Abstract:
A partial surface of a total surface, divided into several partial surfaces, is allocated to one of several mobile units by determining the partial surface of the total surface and allocating one of the several mobile units with a reservation. The mobile unit transmits allocation information indicating the allocation of the partial surface. The reservation is lifted and the allocation of the partial surface is validated when the one of the several mobile units receives no allocation rejection information from at least one of the other mobile units, indicating a rejection of the allocation of the partial surface. If rejection information is received, the reservation is lifted and the allocation of the partial surface is invalidated.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
         [0001]    This application is based on and hereby claims priority to German Application No. 101 50 423.3 filed on Oct. 11, 2001, the contents of which are hereby incorporated by reference.  
         BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The invention relates to an assignment of a part domain of a whole domain which is divided into a plurality of part domains to one of a plurality of mobile units.  
           [0004]    2. Description of the Related Art  
           [0005]    A division of a whole domain into a plurality of part domains and subsequent assignment of one or a plurality of these part domains to mobile units is normally done when a plurality of mobile units jointly and coordinatedly process a large whole domain, for example when a hall is cleaned by a plurality of cleaning robots, as described in H. Endres, W. Feiten, and G. Lawitzky, Field Test of a Navigation System: Autonomous Cleaning in Supermarkets, Int. Conf. on Robotics and Automation (ICRA), 1998, pp. 1779-1781.  
           [0006]    Different methods or approaches are used for dividing the whole domain and for assigning the part domains to the plurality of robots. A static approach or static method and a dynamic approach or dynamic method are used.  
           [0007]    In the case of a static method, i.e. in the case of a static division and assignment, each mobile unit is permanently assigned a predetermined part domain of a whole domain before commencement of an activity which will be carried out jointly by the mobile units, wherein the assignment can no longer be changed during the activity.  
           [0008]    Various such static methods, differing only in the manner in which the whole domain is divided into part domains, are known from Hert et al., “Polygon Area Decomposition for Multiple-Robot Workspace Division”, Special Issue of International Journal of Computational Geometry and Applications on Applied Computational Geometry, vol. 8, no. 4, 1998, pp. 437-466; Bast et al., “The Area Partitioning Problem”, Proceedings of the 12th Canadian Conference on Computational Geometry, 2000, pp.163-171; Bern et al., “Linear-size Nonobtuse Triangulation of Polygons”, Discrete and Computational Geometry, vol. 14, 1995, pp. 411-428; Christou et al., “Optimal Equipartition of Rectangular Domains for Parallel Computation”, Journal of Global Optimization, vol. 8, January, 1996, pp.15-34; I. T. Christou, “Distributed Genetic Algorithms for Partitioning Uniform Grids”, University of Wisconsin Madison, Dept. of Computer Sciences Technical Report MP-TR-96-09, 1996; Yackel et al., “Minimum Perimeter Domain Assignment”, Mathematical Programming, vol. 78, no. 2, Aug. 1997, pp. 283-303.  
           [0009]    Hert et al. and Bast et al. disclose the cutting up of a whole domain into n adjacent part domains of equal size, wherein each part domain must contain a specific point, i.e. a starting point of a robot which is responsible for the respective part domain. The static methods disclosed in Hert et al. and Bast et al. are mathematically correct, but the resulting part domains or areas to be processed by robots are often unusable in practice.  
           [0010]    The static approach disclosed in Bern et al. therefore seeks and specifies equally sized part domains of a whole domain, wherein the part domains preferably contain no sharp angles and can therefore be processed more effectively by robots.  
           [0011]    Conversely, the static methods disclosed in Christou et al., I.T. Christou and Yackel et al. specify part domains of a whole domain such that the part domains have a smallest possible diameter in each case and therefore normally also a small size. It is thereby intended that robots, each processing one of the part domains, encounter each other less frequently at a boundary of the part domain they are to process and therefore the danger of a collision is reduced.  
           [0012]    A significant disadvantage of these known static methods, in particular due to the permanent assignment of part domains in these methods, is that such methods are extremely inflexible and cannot be dynamically adapted to new situations.  
           [0013]    If one of a plurality of robots fails, for example, its work or its part domain to be processed is not taken over by one of the other robots. This part domain remains unprocessed in this case.  
           [0014]    The dynamic method provides the opposite, i.e. a dynamic division and assignment of part domains. With this type of method, the part domains are first divided during an activity of the mobile units. The assignment of the part domains takes place in a plurality of time-staggered stages.  
           [0015]    As a result of these dynamics, the part domains which are currently assigned to a mobile unit change dynamically during the activity of the mobile units. In this case, therefore, a work task is not permanently predefined for the mobile units, but is first dynamically adapted to environmental conditions and/or boundary conditions during the activity of the mobile units.  
           [0016]    A disadvantage of the dynamic division and assignment of part domains is that the mobile units must remain in regular communication contact with each other, in order tell each other about notifications or changes. This communication is normally implemented by a global communication network via which the mobile units communicate with each other.  
           [0017]    One such method, being at least partly dynamic, is disclosed in Hert et al., Multiple-Robots Motion Planning=Parallel Processing+Geometry, 2001. In the mixed-dynamic method disclosed in Hert et al., which method combines a static approach with a dynamic approach, a whole domain is divided into (n+1) part domains before the start of a processing activity by mobile units. n part domains are distributed among the mobile units in accordance with the static approach described above. The (n+1)th part domain is dynamically divided among the mobile units at the end of the processing activity.  
           [0018]    However, since this mixed-dynamic method features mainly static method parts, it also exhibits the disadvantages of such static methods as described above.  
         SUMMARY OF THE INVENTION  
         [0019]    An object of the invention is therefore to specify a method for assigning a part domain of a whole domain which is divided into a plurality of part domains to one of a plurality of interacting mobile units, the method being flexible and adaptable to changed or changing boundary conditions during a processing of the whole domain by the mobile units.  
           [0020]    In the method for assigning a part domain of a whole domain which is divided into a plurality of part domains to one of a plurality of mobile units, a part domain of the whole domain which is divided into a plurality of part domains is specified and provisionally assigned to the one of the plurality of mobile units.  
           [0021]    The one of the plurality of mobile units transmits an assignment notification which indicates the assignment of the part domain of the whole domain which is divided into a plurality of part domains to the one of the plurality of mobile units.  
           [0022]    The proviso is removed and the assignment of the part domain becomes valid if the one of the plurality of mobile units does not receive an assignment rejection notification from at least one other of the plurality of mobile units, the assignment rejection notification indicating a rejection of the assignment of the part domain. Otherwise the proviso is removed and the assignment of the part domain becomes invalid.  
           [0023]    The system for assigning a part domain of the whole domain which is divided into a plurality of part domains to one of a plurality of mobile units includes an assignment unit which allows the specification of the part domain to be assigned and the provisional assignment of the part domain to the one of the plurality of mobile units.  
           [0024]    The system also includes a communication unit which allows the transmission of an assignment notification which indicates the assignment of this part domain of the whole domain which is divided into a plurality of part domains to the one of the plurality of mobile units.  
           [0025]    The assignment unit is also configured in such a way that the proviso can be removed and the assignment of the part domain becomes valid if the one of the plurality of mobile units does not receive an assignment rejection notification from at least one other of the plurality of mobile units, the assignment rejection notification indicating a rejection of the assignment of this part domain, otherwise the proviso can be removed and the assignment of this part domain becomes invalid.  
           [0026]    A computer program and computer program product according to the invention also include those computer programs or computer program products which are implemented decentrally, i.e. distributed over a plurality of systems or divided into a plurality of individual computer programs or computer program products, and execute a method according to the invention as an entirety or while interacting as an entirety.  
           [0027]    The developments described below relate both to the method and to the system. The invention and the developments described below can be implemented both in software and in hardware, for example using a special electric circuit.  
           [0028]    In one embodiment, the provisional specification and/or assignment of the part domain is done when the one of the plurality of mobile units is at a predeterminable assignment distance, or at less than the predeterminable assignment distance, in relation to the part domain.  
           [0029]    Furthermore, the provisional specification and/or assignment of the part domain can be done actively by the one of the plurality of mobile units, i.e. by a request for the part domain by the one of the plurality of mobile units, or also passively, i.e. by assignment to the one of the plurality of mobile units by a third party.  
           [0030]    In a further embodiment, the provisional specification and/or assignment of the part domain is done during a processing of other part domains of the whole domain by the mobile units. Interruptions or delays in the processing of the part domains can thereby be avoided.  
           [0031]    The assignment notification can also include an importance notification relating to the part domain to be assigned, the importance notification describing how important the assignment of the part domain to be assigned is for the one of the plurality of mobile units.  
           [0032]    A connectivity graph as disclosed in J. C. Latombe, Robot Motion Planning, Kluwer Academic Publishers, Boston, 1991 can be used for specifying the part domain to be assigned to the one of the plurality of mobile units.  
           [0033]    It is also effective—because it is beneficial to processing—to specify the part domain, which is to be provisionally assigned, in such a way that the processing domain produces an area which is as compact as possible.  
           [0034]    The part domain which is assigned to the one of the plurality of mobile units can also be combined with further part domains which are assigned to the one of the plurality of mobile units, thereby forming a processing area.  
           [0035]    A processing path for the one of the plurality of mobile units can be determined for such a processing domain by using a path planning method. Path planning methods are disclosed in Arkin E. M. et al., “Approximation Algorithms for Lawn Mowing and Milling”, Angewandte Mathematik und Informatik, Universität zu Köln, Report No. 97.255, 1997 or DE 198 04 195 A1, for example.  
           [0036]    It is also effective in terms of processing for each of the plurality of mobile units to store a map of the whole domain, in which are entered at least the part domains which are assigned to the mobile unit concerned. The assigned part domain is then additionally entered into the map of the one of the plurality of mobile units.  
           [0037]    In a development, an exchange of notifications between the plurality of mobile units takes place in such a way that the plurality of mobile units exchange notifications with each other whenever two of the plurality of mobile units are able to communicate. This is possible when two mobile units which have been configured for communication, i.e. configured for sending and receiving messages, are at a predeterminable communication distance, or at less than the predeterminable communication distance, in relation to each other.  
           [0038]    A global communication network is not necessary in this case. The notifications are successively forwarded from one of the plurality of mobile units to another of the plurality of mobile units. This exchange of notifications makes it possible to carry out a map synchronization for the maps of the plurality of mobile units.  
           [0039]    An agreement method can also be carried out if the part domain assigned to the one of the plurality of mobile units has already been assigned to another of the plurality of mobile units. This agreement method then provides for definitively assigning the part domain to one of the two mobile units.  
           [0040]    In one embodiment, the invention is used in the cleaning of a whole domain by a plurality of cleaning robots. In this case, the plurality of mobile units are the cleaning robots. The whole domain to be cleaned is the whole domain. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0041]    These and other objects and advantages of the present invention will become more apparent and more readily appreciated from the following description of the preferred embodiments, taken in conjunction with the accompanying drawings of which:  
         [0042]    [0042]FIG. 1 is a drawing of a room  100  to be cleaned, the room being subdivided into polygons  101  in accordance with an exemplary embodiment,  
         [0043]    [0043]FIG. 2 a  is a drawing of a part  200  of a room  100  to be cleaned, the part being subdivided into polygons  101 ,  202 ,  203  in accordance with an exemplary embodiment,  
         [0044]    [0044]FIG. 2 b  is a drawing of an associated connectivity graph  210  for the part of a room to be cleaned in accordance with an exemplary embodiment,  
         [0045]    [0045]FIG. 3 is a drawing of a room  100  to be cleaned, three cleaning robots  304 , communication distances  305  of the three robots  304 , assigned cleaned part domains  301 , assigned uncleaned part domains  302  and unassigned uncleaned part domains  303  in accordance with an exemplary embodiment,  
         [0046]    [0046]FIG. 4 is a drawing of a room  100  to be cleaned, with two isolated part domains  401  (polygons) in accordance with an exemplary embodiment,  
         [0047]    [0047]FIG. 5 is a drawing of a ground plan  500  of a supermarket to be cleaned,  
         [0048]    [0048]FIGS. 6A and 6B are a table of simulation results  600 ,  
         [0049]    [0049]FIG. 7 is a flowchart of operations during an assignment of a part domain in accordance with an exemplary embodiment. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0050]    Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout.  
         [0051]    The procedure described below in the context of the exemplary embodiment is based on a dynamic division of a room to be cleaned by cleaning robots.  
         [0052]    Fundamentals of the Procedure  
         [0053]    The fundamental idea, which forms the basis of the procedure described below, is to subdivide the room  100  to be cleaned into individual polygons  101 , i.e. part domains  101 , as illustrated in FIG. 1.  
         [0054]    The individual robots then allocate and clean these polygons  101 . In this case, allocating a polygon  101  means that a robot undertakes to clean a specific polygon  101  and declares this.  
         [0055]    Unlike other known dynamic methods, the procedure described below does not require that the individual robots be able to communicate with each other at all times. Consequently a global communication network is not required. It is entirely sufficient if the robots can communicate from time to time in order to exchange notifications.  
         [0056]    Procedure  
         [0057]    The procedure in the exemplary embodiment is based on a dynamic division of the room  100  to be cleaned. The room  100  is first divided into polygons  101 . Individual polygons  101  are then selected and allocated using a connectivity graph (FIG. 2 b ,  210 ).  
         [0058]    After a robot has allocated one or a plurality of polygons, it begins to clean them. When a robot has allocated or cleaned polygons, it naturally must notify the other robots of this, since they would otherwise allocate and clean these polygons also. This is not always possible, however, since the individual robots cannot always communicate with each other.  
         [0059]    The following assumes that two robots can communicate with each other when their communication distance is less than a predetermined distance. In this context, the predetermined communication distance represents a communication radius of a robot (FIG. 3, 305).  
         [0060]    The work of a robot is complete when it knows that all polygons are allocated and when it has cleaned all the polygons allocated to it.  
         [0061]    Since robots can meet in the procedure and can therefore collide in the worst possible case, collision avoidance is very important. A special decentralized collision avoidance method as described in Jäger et al., “Decentralized Collision Avoidance, Deadlock Detection and Deadlock Resolution for Multiple Mobile Robots”, Int. Conf. On Intelligent Robots and Systems (IROS), 2001 is used for collision avoidance.  
         [0062]    Possible enhancements and alternatives to the exemplary embodiment are described below.  
         [0063]    Division into Polygons  
         [0064]    The room  100  which has to be divided is overlaid with a grid  102  (FIG. 1), wherein a number of polygons are created.  
         [0065]    The room is divided among the robots on the basis of these polygons  101  as the robots allocate and clean the individual polygons  101  one by one.  
         [0066]    Creation of a Connectivity Graph (FIG. 2 a  and FIG. 2 b )  
         [0067]    A connectivity graph  210  is created by establishing a node  201  for every polygon  101  and establishing an edge  206  for every polygon pair  202 - 203  which has a shared edge  204 . The connectivity graph  210  provides information about how the individual polygons  101  are interconnected.  
         [0068]    Notifications which are stored at the nodes  201  in the connectivity graph indicate whether a polygon is already allocated and whether a polygon  101  has already been cleaned.  
         [0069]    A connectivity graph  210  is a known concept in robotics J. C. Latombe, but is mainly used for navigation purposes.  
         [0070]    Selection of the Polygons to be Allocated  
         [0071]    The selection of the polygons which are allocated by a robot takes place in accordance with two principles. The first principle is that the robots always ensure that they have a reserve of a few polygons to be processed.  
         [0072]    Polygons to be processed are polygons which have been allocated but not yet fully processed. The second principle is that further polygons are added when it appears advantageous to do so.  
         [0073]    One restriction is that a polygon can in principle be allocated only if it is within the transmission range of the robot concerned, i.e. a robot must be less than a predetermined assignment distance from the center of the polygon.  
         [0074]    A suitable selection of the communication distance and of the assignment distance ensures that two robots wanting to allocate the polygon at the same time can communicate with each other.  
         [0075]    If a robot has no more polygons to process and cannot allocate a new polygon because none is within transmission range, the robot moves towards a new polygon.  
         [0076]    Allocation in Reserve (FIG. 3)  
         [0077]    Since a robot always allocates a few polygons in reserve  302 , it begins to allocate again as soon as the number of polygons  302  to be processed falls below a specified threshold.  
         [0078]    A restriction in this case is that the robot only allocates new polygons if the zone of the polygons which are to be processed is adjacent. This restriction is necessary in order to prevent the excessive fracturing of an area which is to be processed.  
         [0079]    The selection of the polygons to be newly allocated is done according to the following criteria:  
         [0080]    a) Only polygons which have not already been allocated by other robots (or by the robot itself) are allocated.  
         [0081]    b) Polygons must be adjacent to the polygons which are already allocated.  
         [0082]    c) The newly allocated polygons should, in combination with the polygons which have just been processed, have the smallest possible diameter. This reduces the danger of a collision with other robots on the one hand Christou et al., I.T. Christou, Yackel et al., and on the other hand it benefits the cleaning because a compact area is advantageous in this case.  
         [0083]    Special Allocation (FIG. 4)  
         [0084]    The special allocation is essentially for preventing isolated polygons  401 . A polygon is considered isolated if it has no more unallocated neighboring polygons  402 .  
         [0085]    Without special handling of such isolated polygons  401 , it is possible that all polygons  101  in the neighborhood of an isolated polygon  401  might already be cleaned, without the isolated polygon  401  being cleaned. This means that a robot might be required to make a long detour in order nonetheless to processes the remaining isolated polygon  401 .  
         [0086]    Therefore, if a robot finds that the area which it is currently processing borders an isolated polygon  401 , the robot allocates this isolated polygon  401 .  
         [0087]    Allocation of a Polygon (FIG. 3 and FIG. 7)  
         [0088]    Supposing that a robot has now selected a polygon for allocation  701 , it must agree this with all other robots which also wish to allocate the polygon. This is performed by a “Provisional Allocation Procedure” (AVV) described below (FIG. 7, 701 to  705 ).  
         [0089]    The polygon for allocation must be within transmission range, thereby ensuring that the robots can communicate in this case.  
         [0090]    The selected allocation strategy or AVV is based on a mixture of a selection algorithm Chang et al., “An Improved Algorithm for Decentralized Extrema-finding in Circular Configurations of Processes”, Communications of the ACM, vol. 22, 1979, pp. 281-283 and a Contract Net Protocol R. G. Smith, “The Contract Net Protocol: High-level Communication and Control in a Distributed Problem Solver”, In IEEE Transactions on Computers, number  12  in C-29, 1980, pp.1104-1113 in this case.  
         [0091]    a) According to this allocation strategy, a robot which wishes to allocate a polygon  701  sends an AllocationRequest message  702  to all the other robots it is able to communicate with. The message contains the ID of the polygon which the robot wishes to allocate, and an Importance Value (IV) which indicates the importance to the robot of this allocation.  
         [0092]    The IV is determined as follows:  
               IV        (   poly   )       =     1   -         ∑     p   ∈   SP              min        (       dist        (     p   ,   poly     )       ,   MAXDIST     )       MAXDIST            SP                    (   1   )                               
 
         [0093]    where SP is a number of generated polygons, dist( . . . , . . . ) is a function for determining the distance between two polygon centers, min( . . . ) is a function for determining a minimum, I . . . I is an amount function, MAXDIST is a maximum distance between two polygon centers, and poly or p is an index for a polygon.  
         [0094]    b) If a robot receives an AllocationRequest message,  
         [0095]    it sends an AllocationRefuse message  703 ,  704  if it has itself already sent an AllocationRequest message for the same polygon and its IV is greater than the IV of the received AllocationRequest message (if the IV is the same, a decision is made on the basis of the robot IDs),  
         [0096]    it sends an AllocationAccept message  703 ,  705  if it has itself already sent an AllocationRequest message for the same polygon and its IV is smaller than the IV of the received AllocationRequest message,  
         [0097]    it sends an AllocationAccept message  703 ,  705  if it has not itself sent an Allocation Request message for the polygon,  
         [0098]    c) If a robot receives an AllocationRefuse message, it knows that its allocation cannot succeed and cancels it  704 .  
         [0099]    d) If a robot receives AllocationAccept messages in response to all the Allocation Request messages is has sent, the allocation is successful and is complete. The same applies accordingly if the robot does not receive any AllocationRefuse messages  703 ,  705  (see below).  
         [0100]    e) After a robot has allocated a new polygon, it notifies all the others (see ‘Forwarding of notifications’ below).  
         [0101]    It should also be noted that during the process of allocation, the number of robots participating in the allocation can change. New robots can come into communication transmission range, for example, or robots which are already known can move too far away.  
         [0102]    Clearly this must also be considered in the allocation strategy described above or in the AVV. Consequently, it might be necessary to send further AllocationRequest messages to newly arriving robots (Point a), or it might not be necessary to wait for all AllocationAccept messages (Point d)  703 ,  705 .  
         [0103]    Forwarding of Notifications (FIG. 3)  
         [0104]    Since the individual robots are not always able to communicate with each other due to the limited communication distance  305 , each robot develops its own local view of allocated and cleaned polygons during the course of processing or cleaning the room.  
         [0105]    For example, if one robot allocates a polygon and another robot is not within communication transmission range at that moment, the other robot clearly knows nothing of the allocation. Therefore it has a different view.  
         [0106]    In order to synchronize the local views of the robots, they exchange notifications about allocated  302  and cleaned  301  zones as soon as they are able to communicate with each other. They therefore synchronize their local views and develop a common view.  
         [0107]    The smaller the communication radius  305 , the less frequently the robots can communicate with each other, and the greater the variation in the individual local views of the robots.  
         [0108]    If the local views vary too much, polygons are allocated and cleaned more than once as a result.  
         [0109]    Enhancements and alternatives to the exemplary embodiment are described below.  
         [0110]    a) The introduction of assembly points where the robots meet at regular intervals in order to synchronize their local views.  
         [0111]    b) The use of a special robot which does not clean but travels regularly back and forth among the other robots in order to distribute notifications.  
         [0112]    c) The release of a polygon which has already been allocated if another robot has completed its work and could therefore process this polygon.  
         [0113]    d) The dynamic adaptation of the number of polygons which can be allocated in reserve, i.e. if only very few polygons overall remain to be allocated, fewer polygons are allocated in reserve (whereby the robots all finish at approximately the same time).  
         [0114]    Simulation and Simulation Results (FIG. 5 and FIG. 6)  
         [0115]    Under the heading ‘Forwarding of notifications’ above, it was shown that the limited communication opportunities of the robots result in different local views of the robots, which can then result in unnecessary work.  
         [0116]    In order to establish the extent of the effect of the local views on the cleaning performance, simulations are carried out.  
         [0117]    A CAD plan  500  of a large supermarket (FIG. 5) was used as a basis for this. FIG. 5 shows the supermarket and three (cleaning) robots  501 .  
         [0118]    Three simulations were carried out in each case for different communication radii and quantities of robots.  
         [0119]    [0119]FIG. 6 shows the results of the simulations in tabular format, where the first two columns  1  and  2  of the table  600  represent the communication radius and the relevant quantity of robots in each case.  
         [0120]    Columns  3  and  4  of the table  600  specify the proportion of polygons which were double allocated and double cleaned. In this case, the values always relate to the total domain to be cleaned. The final two columns  5  and  6  of the table  600  show the average values of the three simulations.  
         [0121]    The table  600  in FIG. 6 demonstrates that the proportion of duplicated work increases when the communication radius or the quantity of robots is reduced. When the communication radius is smaller, the robots cannot communicate with each other so often. When more robots are used, the notifications are distributed more quickly.  
         [0122]    The described method is a fully dynamic method. The division of the room takes place entirely at runtime.  
         [0123]    Furthermore, the method is based on a fully decentralized approach. There is no need for central components, nor is there a requirement for global coordination.  
         [0124]    The method does not presuppose a global communication network. The worst consequence of the restricted communication abilities of the robots is duplication of effort, though this is limited even under unfavorable conditions. The simulation results substantiate this.  
         [0125]    The invention has been described in detail with particular reference to preferred embodiments thereof and examples, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention.