Proceedings of the 2003 IEEURSJ
`Intl. Conference on Intelligent Robots and Systems
`Las Vegas. Nevada ’ October 2003
`A Real-time World Model for Multi-Robot Teams
`with High-Latency Communication
`
`Maayan Roth, Douglas Vail, and Manuela Veloso
`School of Computer Science
`Carnegie Mellon University
`Pittsburgh PA, 15213-3891
`{moth, dvail2, mmv}@cs.cmu.edu
`
`this paper, we present in detail our approach
`Abstract-In
`to constructing a world model in a multi-robot team. We
`introduce two separate world models, namely an individual
`world model that stores one robot’s state, and a shared world
`model that stores the state of the team. We present procedures
`to effectively merge information in these two world models in
`real-time. We overcome the problem of high communication
`latency by using shared information on an as-needed basis.
`The snccess of our world model approach is validated by
`experimentation in the robot soccer domain. The results show
`that a team using a world model that incorporates shared
`information is more successful at tracking a dynamic object
`in its environment than a team that does not use shared
`information.
`
`I. INTRODUCTION
`The need to operate under partial observability and
`interact with objects in the environment makes the creation
`of a world model a necessity for most robotic systems.
`In a multi-robot system, where several agents interact
`simultaneously with each other and also with shared
`portions of the environment, the need for a consistent
`view of the world is even greater. For systems where the
`primary goal of the system is to cooperatively map an area
`using several robots, the challenge is to merge information
`from several agents coherently. (e.g. [7], [SI) However,
`these observations do not need to be merged in real-time,
`as the environment tends to be static.
`In adversarial domains, such as robot soccer, the envi-
`ronment is dynamic. In addition to knowing the positions
`of its teammates to facilitate cooperation, the robot must
`be able to quickly locate the ball and avoid adversarial
`agents. When using local vision as the primary sensor,
`soccer-playing agents are usually unable to observe their
`entire environment. Unless communication between team-
`mates is available, each robot must model its environ-
`ment without input from other agents. Until recently, it
`was common for teams competing in RoboCup to build
`their world models without using shared information.
`The 1999 RoboCup Agilo RoboCuppers mid-sized robot
`team provides an example of world model design without
`communication [l]. In the Sony legged-robot league, the
`hardware for communication was not available on the
`robots until 2002. In the absence of communication, teams
`
`relied on local sensing to build their world models, and
`fixed roles for team behavior. (e.g. [Ill)
`
`The advantages of utilizing communication when it
`becomes available are obvious. In the RoboCup middle-
`sized robot competition, each team is able to design their
`own hardware platform. From the beginning, teams have
`taken advantage of this freedom by incopmating com-
`munication hardware into their team design. For example,
`the Agilo RoboCuppers added communication to their
`system for the RoboCup 2000 competition. By using a
`Kalman filter to fuse information about the locations of
`objects in the environment, they enabled each robot on
`their team to use a global world model as if it were its own
`local model [5]. In another highly successful mid-sized
`robot team, CS Freiburg, each robot maintains a local
`world model, hut contributes information to a global world
`model on a single off-board server. This server then sends
`global world model information back to the individual
`teammates, allowing them to update their state of the
`world [4], [31. However, the presence of communication
`presents additional challenges. High communication la-
`tency can easily prevent teammate agents from forming
`a synchronized world-view in real-time. Trusting delayed
`information can introduce more error into an agent’s world
`model than is removed by integrating shared information.
`
`The focus of this paper is to present our solution to
`the problem of building a real-time world model for a
`multi-robot team with high-latency communication within
`the context of the RoboCup Sony AIBO competition. We
`assume for the purposes of this paper that the robots are
`able to sense task-relevant objects such as the soccer ball,
`teammate robots, and opponent robots. The techniques that
`we describe are applicable to any domain where a robot
`interacts with a combination of passive objects that can
`be sensed and manipulated, intelligent agents that can be
`detected but with whom the robot cannot communicate,
`and intelligent agents that can communicate with the robot
`for the purpose of sharing information.
`
`0-7803-7860-1/03/$17.00 0 2003 IEEE
`
`2494
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on December 26,2023 at 16:13:51 UTC from IEEE Xplore. Restrictions apply.
`
`RoboticVisionTech EX2013
`ABB v. RoboticVisionTech
`IPR2023-01426
`
`

`

`Fig. I. This is one the Sony AIBO robots for which this world model
`was implemented. The round aperture at the tip of the robot’s nose is
`the CCD camem that is used IO capture visual sensor data.
`
`on the field [6], [lo]. The output of the localization is two
`2-dimensional Gaussian distributions, one for the robot’s
`position and one for the robot’s heading. Each Gaussian
`distribution is characterized by:
`
`- ‘ p , the mean, a 2-d vector.of (x. y) position
`
`U, the standard deviation, a 2-d vector of (%q)
`This year, wireless communication, in the form of
`802.11 Ethernet, was available on the AIBO robots. This
`communication, although it has low bandwidth and high
`latency, allows the sharing of state information between
`teammates. This paper presents our solution to utilizing
`communicated information effectively, despite being un-
`able to synchronize data streams from different robots due
`to high latency, and without relying on an external server
`for centralized information processing.
`Using the information acquired by each robot through
`its own vision and integrating the information commu-
`nicated between teammates on an as-needed basis, we
`introduce an approach for representing the world with two
`separate world models: an individual world model that
`describes the state of one robot, and a shared world model
`that describes the state of the team.
`
`Fig. 2. This image shows two AIBO robots on a regulation-sized field.
`The vertical cylinders in the comers of the field .we the color-coded
`markers that are used by the robots for localization.
`
`11. SOURCES OF KNOWLEDGE FOR BUILDING
`STATE
`The 2002 AIBO robots perform all computation and
`sensing on-hoard, with the team forming a fully distributed
`system. The robots have two sources of information that
`are used to build state: vision and communication. Each
`robot is equipped with a CCD camera located at the front
`of its head. (See Figure 1) All relevant objects in the world
`are color-coded, allowing the identification of an object by
`its color. The camera information is processed to produce
`output in the form of (x, y , e), oriented in the robot’s local
`coordinate system, for all of the objects in the current
`field of view [Ill. The objects that the vision is able to
`recognize are six color-coded markers at known locations
`around the field, two goals at either end of the field, the
`orange ball, and the other robots, which are either blue or
`red. Figure 2 shows an image of the field.
`The robots have an a priori map of the field that gives
`locations for each of the markers. The locations of the
`markers as observed by vision are compared to the map
`and are used by each robot to compute its own location
`
`111. INDIVIDUAL WORLD MODEL
`
`Each robot maintains for itself an individual world
`model that contains its perception of the state of the world.
`The individual world model is a vector containing the
`positions of all the task-relevant objects in the robot’s
`environment. In our robot smcer task, it is comprised of:
`wmpusitiun, the robot’s position
`
`- wmheading, the robot’s heading
`
`wmball, the location of the ball
`wmfeammnte, a vector of n teammate positions
`wmnppunent, a vector of m opponent positions
`Each element of the individual world model contains
`two components: a 2-dimensional position stored in global
`coordinates, and a timestamp, 5. The position is stored
`as a Gaussian structured to contain the same format
`of information as the Gaussian parametric distributions
`described in Section 2.
`We identify three distinct classes of objects that are
`stored in a world model. These are objects that are updated
`either entirely from vision information, entirely from
`communicated information, or by using a combination
`of the two. It is necessary to choose among these three
`policies to determine an appropriate update procedure
`for each component of the world model. In our task, a
`vision-only update is used for the robot’s own position
`wmpusitiun and wmheading, and for the opponent posi-
`tion vector, wmdpponent. The teammate position vector,
`wmfeanimate, relies entirely upon shared information
`broadcast by each robot. Only the ball position, wnidall,
`
`2495
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on December 26,2023 at 16:13:51 UTC from IEEE Xplore. Restrictions apply.
`
`

`

`relies on both sources of information, combining its posi-
`tion as returned by vision with information that is shared
`between teammates.
`The updates to the robot's location, wmposition and
`wmheading, come directly from localization, which in
`turn relies entirely on vision and the robot's internal map
`of the field. Although the vision returns positions for
`robots of both colors, making it theoretically possible for
`teammates to observe each other, the robots are physically
`identical, making it impossible to distinguish visually
`between robots on the same team. Therefore, a robot will
`not be able to improve its own localization estimate by
`integrating estimates of its position broadcasted by its
`teammates. For this same reason, it is difficult to accu-
`rately update the opponent position vector, wmapponent.
`The vision module returns a vector of the positions of
`all opponent robots that were observed. Again, there are
`no visual characteristics that distinguish one opponent
`from another. In solving this data association problem,
`we utilize a greedy approach. The world model attempts
`to match a new observation of an opponent to a previous
`observation already stored in the world model by updating
`the stored position that is physically closest to the newly
`observed position.
`For the reasons detailed above that indicate that a
`robot's own localization is more accurate than estimates
`of its position broadcasted by teammates, it is preferable
`to use the position provided shared by each robot to its
`teammates when updating the teammate position vector,
`wmfeammate, rather than attempting to integrate both
`sources of information. When updating, the position of
`each teammate is requested from the shared world model
`and stored directly in wmfeammate.
`The position of the ball, wmAall, is the only element
`of our world model that benefits from combining sensing
`information returned by vision with shared information
`transmitted between teammate. The procedure to update
`ball position can be broken down into two steps: an update
`from vision and an update from shared information.
`
`A. Update f " Vision
`The most accurate estimate of ball position, wmbail,
`is extracted from the information returned by vision and
`updated as described in Table I. Because vision returns
`the locations of objects in coordinates local to the robot,
`whereas the positions are stored in global coordinates in
`the world model, it is necessary to convert all object
`positions into global Coordinates. If vision reports that the
`ball has been seen, it is merged with the old ball position
`[9]. [21. The merge method takes advantage of the property
`of Gaussian distributions that states that the product of
`two Gaussians is also a Gaussian. By multiplying the
`two position estimates, taking into account their standard
`deviations, we end up with an estimate that is a weighted
`
`average of the old position and the new observation.
`Because we grow uncertainty with time, old information
`is given less weight than new information that starts
`with the default small standard deviation, SMALLLRROR,
`allowing us to converge to the correct ball position with
`relatively few observations. However, by not discarding
`the old ball position out of hand, we are able to maintain
`a smoother estimate of ball position that does not fluctuate
`drastically as a result of spurious sensor readings. When
`merging the ball positions, it is important to limit the
`standard deviation, own,baii,
`to no less than the default
`to prevent it
`minimum confidence value, SMALL-ERROR,
`from becoming vanishingly small.
`
`TABLE I
`PROCEDURE TO UPDATE FROM VISION
`
`B. Update from Shared Information
`When vision has failed for a certain period of time to
`provide information about the position of the ball, the ball
`position is updated, as in Table II, from information stored
`in the shared world model. The format of the shared world
`model is described in Section 4.
`As explained in Section 2, the communication latency
`between robots is extremely high. Each robot receives
`information from its teammates, on average, every .5
`seconds, but the latency was occasionally observed to be
`as high as 5 seconds. Additionally, because timestamps
`associated with the data are local to each robot and
`cannot be matched between robots, it is impossible to
`integrate shared information via a Kalman filter, unlike
`other implementations that did allow this approach [5].
`Because of these restrictions, we use the shared ball infor-
`mation sparsely, and only when the ball cannot be easily
`located by an individual robot. If the ball has not been
`observed by the robot for a period of time greater than
`?,h,e,hoid, the best available ball location is requested from
`the shared world model, using the GETBALLLOCATION
`function. (See Table IV and the accompanying description
`in Section 4.)
`
`C. Accounting for Aging Information and Localization
`Changes
`Because the robot soccer environment is dynamic, we
`expect objects to move over time from where the robot last
`
`2496
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on December 26,2023 at 16:13:51 UTC from IEEE Xplore. Restrictions apply.
`
`

`

`Procedure UPDATESHAREDINFORMATION(T~,.,,N)
`
`if ' c u r m ! ~ - 'wnholl ' ' l h m h d d
`stzaredball= GETBALI.LOCATION(T,,,, roborid)
`if shredhall # NIL
`w m b d = M E R G E ( W ~ ~ ~ / ,
`shoredball)
`'>v,,,h;r = Tcurmu
`
`TABLE I1
`PROCEDURE TO UPDATE FROM SHARED INFORMATION
`
`observed them. Although we intend to investigate velocity-
`tracking in the future, we present here a position-only
`world model that does not attempt to track velocities. To
`account for unobserved motion of objects without knowing
`their velocities, we grow our uncertainty for any object in
`the individual world model that was not observed in the
`to each object's
`last time step by adding SMALL€RROR
`standard deviation.
`The localization module and the individual world model
`are updated at different times during the system execution,
`making it necessary to correct the world model to account
`for changes in localization information. When the robot
`executes a localization update due to seeing a marker,
`its estimate of its own position changes, even though its
`physical position has not changed. To ensure consistency
`between the individual and the shared world models,
`objects in both .'world models are stored in global coor-
`dinates. However,'this means that changes in the robot's
`knowledge of its position caused by seeing a marker also
`make it appear"to the robot as if the other objects in its
`environment have suddenly changed position with respect
`to itself. Because we need to know the position of the
`ball with high accuracy at all times, it is necessary to
`correct the position of the ball to account for this shift
`immediately (Table m).
`
`Procedure SHIFTBALL()
`Get mborposirion and robotan&de
`Shift the ball position into local coordinates:
`
`Y J ~ ~ I = ROTAT"(grobt+virion' -~fobo,ang;e)
`k m h r ! = I w m h l l - !-"dwd
`Do the localization update from the sensor reading
`Get the updated robot position and heading.
`Shift the ball back into global coordinates:
`Ilro~lobnl = RoTATE(H,~;,~~',s',,h)
`Yvnhl;
`jh"or;t;on
`- f i t o ~ o c a ~
`TABLE Ill
`CORRECTION FOR LOCALIZATION SHIFT
`IV. SHARED WORLD MODEL
`The shared world model is a fully distributed data
`Structure, with each robot maintaining its own on-board
`copy. The contents of each robot's shared world model
`are:
`
`swmposirion, a vector of n teammate positions
`
`- swm-goak a vector containing a flag for each team-
`
`swmdall, a vector containing each teammate's esti-
`mate of the ball position
`
`mate, indicating whether or not that robot is the goal
`keeper
`swmsawball, a vector containing a flag for each
`teammate, indicating whether or not that robot saw
`the ball in the last time step
`The last flag, swmsawball is important because it pre-
`vents other robots from incorporating old or second-
`hand information into their individual world models when
`they receive an update from this robot. Each element in
`swmposition and swmball is made up of a 2-dimensional
`Gaussian and a timestamp, T , as in the individual world
`model.
`Updates to the shared world model occur asyn-
`chronously, with each robot updating its model whenever
`it receives a broadcast from a teammate. This means that
`communication latency or dropped messages may cause
`the shared world model contents to differ among robots.
`By not requiring synchronization between teammates, we
`avoid the communication overhead required to synchro-
`nize. Each robot broadcasts its own shared information at
`a rate of 2 He. Although this seems slow, it is due in part
`to bandwidth limitations. Additionally, because the high
`and variable latency prevents us from using the shared
`information for fine-grained control, there is no reason to
`broadcast at a higher rate.
`Table IV shows the procedure that is used by the
`individual world model to access information stored in the
`shared world model. The GETBALLLOCATION procedure
`determines which, among all the ball positions estimates
`reported by the team members, is the 'best' estimate
`of the true ball position. In the current implementation,
`we attempt to select the hall estimate that has the low-
`est uncertainty, and which has been observed within a
`We do not allow a
`reasonable period of time, T
`,
`~
`~
`~
`~
`~
`~
`robot to retrieve its own reported estimate from the shared
`world model, as this would only reinforce the robot's
`belief without adding new information. Additionally, we
`
`require the uncertainty to be below o,hrerhord. a maximum
`allowable uncertainty.
`V. EXPERIMENTAL RESULTS
`The shared and individual world models contributed
`in this paper are fully implemented and were used by
`the CM-Pack'OZ legged-robot team in the 2002 RoboCup
`competition. The team performed extremely well, winning
`the competition to become the world champion.
`In order to experimentally verify the efficacy of the
`world model separate from the overall performance of the
`team in competition, we designed a controlled experiment
`in the lab. We compare the behavior of a robot team using
`our world model, constructed with both sensor and shared
`
`2497
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on December 26,2023 at 16:13:51 UTC from IEEE Xplore. Restrictions apply.
`
`~
`
`~
`
`.
`
`
`
`

`

`Procedure GETBALLLOCATIoN(~~,,,~=,*~,
`roborLi4
`ball = NIL
`besfranpence = qfhreshoId
`for i = 1 ... n
`if i # mborid
`if ISVALIo(i, T,,,,~,,,)
`if u~,vmhll, < besrronjdence
`besrronjdence = asriVnihll,
`boll = swmba[li
`
`return ball
`
`Procedure IS VALID(^, T ~ ~ , , ~ ~ , )
`if i < 0 or i > n
`return FALSE
`if ‘currmt - 7 s n d d l , > ‘threshold
`return F A L S E
`if “$slvmboll. > “threshold
`return F A L S E
`if swmsawba/li # false
`return FALSE
`return TRUE
`
`TABLE IV
`P n O c E D u n E TO GET THE BEST BALL LOCATION
`Ball seen
`
`Fig. 3. Different degrees of certainty about ball position through which
`the robot transitions during execution.
`
`information, to an identical robot team using only local
`sensor information for determining ball location.
`The robot behaviors are comprised of many bebav-
`ior states, some of which can execute simultaneously.
`Each robot transitions between states as a function of
`its individual world model, its localization, and some
`teamwork objective functions [12]. A new behavior is
`chosen 20 times per second. During the execution of most
`behaviors, such as positioning itself on the field or walking
`towards the ball, the robot opportunistically observes the
`world, updating its world model and localization as it sees
`markers or objects. As the robot’s uncertainty about the
`position of the ball grows, it transitions between the states
`illustrated in Figure 3.
`The robot’s certainty about the position of the ball is
`highest in State 1, when the ball has been seen within
`
`n
`
`II
`
`I cycles in I % cycles I
`I
`1 cycles I aearch
`I searching 1 stms
`total
`#
`I 1.84 %
`I 95437 I 1754
`I 74
`SHARED
`NOSHARED 1 101076 I 19683
`I 19.47 % I 330
`TABLE V
`COMPARING H O W OFTEN THE BALL IS LOST B Y COUNTING
`BEHAVIOR CYCLES SPENT IN THE SEARCHSPIN BBHAVWIOR, WITH
`AND WITHOUT SHARED INFORMATION
`
`
`
`the last time step. If the ball has been seen recently, the
`robot operates in State 2, using the position of the ball
`saved in its individual world model. State 3 is triggered
`when the robot chooses to request information from its
`shared world model, as described in Section 3, and valid
`shared information is returned. If there is no valid shared
`information available, and the age of the ball position
`information in the individual world model’grows beyond
`a threshold, T
`the ball is considered “lost”, and
`~
`~
`~
`~
`~
`~
`,
`the robot transitions into State 4, where the behavior
`SEARCHSPIN is executed. The threshold of time without
`knowing the position of the ball that triggers a transition
`into the SEARCHSPIN behavior was chosen to be ap-
`proximately 5 seconds. In this behavior, which interrupts
`the robot’s previous behavior, the robot spins in place,
`attempting to locate the ball on the field. Because this
`behavior interrupts other behaviors, we seek to minimize
`its occurrence.
`In the experiment that we conducted, we ran two teams,
`each comprised of three robots, in two soccer games
`against each other. The teams are identical, with three
`attacker robots each. However, in one team, the robots
`were not permitted to use shared information to update the
`ball position. This is equivalent to forbidding transitions
`into State 3 as it is depicted in Figure 3. Each game lasted
`around 10 minutes, during which the ball was replaced
`in the center of the field whenever a goal was scored,
`but the robots were not moved back to their starting
`positions. Each attacker robot wrote to an on-board log
`file every frame, and indicated whether or not it was
`currently executing the SEARCHSPIN behavior, and if
`this cycle was a new transition into the SEARCH-SPIN
`behavior. Table V shows the results of our experiment. In
`this table, SHARED refers to the teams that used shared
`information and NOSHARED refers to the teams that did
`not share ball information. The “#starts” column indicates
`the number of times that the robots transitioned into the
`SEARCHSPIN behavior. The “cycles in search” column
`gives the total number of behavior cycles in which the
`SEARCHSPIN behavior was executed.
`The robots use the confidence and timestamp values
`stored in the individual world model to determine when to
`transition into the SEARCHSPIN behavior. Therefore, we
`consider the SEARCHSPIN behavior to provide an accu-
`rate estimate of how frequently the individual world model
`
`2498
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on December 26,2023 at 16:13:51 UTC from IEEE Xplore. Restrictions apply.
`
`

`

`considers the hall to be lost. Without shared information
`from their teammates, the robots considered the ball to
`he lost for 19.47% of the game time, over 10 times more
`than the robots that did incorporate shared information.
`They were forced to interrupt their game-playing behavior
`to search for the ball on average every 306 frames,
`4.2 times more often than the team incorporating shared
`information. By effectively integrating information that is
`shared between cooperative agents, as demonstrated by
`these results and the results shown in [U], we are able
`to minimize the instances in which the robots are unable
`to locate the ball, thus improving the performance of our
`robots over what they would be able to achieve without
`cooperation.
`
`VI. CONCLUSION
`In this paper, we presented OUT approach for building
`a real-time world model for a fully distributed multi-
`robot team. Communication between teammates on our
`hardware platform had high and variable latency, making
`it impossible to synchronize with sensor data that anived
`predictably at 20 Hz. Despite this challenge, we were able
`to utilize shared information effectively by building both
`an individual and a shared world model for each agent,
`and using shared information only when appropriate and
`..
`on an as-needed basis.
`Our experimental results clearly show that sharing infor-
`mation about the state of the world with teammates helps
`robots to overcome the problem of partial observability
`when locating relevant objects in their environment. By
`using both the individual and the shared world models, the
`robots were more aware of the position of the task relevant
`dynamic object (e.g the ball), and needed to interrupt
`their goal-directed behaviors to re-acquire its position with
`lower frequency.
`Communication, even with lower latency, and the need
`to merge state information gathered by local sensing with
`collaborative information shared between robots on the
`same team, are ongoing challenges for the multi-robot
`domain. Our approach, detailed in this paper, contributes a
`step towards meeting this challenge by providing a method
`that is applicable to any multi-robot team that operates un-
`der equivalent real-time and high latency communication
`conditions.
`
`VII. ACKNOWLEDGMENTS
`This research was sponsored by Grants No. DABT63-
`99-1-0013, F30602-00-2-0549, and by generous support
`by Sony, Inc. This material was based upon work sup-
`ported under a National Science Foundation Graduate
`Research Fellowship. The content of this publication does
`not necessarily reflect the position of the funding agencies
`and no official endorsement should be inferred.
`
`VIII. REFERENCES
`[l] Thorsten Bandlow, Michael Klupsch, Robert Hanek
`and Thorsten Schmitt. Fast image segmentation,
`object regocnition and localization in a RoboCup
`scenario. In RoboCup-99: Robot Soccer World Cup
`Ill, pages 174-185, 2000.
`[2] Silvia Coradeschi and Alessandro Saffiotti. Anchor-
`ing symbols to vision data by fuzzy logic. Lecture
`Nofes in Computer Science, 1638:104-115, 1999.
`[3] Markus Dietl, Jens-Steffen Gutmann, and Bernhard
`Nebel. CS Freiburg: Global view by cooperative
`sensing. In RoboCup 2001 Intenwtional Symposium,
`2001.
`[4] Jens-Steffen Guttman, Wolfgang Hatzack, Immanuel
`Herrmann, Bernhard Nebel, Frank Rittinger, Au-
`gustinus Topor, and Thilo Weigel. The CS Freiburg
`team: Playing robotic soccer based on an explicit
`world model. The AI Magazine, 2000.
`[5] R. Hanek, T. Schmitt, M. Klupsch, and S. Buck.
`From multiple images to a consistent view.
`In
`RoboCup 2000: Robot Soccer World Cup IV, pages
`169-178, 2001.
`[6] Scon Lenser and Manuela Veloso. Sensor resetting
`localization for poorly modelled mobile robots. In
`Proceedings of ICRA-2000, 2000.
`[7] Lynne E. Parker, Kingsley Fregene, Yi Guo, and Raj
`Madhavan. Distributed heterogeneous sensing for
`outdoor multi-robot localization, mapping, and path
`planning. In Alan C. Schultz and Lynne E. Parker,
`editors, Multi-Robot Systems: From Swarms to Intel-
`ligent Automata. Kluwer Academic Publishers, 2002.
`[8] Ioannis M. Rekleitis, Gregory Dudek, and Evange-
`10s E. Milios. Multi-robot collaboration for robust
`exploration. Annals of Mathematics and Artificial
`Intelligence, 31(1-4):7-40, 2001.
`[9] Ashley W. Stroupe, Martin C. Martin, and Tucker
`Balch. Distributed sensor fusion for object position
`estimation by multi-robot systems. In Proceedings
`of ICRA 2001, 2001.
`[lo] Ashley W. Stroupe, Kevin Sikorski, and Tucker
`Balch. Constraint-based landmark localization. In
`Proceedings of 2002 RoboCup Symposium, 2002.
`[ l l ] William Uther, Scott Lenser, James Bruce, Martin
`Hock, and Manuela Veloso. CM-Pack'Ol: Fast
`legged robot walking, robust localization, and team
`behaviors. In RoboCup-2001: The FiJth RoboCup
`Competitions and Conferences, 2001.
`[I21 Douglas Vail and Manuela Veloso. Dynamic multi-
`robot coordination. In Multi-Robot Systems. Kluwer,
`2003.
`
`2499
`
`Authorized licensed use limited to: Sterne Kessler Goldstein Fox. Downloaded on December 26,2023 at 16:13:51 UTC from IEEE Xplore. Restrictions apply.
`
`