the V that birdss of the same feather flock together of each nodeiAll corresponding our region vehicle is sent to.In certain embodiments, we are by the node in vehicle sending to Voronoi diagram, and described node is the point that distance is local minimum of nearest obstacle with figure.There is scholar it is proposed that node diagram can be split by so-called critical point.Here, critical point be exactly those in her node diagram of voronoi with the node that distance is local minimum of nearest obstacle in map.This method is applicable to narrow passage.
Although this method is applicable to identify slype, but in mixed and disorderly environment, it can generate the positive recognition result (namely by mistake the part of slype non-in environment being identified as slype) of many mistakes.In order to eliminate the positive recognition result of these mistakes, we go to use restraint to result using the following method: first, and critical point must be the node having two limits；Secondly, critical point must be the neighbor point of a cross knot chalaza (having the node on three limits).In addition, we to require that these can lead us to drive towards the band of position from known region, this is because those segmentation clusters not comprising zone of ignorance should be removed by drawing from our exploration task.In order to examine this item constraint condition, put, for each, the distance that we are required for calculating this point to nearest, that can contact, unknown cell.This calculating can draw by the method similar to computed range map effectively.Fig. 2 illustrate one through her the node diagram sample of voronoi pruned, and the critical point found by our algorithm.
The sample that one part of environment is split by Fig. 3.Labeled node is the candidate's critical point for segmentation map that our algorithm finds.As it is shown on figure 3, the entrance of all of slype is the most selected for positive findings, and the quantity of the positive recognition result of mistake is much smaller than the quantity of all critical points.
Through experiment, we have confirmed that this partitioning scheme can produce enough sufficiently result so that vehicle can successfully be spread out by the environment.In more complicated environment, the training data that we can use handmarking to cross carries out finer map segmentation.
2.3 by vehicle sending to target area
One of them common objective of representative collaborative heuristic approach is exactly to complete vehicle sensors with the minimum time to treat the complete covering of exploration environment.Therefore, as a rule using more than a unwheeling same regional area of exploration is not optimal scheme.Use more than a unwheeling at regional area, the visual range of the sensor of vehicle can be made to have serious overlap, the potentiality of many Vehicular systems can not be made full use of.In reality, as a rule being scatter by multi-system vehicle makes a return journey explores different subregion and wants efficient many.Therefore, how by vehicle sending to the most different exploration regions so that the distance between these vehicles will not be too close in heuristic process, is an important problem.
In our method, each frame separate vehicle is dispatched to the different cut zone in region to be explored by us.Cut zone can be a lane, a square, or a part for a road.Segmentation needs the framework in view of environment itself, it is to avoid the clustering phenomenon of vehicle occurs.
Table 1 task allocation algorithms.
Whenever the goal seeking that any one frame vehicle needs is new, we will carry out a subtask distribution.First, local based on the node diagram map dividing method that we use 2.2 parts to be introduced generates independent disjoint cut zone S={s1,s2,…,sn}.Then, by identifying the edge cells lattice in cut zone, the impact point in cut zone is generated.Vehicle i arrives the corresponding cost of cut zone s ∈ SDefinition be from current vehicle position, travel the expectation route cost to edge cells lattice nearest in cut zone s.If vehicle i is in cut zone s, we will use a discount factor (typically one Changshu) to carry out this costThe effect devalued accordingly-so obtain is exactly that vehicle i will continue to stay in cut zone s it is known that this region is explored complete.After all calculated the cost arriving each cut zone for each unwheeling, we can obtain a cost value matrix.Based on this cost value matrix, the hungarian method that application 2.1 is introduced, we just can calculate the new exploration task of this vehicle: or continue to explore in staying this cut zone, or leaving one's respective area goes to the cut zone that next route cost is minimum.
Generally under hungarian method, do not have the phenomenon being dispatched to same cut zone more than a unwheeling, unless the vehicle fleet size that can call is more than the quantity not exploring cut zone.It is sent to the phenomenon of same cut zone to preferably process this multi rack vehicle, it would be desirable in this cut zone, find the edge cells lattice of cost minimization, runs a local task allocation algorithm, vehicle is sent to the edge cells lattice of cost minimization.For from this angle, if an environment (or the sub regions in environment) cannot be divided, the algorithm that so our algorithm is based entirely on edge cells lattice in this environment (region) neutralization is the same, and in other words, only one of which cut zone exists.
By vehicle is assigned to different isolated areas, we enable to vehicle and present an appropriate distribution in the environment.It is demonstrated experimentally that by using our above-mentioned method for allocating tasks and algorithm, we can substantially reduce the time explored required for whole environment.Vehicle is no longer with nearest edge cells lattice as target, but goes to share exploration task from the angle of an overall system, thus efficiently completes to explore.
It should be noted that the vehicle that the application of the algorithm that we are proposed is not required in system is all identical.For giving an example, a certain unwheeling in possible system, owing to the restriction of volume cannot travel one narrow alley of entrance, but the vehicle that in system, an other frame is less is permissible.In this case, we can be by using the cut zone cost of a modified versionApply above-mentioned algorithm:
Pass through said method, lattice point is occupied formula Map recognition and is divided into the skeleton map of node (Voronoi diagram) by the present invention, advantageously reduce the repeatability of map segmentation, Voronoi diagram is used to calculate the mobile cost of vehicle therewith, the node each car being moved to each Voronoi diagram has response cost, vehicle is substituted into hungarian method with cost, tries to achieve the method moving integrally cost minimization.Reach the raising many vehicles purpose to environment heuristic approach efficiency.Solve many vehicles and work in coordination with the problem exploring circumstances not known.
In some embodiment shown in Fig. 4, illustrate a kind of many vehicles utilizing environment to split and work in coordination with exploration device, including map segmentation module 400, cost calculation module 402, plan as a whole to send module 404,
Described map segmentation module, for identifying the cut zone in map, determines the edge point set of each cut zone in map；
Described cost calculation module arrives the corresponding cost of each cut zone for calculating each vehicle；
Described pool send module for by corresponding cost substitute into cost value matrix calculus optimum allocation mode, according to optimum allocation mode by vehicle sending to target area；Designed by above-mentioned module, it is possible to plan as a whole cost, reasonable arrangement vehicle and the corresponding relation explored between environment, save total exploration cost, solve and utilize environment segmentation to carry out the problem that exploration worked in coordination with by many vehicles efficiently.
In further embodiment, described cost calculation module be additionally operable to when vehicle the most in an area, then vehicle is arrived this region cost devalue.By above-mentioned design, more scientifically the relation between apportioning cost and distance, preferably solves the problem that exploration worked in coordination with by many vehicles.
Further, described pool module is additionally operable to, and vehicle is sent to the marginal point of target area.By above-mentioned design, it is possible to make this device more thorough for the exploration of environment.
In some concrete embodiment, described map segmentation module is additionally operable to, and individual point occupies formula map skeletonizing, generates Voronoi diagram.Voronoi diagram is used to carry out environment segmentation, it is possible to preferably to show that map interior joint explores the trunk relation in region with band, improve the accuracy of map segmentation.
Preferably, described pool sends module to be additionally operable to the node in vehicle sending to Voronoi diagram, and described node is the point that distance is local minimum of nearest obstacle with figure.By distributing vehicle to node, it is possible to make vehicle quickly marginal area be explored, save resource.
It is different from prior art, technique scheme is divided into the skeleton map of node (Voronoi diagram) by lattice point occupies formula Map recognition, advantageously reduce the repeatability of map segmentation, Voronoi diagram is used to calculate the mobile cost of vehicle therewith, the node each car being moved to each Voronoi diagram has response cost, vehicle is substituted into hungarian method with cost, tries to achieve the method moving integrally cost minimization.Reach the raising many vehicles purpose to environment heuristic approach efficiency.Solve many vehicles and work in coordination with the problem exploring circumstances not known.
It should be noted that, in this article, the relational terms of such as first and second or the like is used merely to separate an entity or operation with another entity or operating space, and not necessarily requires or imply the relation or sequentially that there is any this reality between these entities or operation.And, term " includes ", " comprising " or its any other variant are intended to comprising of nonexcludability, so that include that the process of a series of key element, method, article or terminal unit not only include those key elements, but also include other key elements being not expressly set out, or also include the key element intrinsic for this process, method, article or terminal unit.In the case of there is no more restriction, statement " including ... " or " comprising ... " key element limited, it is not excluded that there is also other key element in including the process of described key element, method, article or terminal unit.Additionally, in this article, " being more than ", " being less than ", " exceeding " etc. are interpreted as not including this number；More than " ", " below ", " within " etc. be interpreted as including this number.
Those skilled in the art are it should be appreciated that the various embodiments described above can be provided as method, device or computer program.These embodiments can use complete hardware embodiment, complete software implementation or combine software and hardware in terms of the form of embodiment.All or part of step in the method that the various embodiments described above relate to can instruct relevant hardware by program and complete, described program can be stored in the storage medium that computer equipment can read, for performing all or part of step described in the various embodiments described above method.Described computer equipment, includes but not limited to: personal computer, server, general purpose computer, special-purpose computer, the network equipment, embedded device, programmable device, intelligent mobile terminal, intelligent home device, wearable intelligent equipment, vehicle intelligent equipment etc.；Described storage medium, includes but not limited to: the storage of RAM, ROM, magnetic disc, tape, CD, flash memory, USB flash disk, portable hard drive, storage card, memory stick, the webserver, network cloud storage etc..
The various embodiments described above are with reference to describing according to the method described in embodiment, equipment (system) and the flow chart of computer program and/or block diagram.It should be understood that can be by the flow process in each flow process in computer program instructions flowchart and/or block diagram and/or square frame and flow chart and/or block diagram and/or the combination of square frame.These computer program instructions can be provided to produce a machine to the processor of computer equipment so that the instruction performed by the processor of computer equipment is produced for realizing the device of function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.
These computer program instructions may be alternatively stored in the computer equipment readable memory that computer equipment can be guided to work in a specific way, the instruction making to be stored in this computer equipment readable memory produces the manufacture including command device, and this command device realizes the function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.
These computer program instructions also can be loaded on computer equipment, make to perform on a computing device sequence of operations step to produce computer implemented process, thus the instruction performed on a computing device provides for realizing the step of function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.
Although the various embodiments described above being described; but those skilled in the art once know basic creative concept; then these embodiments can be made other change and amendment; so the foregoing is only embodiments of the invention; not thereby the scope of patent protection of the present invention is limited; every equivalent structure utilizing description of the invention and accompanying drawing content to be made or equivalence flow process conversion; or directly or indirectly it is used in other relevant technical fields, within being the most in like manner included in the scope of patent protection of the present invention.
Claims (10)
1. heuristic approach worked in coordination with by the many vehicles utilizing environment to split, it is characterised in that comprise the steps,
Identify the cut zone in map, determine the edge point set of each cut zone in map；
Calculate each vehicle and arrive the corresponding cost of each cut zone；
Corresponding cost is substituted into cost value matrix calculus optimum allocation mode, according to optimum allocation mode by vehicle sending to target area.
Heuristic approach worked in coordination with by the many vehicles utilizing environment to split the most according to claim 1, it is characterized in that, described step " calculates each vehicle and arrives the corresponding cost of each cut zone " and also includes, if vehicle is the most in an area, then the cost that vehicle arrives this region devalues.
Heuristic approach worked in coordination with by the many vehicles utilizing environment to split the most according to claim 1, it is characterised in that also include step, vehicle is sent to the marginal point of target area.
Heuristic approach worked in coordination with by the many vehicles utilizing environment to split the most according to claim 1, it is characterised in that described step " identifies the cut zone in map " and specifically includes step, and individual point occupies formula map skeletonizing, generates Voronoi diagram.
Heuristic approach worked in coordination with by the many vehicles utilizing environment to split the most according to claim 4, it is characterised in that also include step, and by the node in vehicle sending to Voronoi diagram, described node is the point that distance is local minimum of nearest obstacle with figure.
6. exploration device worked in coordination with by the many vehicles utilizing environment to split, it is characterised in that includes map segmentation module, cost calculation module, plan as a whole to send module,
Described map segmentation module, for identifying the cut zone in map, determines the edge point set of each cut zone in map；
Described cost calculation module arrives the corresponding cost of each cut zone for calculating each vehicle；
Described pool send module for by corresponding cost substitute into cost value matrix calculus optimum allocation mode, according to optimum allocation mode by vehicle sending to target area.
Exploration device worked in coordination with by the many vehicles utilizing environment to split the most according to claim 6, it is characterised in that described cost calculation module be additionally operable to when vehicle the most in an area, then vehicle is arrived this region cost devalue.
Exploration device worked in coordination with by the many vehicles utilizing environment to split the most according to claim 6, it is characterised in that described pool module is additionally operable to, and vehicle is sent to the marginal point of target area.
Exploration device worked in coordination with by the many vehicles utilizing environment to split the most according to claim 6, it is characterised in that described map segmentation module is additionally operable to occupy individual some formula map skeletonizing, generates Voronoi diagram.
Exploration device worked in coordination with by the many vehicles utilizing environment to split the most according to claim 6, it is characterized in that, described pool sends module to be additionally operable to the node in vehicle sending to Voronoi diagram, and described node is the point that distance is local minimum of nearest obstacle with figure.
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