=Paper=
{{Paper
|id=Vol-408/paper-8
|storemode=property
|title=Coordinated multi-agent exploration
|pdfUrl=https://ceur-ws.org/Vol-408/Paper08.pdf
|volume=Vol-408
|dblpUrl=https://dblp.org/rec/conf/lanmr/LopezP08
}}
==Coordinated multi-agent exploration==
https://ceur-ws.org/Vol-408/Paper08.pdf
Coordinated multi-agent exploration
Abraham Sánchez L. and Alfredo Toriz P.
Facultad de Ciencias de la Computación, BUAP
14 Sur esq. San Claudio, CP 72570 Puebla, Pue., México
asanchez@cs.buap.mx, alfredot@hotmail.com
Abstract. Many successful robotic systems use maps of the environ-
ment to perform their tasks. In this paper, we propose a cooperative
exploration strategy for multi-agent robots. This proposal is a para-
llelization of the basic SRT method, the following functionalities were
added to it: cooperation to increase the efficiency, coordination to avoid
conflicts and communication to cooperate and to coordinate. The goal
in robot exploration must be to minimize the overall exploration time,
and multiple robots produce more accurate maps by merging overlapping
information that helps to stabilize the sensor uncertainty and to reach
the goal. We present simulation results to show the performance of the
proposed technique.
1 Introduction
Although most mobile robotic systems use a single robot that only operates in
its environment, a number of researchers have considered the advantages and
disadvantages of the potential use of a group of robots that cooperate for the
accomplishment of a required task [1], [2], [3]. Multi-agent systems (MAS), may
be regarded as a group of entities called agents, interacting with one another to
achieve their individual as well as collective goals.
The research domain of multi-agent robot systems can be divided into subdo-
mains according to the task given to the robot group [4]. At present well-studied
subdomains are motion planning, formation forming, region-sweeping and com-
binations of the foregoing. We focused this paper in the region-sweeping task.
In the region-sweeping task, one can consider two activities.
In the first activity, a group of robots receives the order to explore/map an
unknown region. The goal is to obtain a detailed topography of the desired area.
In most exploration approaches, the boundary between know and unknown te-
rritory (the frontier) is used in order to maximize the information gain. In [5],
the robots merge the acquired information in a global grid-map of the envi-
ronment, from which the frontier is extracted and used to plan the individual
robot motions. The frontier-based approach lacks of an arbitration mechanism
preventing the robots from approaching the same frontier region. The approach
presented in [3] proposed to negotiate robot targets by optimizing a utility func-
tion which takes into account the information gain of a particular region, the cost
of reaching it and the number of robots currently heading there. The utility of a
2 Abraham Sánchez L. and Alfredo Toriz P.
particular frontier region from a viewpoint of relative robot localization and the
accuracy of map merging were considered in [6]. The incremental deployment al-
gorithm considers that the robots approach the frontier while they retain visual
contact with each other [7]. A multi-robot architecture proposed in [8] guide the
exploration by a market economy, whereas [9] proposes a centralized approach
which uses a frontier-based search and a bidding protocol assign frontier targets
to the robots.
Closely related to the exploring/mapping activity, the second one is called
complete coverage, where the robots have to move over all of the free surface in
the space.
Since exploration algorithms are already devised for a single robot it seems
straightforward to divide the area to be explored into disjunct regions, each of
which is assigned to a single robot. The robots communicate to each other the
area they have explored so that no part of the free space will be explored twice
unnecessarily. At no point during the task are the robots trying to form a fixed
formation. Each robot explores a different part of the unknown region and sends
its finding to a central device which combines the data received from the robots
into one global map of the area.
This paper presents a strategy to explore an unknown environment by multi-
agent robots. The strategy is a parallelization of the SRT (Sensor-based Random
Tree) method, which was presented in [10]. The SRT method, is an exploration
method based on the random generation of robot configurations within the local
safe area detected by the sensors. A data structure is created, which represents
a roadmap of the explored area with an associated safe region (SR). Each node
of the SRT consists of a free configuration with the associated local safe region
(LSR) as reconstructed by the perception system; the SR is the union of all the
LSRs. The LSR is an estimate of the free space surrounding the robot at a given
configuration. In general, its shape will depend on the sensor characteristics but
may also reflect different attitudes towards perception (see for example [11] for an
interesting extension of the SRT method). The extension of the SRT method to
multi-agent robots is essentially a parallelization of the basic method, we called
this extension, the Multi-SRT method. A decentralized cooperation mechanism
and two coordination mechanisms are introduced to improve the exploration
efficiency and to avoid conflicts. The basic steps of the exploration approach are
presented in Section II. Simulation results in different environments are discussed
in Section III. Finally, conclusion and future work are detailed in Section IV.
2 Cooperative exploration
MAS may be comprised of homogeneous or heterogeneous agents, it is considered
as crucial technology for the effective exploitation of the increasing availability
of diverse of heterogeneous and distributed on-line information sources. MAS
is a framework for building large, complex and robust distributed information
processing systems which exploit the efficiencies of organized behavior. Team-
Coordinated multi-agent exploration 3
work and communication are two important processes within multi-agent robots
designed to act in a coherent and coordinated manner.
Consider a population of n identical robots. Each robot is equipped with a
ring of range finder sensor or a laser range finder, the sensory system provides the
local safe region (LSR) S(q). The robots move in a planar workspace, i.e., R2 or a
connected subset of it; the assumption of planar workspace is not restrictive, 3D
worlds are admissible as long as the sensory system allow the reconstruction of
a planar LSR for planning the robot motion. Each robot is a polygon or another
shape subject to non-holomic constraints. The robot also knows its configuration
q, one can eliminate this assumption by incorporating a localization module in
the method. The robots know its ID number and each robot can broadcast within
a communication range Rc the information stored in its memory (or relevant
portions of it) at any time. The robot ID number is included in the heading of
any transmission. The robot is always open for receiving communication from
other robots inside Rc .
The design of the cooperative exploration strategy proceeds from the pa-
rallelization of the basic SRT method, each robot builds one or more partial
maps of the environment, organized in a collection of SRTs. Each node of an
SRT represents a configuration q which was visited by at least one robot, together
with the associated Local Safe Region S(q). An arc between two nodes represents
a collision-free path. The tree is incrementally built by extending the structure
in the most promising direction via a biased random mechanism. The presence
of other robots in the vicinity is taken into account at this stage in order to
maximize the information gain and guarantee collision avoidance.
The exploration algorithm for each robot is shown in Figure 1. First, the pro-
cedure BUILD SRT is executed, i.e., each robot builds its own SRT, T is rooted
at its starting configuration qinit . This procedure terminates when the robot
can not further expand T . Later, the robot executes the SUPPORT OTHERS
procedure, this action contributes to the expansion of the SRTs that have been
built by others robots. When this procedure finishes, the robot returns to the
root of its own tree and finishes its exploration.
BUILD Multi-SRT(qinit )
1 T .init(qinit )
2 BUILD SRT(qinit .T );
3 SUPPORT OTHERS(qinit );
Fig. 1. The Multi-SRT algorithm.
The procedure BUILD SRT is shown in Figure 2. In each iteration of the
BUILD SRT, the robot uses all available information (partially collected by
itself and partially gained through the communication with other robots) to
identify the group of engaged robots (GER), i.e. the other robots in the team
4 Abraham Sánchez L. and Alfredo Toriz P.
with which cooperation and coordination are adequate. This is achieved by the
construction of the first group of pre-engaged robots (GPR), or robots that
are candidates to be members of the GER, and are synchronized with them
(BUILD AND WAIT GPR). Then, the robot collects data through its sensory
systems, it builds the current LSR (PERCEIVE) and updates its own tree T .
The current GER can now be built (BUILD GER). At this point the robot pro-
cesses its local frontier (the portion of its current LSR limit leads to areas that
are still unexplored) on the basis of T as well as any other tree Ti gained through
communication and stored in its memory (LOCAL FRONTIER).
If the local frontier is not empty, the robot generates a random configuration
contained in the current LSR and headed towards the local frontier, if not,
the target configuration is fixed to the node father with a backward movement
(PLANNER). If the GER is composed only by the same robot, the robot moves
directly to its target. Otherwise, the paths advanced by the robot in the GER
are checked for mutual collisions, and classified in feasible and unfeasible paths
(CHECK FEASIBILITY). If the subset Gu of robots with unfeasible paths is
vacuum, a coordination stage takes place, perhaps, confirming or modifying the
current target of the robot (COORDINATE). In particular, the motion of the
robot can be banned by simply readjusting the target to the current configu-
ration. Then, the function MOVE TO transfers the robot to the target (when
this is different from qact ). The loop is repeated until the condition in the output
line 15 is verified: the robot is unable to expand the tree T (no local frontiers
remaining) and therefore it has to move back to the root of its SRT.
BUILD SRT(qinit , T )
1 qact = qinit ;
2 do
3 BUILD AND WAIT GPR();
4 S(qact ) ← PERCEIVE(qact );
5 ADD(T , (qact , S(qact )));
6 G ←BUILD GER(); S
7 F(qact ) ← LOCAL FRONTIER(qact , S(qact ), T , Ti );
8 qtarget ← PLANNER(qact , F(qact ), qinit );
9 if qtarget 6= N U LL
10 if |G| > 1
11 (Gf , Gu ) ← CHECK FEASIBILITY(G);
12 if Gu 6= ∅
13 qtarget ← COORDINATE(Gf , Gu );
14 qact ← MOVE TO(qtarget );
15 while qtarget 6= N U LL
Fig. 2. The BUILD SRT procedure.
We detail the most important stages of the BUILD SRT procedure [12]:
Coordinated multi-agent exploration 5
Construction of GPR/GER. At the start of BUILD SRT, the robots are
stationary and need to identify the other robots whose LSRs may overlap
with its own, in order to cooperate (optimize the exploration) and coordinate
(avoid conflicts) with them. The other robots may be stationary as well (in
this case, their targets coincide with the current configuration) or moving to
the target, therefore a synchronization phase is necessary.
Two robots are GPR-coupled if the distance between their target configu-
rations is less than 2Rp , i.e. twice the range of perception of the sensorial
system. The GPR of the robot is then built by grouping together all robots
and connecting a chain of coupled GPRs (see Figure 3, left). To achieve
synchronization, the GPR is calculated and updated until all its members
are stationary (BUILD AND WAIT GPR). The communication range, Rc ,
clearly plays an important role in the construction of the GPR; for this
method two cases have been considered, according to the communication
range:
1. Limited communication range. Since the maximum distance between
the robot and any other robot GPR-coupled is 3Rp (the other robot can
still be moving to its target, which however could not be further away
than Rp of the current configuration) , it is sufficient to assume that
Rc ≥ 3Rp to ensure that the GPR accounts for all the robots that are
candidates to belong to the GER.
2. Unlimited communication range. Given the nature of this commu-
nication, the robot always knows the status of the other robots, and
therefore will know which robots are candidates to be GPR-coupled; the
distance to be GPR-coupled as in the above case will remain 3Rp . In
this way, as in the previous case, it is ensured that the GPR accounts
for all the robots that are candidates to belong to the GER.
The synchronization phase ensures that all robots in the GPR are stationary
when the GER is processed. The GER is a symmetric structure, this is the
same for all robots in the group. The GER is a cornerstone in our approach,
as it identifies a group of robots that, in view of its vicinity, spontaneously
agree to cooperate and coordinate with each other on a temporary basis.
Frontier extraction. Once the robot has been synchronized with its GER,
the procedure LOCAL FRONTIER is called to process the portion of the
limits of the LSR S(qact ), leading to areas that are unexplored according
to the information available. To this end, the robot uses its own tree T
as well as any other tree stored in its memory and received by present or
past communications. To find promising directions in S(qact ), its boundary
is divided into arcs with obstacles, free arcs and frontier arcs (see Figure 4).
Planner. The planner determines the new target configuration on the basis of
the local an open frontiers associated to the current node. The open frontier
of a tree (subtree) is the sum of the lengths of the local frontiers associated
to its nodes. If the local frontier F(qact ) of the current LSR is not empty,
the planner generates a random configuration in the direction of F(qact ).
Thanks to synchronization done by the function BUILD AND WAIT GPR,
all the robots in a GER plan at the same time, and therefore the cooperation
6 Abraham Sánchez L. and Alfredo Toriz P.
mechanism intrinsic to the definition of the local frontier is strengthened
throughout the GER. This agreement attempt is performed without any
centralized decision module.
The possibility that the robot is subject to non-holonomic constraints is
considered by the function MOVE TO, which is responsible for generating
feasible paths. The controllability of the robot ensures that any goal confi-
guration in the LSR can be reached by paths that are feasible in the LSR.
GER path feasibility check. Although the robot’s local frontier can not be-
long to the LSR of another robot of the GER, the two prospective paths
can still intersect. The function CHECK FEASIBILITY verifies whether the
prospective paths of the robots in the GER G are all simultaneously feasible
or not. To this end, all pairs of paths that intersect with others are identified,
and the corresponding robots stored in the unfeasible subset Gu of the GER.
The remaining robots constitute the feasible subset Gf of the GER.
Coordination. If the subset Gu of robots with unfeasible paths is not vacuum,
the coordination function is invoked. The first step is to choose a master
robot within G. This can be complemented in many ways through a deter-
ministic procedure known by all the robots, for example, the robot with the
highest ID number can be elected. Two cases are possible then:
1) If the robot is the master, it invokes an ORGANIZE function, whose
task is to rearrange the vector Qg that contains the targets of the robots
in the GER and obtain a feasible collective motion. Here, the change may
mean whatever, simply accepting or readjusting the target of a robot to the
current configuration (i.e., authorizing/prohibiting the motion) or adding a
third option, for example, changing to a new target.
2) If the robot is not the master, it enters in a waiting phase, which ends
with the receipt of a specified signal from the master.
The final operation is to retrieve and return the robot’s (possibly modified)
own target from Qg .
Fig. 3. An example of GPR/GER. At the left, the GPR of robot 1 consists of robots
0, 1, 2 and 3; robot 0 is still moving towards its target point, while robots 1, 2, 3 are
stationary. At the right, once the LSR have been computed, only robots 1, 2 and 3
belong to the GER of robot 1 since their LSRs overlap in pairs.
Coordinated multi-agent exploration 7
Fig. 4. Definition of frontier, free and obstacle arcs in the Local Safe Region S.
The procedure SUPPORT OTHERS (see Figure 5) can be divided into two
major phases, which are repeated over and over again. In the first phase, the
robot picks another robot to support it in his exploration, or, more precisely,
another tree that helps it to expand (there may be more than one robot acting
on a single tree). In the second phase, the selected tree is reached and the robot
tries to expand it, tying subtrees constructed by the procedure BUILD SRT.
The main cycle is repeated until the robot has received confirmation that all the
other robots have completed their exploration.
The loop is repeated until the robot has received confirmation that all the
other robots have finished their exploration.
S At the beginning, the robot collects
in a set I the trees belonging to Ii that may require support for expansion.
In particular, defining the open frontier of a tree (subtree) as the sum of the
lengths of local frontiers associated with its nodes, a tree Ti is put in I, if its
open frontier is at least equal to a constant F̄ multiplied by the number of
robots that are active in Ti , according to the most recent information available
(ACTIVE ROBOTS). If I is not empty, the robot selects a particular tree Ts
of I, according to some criterion (for example, the tree with the closest root,
or the most recent update), and move to its root. Once there, the robot begins
a subtree expansion using the BUILD SRT procedure. During this process, the
robot keeps on trying to add subtrees to Ts until it has returned to the root of
Ts and its open frontier is zero. At this point, the robot returns to the root of
its own tree (i.e. its start configuration) and becomes available to support the
expansion of other trees. This phase is only used when an unlimited communi-
cation range is handled, because the robot who is providing assistance can count
with updated information of the other robots and its last states at any time,
in contrast with a limited communication range with probably partial and not
updated information.
8 Abraham Sánchez L. and Alfredo Toriz P.
SUPPORT OTHERS(qact )
1 do
2 for i = 1 to n
3 if OPEN FRONTIER(Ti ) ≥ F̄ · ACTIVE ROBOTS(Ti )
4 ADD(T , Ti );
5 Ts ← SELECT(T );
6 if Ts 6= NULL
7 qact ← TRANSFER TO(Ts .root);
8 BUILD SRT(qact , Ts );
9 qact ← TRANSFER TO(T .root);
10 while EXPLORATION RUNNING()
Fig. 5. The SUPPORT OTHERS procedure.
3 Simulation results
In order to illustrate the behavior of the Multi-SRT exploration approach, we
present two strategies, the Multi-SRT Radial and the Multi-SRT Star. The strate-
gies were implemented in Visual C++ V. 6.0, taking advantage of the MSL
library’s1 structure and its graphical interface that facilitates to select the algo-
rithms, to visualize the working environment and to animate the obtained path.
The library GPC developed by Alan Murta was used to simulate the sensors
perception systems2 .
The tests were performed on an Intel ° c Pentium D processor-based PC
running at 2.80 GHz with 1 GB RAM. One can consider two possible initial de-
ployments of the robots. In the first, the robots are initially scattered in the en-
vironment; and in the second, the exploration is started with the robots grouped
in a cluster. Since the Multi-SRT approach is randomized, the results were ave-
raged over 20 simulation runs. Figure 6 illustrates the environments used for the
simulation part. The first is a square region with a garden-like layout, where each
area can be reached from different access points. The second is also a square, it
contains many obstacles of different shapes.
Exploration time for teams of different cardinality are shown in Figure 7, both
in the case of limited and unlimited communication range. In theory, when the
number of robots increases, the exploration time would quickly have to decrease.
This affirmation is fulfilled in the case of the scattered start; note however that,
in the case of the clustered start, there are examples where this affirmation is
not verified. We consider that an increment of the number of evenly deployed
robots corresponds to a decrement of the individual areas they must cover. In
the case of a limited communication range, when the robots are far apart at the
start, they can exchange very little information during the exploration process.
1
http://msl.cs.uiuc.edu/msl/
2
http://www.cs.man.ac.uk/∼toby/alan/software/
Coordinated multi-agent exploration 9
Fig. 6. Environments used for the tests of the Multi-SRT.
The total travelled distance increases with the number of robots because more
robots try to support the others in their expansion.
Fig. 7. Environment 2 exploration with scattered and clustered start. To the left with
unlimited communication range and in the right with limited communication range.
Figures 9 and 10 show the Multi-SRT and the explored region for the envi-
ronment 1 with a team of 5 and 10 robots in the case of unlimited communication
range, also Figure 8 illustrates the SRT and the explored region for the envi-
ronment 1 with 1 robot. We can see the difference when the robots are evenly
distributed at the start or are clustered. At the end, the environment has been
completely explored and the SRTs have been built. In these figures, we can ob-
serve that each robot built its own SRT and when one of them finished, this
entered the support phase.
If we compare the exploration times in the three last figures, we can affirm
that to greater number of robots, the exploration time decreases. If we also
observe the placed figure in the center of both figures 9 and 10, one can note
that the trees are united, this indicates that the support phase took place. Single
robots can not produce accurate maps like multi-robots. The only advantage of
using a single robot is the minimization of the repeated coverage.
10 Abraham Sánchez L. and Alfredo Toriz P.
Fig. 8. The SRT and explored regions with one single robot. Time = 101.408 secs with
112 nodes.
Fig. 9. Environment 1 with 5 robots. The Multi-SRT and explored regions with sca-
ttered start. Time = 54.348 secs with 141 nodes.
Fig. 10. Environment 1 with 10 robots. The Multi-SRT and explored regions with
scattered start. Time = 26.658 secs with 32 nodes.
Coordinated multi-agent exploration 11
However, even though repeated coverage among the robots decreases the mi-
ssion’s efficiency, some amount of repeated coverage is a desirable situation for
better efficiency. Additionally, this better efficiency can be achieved by coordi-
nation among robots.
The two strategies (Multi-SRT Star and Multi-SRT Radial) were compared
through simulations. We used the same environment to prove the efficiency of
Multi-SRT Radial over Multi-SRT Star and the same free parameters.
The authors in [10] presented a method called SRT-Star, which involves a
perception strategy that completely takes the information reported by the sensor
system in all directions; S is a region with the star form because of the union
of several ‘cones’ with different radii each one. Espinoza et al., presented in [11]
an interesting extension of the SRT method. The SRT-Radial strategy proposed
in this work takes advantage of the information reported by the sensors in all
directions, to generate and validate configurations candidate through reduced
spaces without the identification of the cone.
Figure 11 above presents the explored regions and safe region obtained with
the Multi-SRT Star strategy for the environment 2, for a team of 7 robots in
the case of unlimited communication range. On the other hand, Figure 11 down
illustrates the explored regions and the safe region with Multi-SRT Radial. The
final number of nodes in the tree and the exploration time are much smaller with
Multi-SRT Radial that with Multi-SRT Star.
Fig. 11. Environment 2. A comparative between Multi-SRT Star and Multi-SRT Ra-
dial.
12 Abraham Sánchez L. and Alfredo Toriz P.
Architectures for multi-robot exploration are usually classified as centralized
and decentralized or distributed. In centralized architectures a central entity
plans the actions of all the robot team, while in the decentralized approaches each
robot makes use of local information to plan its exploration. Our approach is a
decentralized cooperative exploration strategy for mobile robots, its coordination
mechanisms are used to guarantee exploration efficiency and avoid conflicts.
Decentralization causes serious problems, such as conflicts among the agents
(robots) and their respective goals. This is because the knowledge contained
in each agent might be incomplete, and goals of agents might be in conflict.
Therefore, conflict resolution is a critical and implicit problem in MAS.
The local coordination procedure implemented in our work guarantees that
the collective motion of the robots is feasible from the collision viewpoint. The
approach does not need a central supervision. The selection of exploration actions
by each robot is spontaneous and it is possible on the basis of the available
information.
4 Conclusions and future work
Multi-robot systems are emerging as a the new frontier in Robotics research,
posing new challenges and offering new solutions to old problems. Multi-robot
systems are not a collection of robots performing a once-for-ever fixed task in a
settled and static environment. They are collections of interacting, cooperating
autonomous agents with physical embodiment that impose restrictions on what
they can do, but also give them power to do some specific things. Thus the
paradigms of Multi-Agent and Multi-robot systems are somehow related and the
recognition of this parallelism may foster new avenues for research and solutions.
We have presented an interesting approach for cooperative exploration based
on the SRT-Radial. The Multi-SRT considers two decentralized mechanisms of
cooperation at different levels. The first simply consists in making an appropriate
definition of the local frontier that allows each robot to plan its motion towards
the areas apparently unexplored for the rest of the team. The second allows a
robot that has finished with its individual exploration phase, to support others
robots in their exploration task. Additionally, we compared Multi-SRT Radial
strategy with Multi-SRT Star strategy, the results obtained with our proposal
are more interesting.
Exploration and localization are two of the capabilities necessary for mobile
robots to navigate robustly in unknown environments. A robot needs to explore
in order to learn the structure of the world, and a robot needs to know its
own location in order to make use of its acquired spatial information. However,
a problem arises with the integration of exploration and localization. A robot
needs to know its own location in order to add new information to its map,
but a robot may also need a map to determine its own location. Most exiting
localization approaches refer to the single robot case. This means a posture of
one robot is decided by its own sensor data, the robot should have an expensive
sensor that can measure the robot pose in the global frame. If a robot can use the
Coordinated multi-agent exploration 13
sensor data of other robots, a cheap sensor system can be used. This reveals the
importance of cooperative localization which estimates the pose of each robot
by fusing information obtained from the other robots.
The integration of a localization module into the exploration process based on
SLAM techniques will be an interesting topic for a future research. We can also
consider an extension of the Multi-SRT exploration method, where the robots
constantly maintain a distributed network structure.
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