Ontology-Based Coalition Formation in
Heterogeneous MRS
L.Fanelli, A.Farinelli, L.Iocchi, D.Nardi, G.P.Settembre
University of Roma "La Sapienza.", surname©dis, uniromal, i t
A b s t r a c t . Multi-robot coordination is an important field of study in
the recent years, due to the need of systems designed for complex tasks.
Recently, the capability to perform tasks achievable only by multiple
collaborating robots has been investigated, and there are studies on scenarios where robots can accomplish tasks/missions only if they have some
aid from other robots.
Our work focuses on coalition formation, where a robot coalition is a set
of robots that is able to accomplish tasks that none of its member could
perform autonomously with same effectiveness. We use a knowledgebased approach: we define an ontology for modelling robot capabilities
and, using description logics reasoning systems, we realize a procedure
that yields a partition of a team of robots in coalitions that improves the
overall team performances.
1
Introduction
The use of heterogeneous multi-robot systems requires the definition of specific
strategies that take care not only of the environment characteristics, but also of
the different elements in terms of sensorial and actuation resources each robot
can supply the others with.
The concept of teamwork [1] describes in the best way this kind of problems.
The strategies of teamwork are especially important in all those contexts in
which it is necessary to execute multi-robot tasks, where the members of the
t e a m must act like a single entity to execute, through the sharing of resources
and cooperation, tasks that a single member could not perform.
We need to observe that the different models of teamwork in a multi-robot
context succeed in giving remarkable results in systems t h a t are strongly coordinated (following the terminology proposed in [2]). Notice that effectiveness and
performance of the specific coordination protocols, needed to correctly execute
the tasks, are limited for large teams in which the necessary interactions are
often a small subset of the whole. Moreover, various tasks could often have to
be executed simultaneously and in different places by robots of the same team.
For all these reasons, following a common approach (e.g. [3], [4], [5]), a frequent
choice is to subdivide large groups of robots in small Sub-teams, commonly called
coalitions, everyone weakly coordinated with the others but strongly coordinated
inside itself. Typically, coalitions have a shorter life with respect to the team,
Copyright © held by author
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and can frequently change in time on the basis of the tasks that have to be
executed.
Following [4], the set of all disjoint coalitions is called the coalition structure and finding the optimal coalition structure is called the coalition formation
problem. It has been proved that such a problem can be treated as an instance
of a set partitioning problem which is NP-complete [3].
Important factors to deal with this problem are: the interest on distributed
solutions; the need for robustness related to new events (a new task to be performed, the fault of a robot, or the introduction of a new robot in the team);
the possible use of multi-task robots, in which a single robot contributes to the
task execution performing more than one activity at the same time.
Many models have been suggested by researchers in multi-agent contexts to
provide an efficient and effective cooperation among the members of the same
team, but the validity of each of them cannot be directly carried to multi-robot
contexts, as described in [4], because of the un-transferability of functionalities,
the continuous evolution of the environment, and the different view of the world
by the various robots.
Among the different proposals for coalition formation in multi-robot contexts, an interesting approach is used by Parker, Tang in [5]. It consists in associating robots in coalitions using software reconfiguration, searching for new
not-predefined strategies of teamwork, through the analysis of all the possible
connections among the shared schemas ([6]) of the robots. The coalition formation does not take place on the basis of some manually predefined strategies of
teamwork but it is also introduced the search for all the possible interactions
among the robots that allows the correct execution of the assigned tasks. In particular, Parker's approach solves the coalition formation problem in ST-MR-IA
contexts: Single-Task Robots performing Multi-Robot tasks using Instantaneous
Assignment, following the formal multi-robot task allocation (MRTA) framework
of [7].
Our approach starts from the consideration that a large search problem need
to be solved, if we start from the set of all the available schemas (Potential
Configuration Space), in order to screen all possible connections that can be
useful to execute the requested tasks.
More specifically we have to deal with a configuration problem ([8], [9], [10]).
To this end, we define an ontology of robot capabilities in OWL, Web Ontology
Language [11], that allows us to determine offiine what kind of tasks a robot
is able to execute according to the own configuration and the configuration of
other robots in the team.
The advantages of our approach are multiple:
reduction of the search space for online automatic coalition formation, through
robot classification and offline analysis;
- automatic derivation of the general bounds for coordination (i.e. AND-type
and OR-type relations among the subtasks executed by various robots) that
now are implicit in each type of coalition (useful to implement effective
strategies of teamwork);
-
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- reduction of the number of the messages exchanged at execution time through
the sharing of the same semantic model.
Moreover, our approach is more general with respect to solutions proposed
by previous works. In fact it applies to MT-MR-IA (Multi-Task Robots performing Multi-Robot Tasks using Instantaneous Assignment) and can be extended,
through proper adjustments, to distributed solutions and to MT-MR-TA (Timeextended Assignment, [7]).
The first part of this paper is devoted to the description of the ontology in
which we define the possible configurations of the robots and of the inference
mechanism we use to select the possible cooperation strategies. In the second
part we show our coalition formation strategy, based on an offline selection of
useful cooperation strategies and on an online anytime algorithm that searches
for the optimal coalition structure. Finally the approach is validated with an
experiment in a USAR ( Urban Search And Rescue) scenario and conclusions are
drawn.
2
Modelling
the configuration
problem
The distinguishing element of our methodology of coalition formation is the
search strategy of the possible solutions based on the capabilities of every robot.
Basic idea of our approach is to search all the admissible configurations,
meant as groups of robots correctly connected among themselves, and to analyze
each of them in order to point out new strategies of cooperation and make
effective choices among them.
In the state of art, a similar approach can be found in the ASyMTRe system [5]. ASyMTRe's approach considers robots as sets of possible behaviours
that, given a sequence of inputs, are capable to produce new data or determine the execution of the various activities. These behaviours are results of the
combination of pre-defined specific schemas ([6], [12]).
In our approach, robots are considered as a collection of functionalities that
allow to execute the requested tasks, if used in an appropriate way. In this way
it is possible to define a high level ontology that can be shared also with non
behaviour-based robots. Roughly speaking, configurations are selected solving a
classification problem.
T h e ontology. In this work, we define an ontology that draws its inspiration
from the Robot Description Ontology proposed in [13]. Such an ontology subdivides the analysis of the robotic system in three parts: the first makes reference
to the physical entities that constitute it, the second to its functionalities, and
the third to the possible interactions with other robots.
We use the robot ontology developed by C.Schlenoff and E.Messina [14] as
the taxonomy for the physical entities, and we introduce the concept of software
module to model different possible implementations of processing capabilities.
Concerning the interaction aspect, the ontology is specifically oriented to
cooperation as it allows us to infer the abilities of each of the robots, starting from
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their functionalities, the situations in which they operate and the connections
among them. In our analysis, we have considered a very restricted number of
possible interactions among the robots, however sufficient in our scenario.
The types of data t h a t robots can exchange, can be generally classified in
few important groups (i.e. images, sounds, position...). We have assumed that
each robot is capable to use seamlessly self-obtained information and information
provided by the others.
As for the functionality description, the ontology distinguishes among two
types of capabilities: actuation and sensorial capabilities.
We show in Fig.1 the hierarchical schema of the ontology.
Fig. 1. Hierarchical organization of concepts of the ontology.
As shown, sensorial capabilities, which we have modelled extensively, are subdivided in acquisition and processing capabilities. Both are in direct relationship
with the possible types of sensors and software modules defined in the physical
description of the robot. This simplifies the ontology as the user has to define
only sensors mounted on the robots and their data processing capability, without
caring about the related functionalities that will be inferred by the system.
The actuation capabilities that we consider are distinguished in capabilities
of movement and of manipulation. For this work it is enough to classify the
capabilities of movement based on the type of ground and to consider limited
manipulation capabilities (e.g. shift objects, open doors, etc.).
We have identified some relevant parameters that allow us to provide a measure of the quality and of the cost, in terms of resources needed for execution,
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of the various possible implementations of functionalities on robots and we have
defined them using some OWL data-type properties.
It is worth pointing out that each robotic scenario distinguishes the capability to accomplish a certain task depending on the environment in which robots
operate. In general all the environments are defined depending on situations,
that are the possible events that could happen during task executions. The possible coordination strategies significantly vary depending on situations, so every
different situation has to be considered during the search of possible interactions
among robots.
In order to map at our best all these elements in the selected applicative
scenario (see Sec.4), we introduce a simple ontology for the possible associated
situations and we differentiate the task definitions depending on the characteristics of the environment in which they have to be accomplished.
R e a s o n i n g . The application scenario considered in this work is the USAR
(Urban Search and Rescue) [15] scenario, in which the analysis of the environment (e.g., exploration) is predominant with respect to tasks that interact with
it. Consequently, we focus our attention only to sensorial interactions among
robots, while the analysis of actuation capabilities is reduced as much as possible.
We select a set of tasks that robots could be requested to accomplish in a
USAR environment. These constitute a task ontology that is linked, by means
of logical conditions, to the ontology of functionalities described in the previous section. The capability to perform specific tasks can be derived from the
combined use of functionalities of various types. For instance, the capability to
search and locate victims, with respect to the own position, can be derived from
the capability to recognize human bodies combined with the capability to locate
features in a stereoscopic image and with the presence of a stereo-camera. In a
DL-like formalism this is expressed by the formula:
Victim detection ~ Stereovision N Object positioning N Human body detection
In Fig.2 the hierarchic organization of the task ontology is drawn for the
USAR scenario. At bottom level, tasks are organized with respect to the sensorial
information that are required to accomplish them. E.g. among the Position tasks
there is 2D Obstacle detection, that can be accomplished using stereovision data
(through an appropriate Vision task) or using proximity sensors (PLS, etc....).
Some sets of tasks constitute Missions (as shown in Fig.2) that are the macroactivities that robots can execute. E.g. the "Identification" mission is achievable
if a coalition can do both the "Victim locating" and the "Victim ID detection",
and the "Victim status detection" tasks.
The chosen model for the ontology follows the standard paradigm for configuration problems ([8]), as the ontology of functionalities contains the description
of components, and the ontology of tasks the description of characteristics that
an admissible solution should have to satisfy the requirements (desired configuration).
In particular, our approach follows the component oriented configuration
model, as described by Stumptner in [10]. Robots are individuals in the on-
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I'------J
Functionality
Fig. 2. Tasks and Missions.
tology, defined on the basis of their sensors (components) and each robot is in a
selected scenario with consequent restrictions to the derivable capabilities.
Instance checking provides tasks and missions achievable by each robot autonomously (without collaboration) in the selected location. Connecting together
different robots (through the appropriate properties), it is possible to verify
which tasks and missions are achievable by a coalition of robots. The definition
of tasks implies that, if a robot A can share with other robots information B, B is
available to all robots connected with A. Notice that the configuration problem
is solved through ontology classification.
3
Coalition
formation.
The mechanism we used for coalition formation is partially inspired by the configuration algorithm described in ASyMTRe [5].
The algorithm in [5] searches for the best possible coalitions scanning the set
of previously selected potential solutions. A potential solution is a set of possible
links between schemas, that are distributed among robots, that are able to turn
on, for each of them, a selected motor schema. This definition is feasible only
on behaviour-based robots; moreover, it is valid only for robots that can activate
only one motor schema at the same time (ST-MR-IA contexts).
We use the reasoning capability of description-logics-based systems to deal
with more complex contexts. In particular we show how to solve the problem in
Ontology-Based Coalition Formation in Heterogeneous MRS
lll
a M T - M R - I A context. In order to handle Multi-Task robots we define a strategy
to select the activities that each robot must perform to grant the execution of
the Multi-Robot tasks, based on the notion of Useful coalitions: "possible sets
of robots that, using collaboration, are capable to accomplish more effectively the
requested activity in the chosen scenario". If it is required to increase the robustness of the system, a coalition is considered useful even if a single new redundant
task is achievable with respect to its sub-coalitions. Using an approach that aims
to reduce the number of redundant exchanged messages, a coalition is useful only
if a new mission is achievable with respect to its sub-coalitions. This definition
is feasible also for no behaviour-based robots, as long as they share the same ontology of functionalities and tasks. Moreover in our approach it is known which
missions will be achievable by each entire coalition. The coalition formation procedure uses this information to generate all and only those coalitions that are
able to solve the global task in the selected senario.
3.1
S e a r c h for useful coalitions.
The automatic coalition formation procedure t h a t we propose starts with an
off-line analysis of the team. At this step the application tries to connect robots
of different types, then reasoning to obtain the new capabilities of the team.
If at least one robot is able to accomplish new activities with respect to those
the robot can do autonomously or connected with a sub-set of the robots in the
same actual coalition, t h a n the new coalition is a useful coalition: consequently
the set of achievable tasks by the sets of robots is updated. The procedure goes
on connecting robots until all coalitions with less t h a n a predefined dimension
(Max-cooperation-size) are evaluated.
W i t h respect to the different possible definition for useful coalitions, the
algorithm can be executed with two different policies, if the user strictly prefers
robust coalitions rather maintaining low use of communication channels.
The size of the search space in the worst case is related only to the number
of different types of robots in the t e a m but in the mean case is strongly limited
by the value of the Max-cooperation-size constant. The choice of the constant
can be made with respect to the communication bandwidth limitations.
An interesting feature of this approach is that the ontology is modelled such
that the set of requests that each robot needs from the others is derivable; consequently, the activities that the other robots have to do in order to let the task
be accomplished by a coalition mate are known when the coalition is formed.
So it is possible to generate both the constraints for coordination, as A N D relations between activities, and the coordination specifics, as information to be
exchanged among coalition mates.
3.2
Coalition instantiatlon algorithm.
Solutions of the off-line procedure are inputs for the algorithm, that assigns each
robot to a certain coalition in order to accomplish the requested multi-robot
tasks.
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We aim at a m e t h o d that chooses coalition that can accomplish more complex
missions, in the best possible way. Consequently we must define an order among
the missions and a measure to evaluate the quality of a coalition, typically called
"utility".
M i s s i o n o r d e r i n g . Missions are classified, with a partial order from the
more complex ones to the simplest. Starting with the definition of the whole
mission, e.g. in our scenario it is named Rescue, and splitting iteratively in each
of its parts, we build a partial order of missions t h a t we need to accomplish.
Missions t h a t are not related with any order, will remain in competition. To obtain an optimal assignment of resources we must introduce other sorting criteria
among missions until a total order is reached. Alternatively it is necessary to define strategies t h a t are able to balance the resources among competing missions.
This analysis is outside the scope of this paper.
The coalition instantiation algorithm assigns a robot to a coalition formed to
accomplish a certain mission, only if at present time it is not possible to find a
set of collaborating robots where it can contribute to accomplish more complex
missions.
It is i m p o r t a n t to point out that, since the problem of scheduling resources
among different missions with respect to time and priority constraints is strongly
N P - h a r d ([7]), c o m m o n approaches to multi-robot coalition formation are not
oriented to possible extensions to time-extended assignment contexts. Our missionorder based mechanism makes possible the execution also in such contexts, once
an appropriate mission sorting criterion has been found.
C o a l i t i o n u t i l i t y . Robot utility Ui is evaluated similarly as in [5]:
Qi
G
E qi,j
E ci,j
"--
Ui = w* ~ i - -
- ( 1 - w) *
j=l
Ci
(1)
where each qi,j is one of the Qi quality factors related to functionalities used
by robot i to accomplish the assigned mission and each ci,j is one of the Ci
costs related to using such a functionality, w is a weight used to balance the
importance of quality factors with respect to costs. For our experiments we use
for each functionality three-valued quality factors (modelled in the ontology as
O W L d a t a - t y p e properties).
Even if the used utility evaluation function is very basic (the search for a
better one is not in purposes of this paper), it could be substantially refined
based on the knowlwdge represented in the ontology.
Coalition utility is the average of the utility of robots belonging to it, weighted
by complexity and importance of missions achievable by the coalition. The value
can be differently weighted if one wants to give importance to the number of
members of a coalition, or its robustness. The global utility of the t e a m is the
sum of utilities of its coalitions.
In [5] robot solutions are selected in order to maximize only private utilities
to robots. Instead, our algorithm evaluates the utility of the whole coalition
Ontology-Based Coalition Formation in Heterogeneous MRS
113
considering also the quality of produced and exchanged information (e.g. image
resolution, sound SNR, position reliability, etc.).
The change from local robot utility to coalition utility is necessary to find
the maximum global utility in situations in which robots must choose among
different activities to perform. Even if in a different coalition structure a robot
could perform other tasks with a better private utility, the algorithm tries to
find the assignment of robots to activities such that the team performs best.
D e s c r i p t i o n o f t h e a l g o r i t h m . The search strategy used in our procedure
is the same as in [5], with changes due to the use of coalition utility and mission
ordering.
For each robot (following a chosen order), the procedure selects first available
mates among those that can help it to accomplish the current mission. The search
scans only the already known useful coalitions and goes ahead starting from the
most complex mission and following their ordering. For each robot the solution
with the best coalition utility will be selected.
The algorithm is anytime and the set of solutions that maximize the global
utility can be found only with enough time, by ordering the robots in all possible
ways (O(n!)). The solution is optimal if there is a total order within competing
missions. The algorithm is sound if the weighted utility of a coalition is never
greater than the utility of coalitions that can accomplish more complex missions.
In order to find good solutions in reasonable time we use, as in [5], a heuristic
that consists in ordering robots on the basis of the information that each of them
can obtain autonomously, starting from the less capable one.
The algorithm outputs the selected coalition structure, the set of missions
achievable by each coalition and the coordination specifics related to each robot.
For tasks achievable only through collaboration, all exchanged (sent or received)
information needed to accomplish the task are mentioned.
4
Applicative
context.
The language we use to define our ontology is OWL [11], the description logics
based [16] W3C standard. As it has been remarked in many studies (i.e. [9]), description logics are one of the most appropriate tools to represent configuration
problems. Furthermore, the choice of OWL standard allows us to use an efficient editor as Protege and last generation reasoners. The algorithm described
in section 3 uses java plugins available by the Protege-OWL developers.
As environment for locations and robots, we choose the USAR (Urban Search
and Rescue) [15] scenario. It is an interesting environment both for the high number of sensorial information to provide for the execution of a mission, and for
the variability and unpredictability of the world where robots operate. In particular, in international competitions [15] there are three kinds of environments
(so called arenas), that have growing levels of difficulties, with situations like
obstacles, multi-level environments, steps, unsafe grounds.
In order to show the potential of our ontology-based approach to the configuration problem we describe a representative experiment in this scenario. We
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define four types of robots with different sensors, software modules and communication capability (see Fig.3(a)). We introduce a new type of sensor named
victim-rfid reader that allows to obtain information related to victims in the
arena. Moreover we consider not every robot able to communicate with the human operator.
Due to the lack of necessary information, robots are not autonomously able
to perform all the tasks (described in Fig.2) that are requested in USAR context. We assume each robot to be in the same basic arena where there are not
particular mobility constraints. We search for the possible useful coalitions with
Max-cooperation-size = 2 through the offline analysis and we decide to exclude
coalitions that can not perform new missions with respect to sub-coalitions.
In Fig.3(b) we show the results. Among the possible combinations of max two
robots, six of them have been selected by the algorithm and for each of them all
the implicit coordination constraints are inferred.
Robot type
Sensors
EXPLORER
Range Scanner
INU
BODY
DETECTOR
RFID
FINDER
VICTIM
FINDER
Software modules
Localization module
Explorer modulo
Navigator module
Mapping module
Slope module
Human body detecbon
Disparity map module
Range Scanner
Localization module
Stereo-camera
Navigator module
Rfid reader
Obiect positioning
Range Scanner
Localization module
VictlrmRtid reader
Navigator module
Rfid reader
Object poei~onin 9
(a)
Comm.systerr
Coalition type
Inter robots
Operator
interactmn"
Inter robots
Members types
Performabletasks
Single-1
EXPLORER
Single-2
RFID FINDER
Map building
2D Obstacle detection
Localization
Identification
2D Obstacle detection
Single-3
Coalition-1
Inter robots
Inter robots
VICTIM FINDER
BODY DETECTOR
RF!D FINDER
Coalition-2
EXPLORER
RFID FINDER
Coalition-3 EXPLORER
VICTIM FINDER
Identificalion
2D Obstacle detection
EBeloration
Rescue
(b)
Fig. 3. a)Description of experiment robots, b)Useful coalitions.
In Fig.4(a) is an example of the online procedure output, an instantiation
of a coalition that in Fig.3(b) is named Coalition-& The figure shows as, once
a robot has been assigned to a coalition, it is supplied with the information
regarding the tasks it has to perform and where to find the needed information.
A coordination protocol can handle these outputs to grant the correct execution of activities by the team. In particular, the one in [17] is ontology-based and
could be a useful extension of this paper, in order to realize a fully ontology-based
system.
The time requested to compute coalitions with large number of robots (i.e.50)
of different types is comparable with other previous solutions. We can generate
coalitions in a few seconds in multi-task robot contexts. With higher probability,
by choosing a suitable ordering, coalitions with high utility can be found at the
beginning of the coalition instantiation algorithm. Anyway, other sorting criteria
can be selected in order to better fit specific situations.
To test the validity of the approach, we used a recently developed graphic 3D
simulator, named Usarsim [18]. The useof such a simulation allows to efficiently
Ontology-BasedCoalitionFormationin Heterogeneous MRS
115
Robot,1 (Type:EXPLORER}
Name
Used info Race!red by
Tasks
Laser reading
Exploration
INU reading
Rfid
Robot-2
Type
Sent to
Received by
Map
Base
Sent Info Victim position
Base
Robot-2
Victim status
Base
Robot-2
Victim ID
Base
Robot-2
Robot-2 (T~/pe:VICTIM FINDER}
Name
Used Info Received by
_
Tasks
Victim
Victim Rfid
management Laser reading
Type
Sent to
; Received by
Rfid
Robot-1
Sent Info Victim position
Robot-1
Victim status
Robot-1
Victim 1[3
Robot-1
(a)
(b)
Fig. 4. a)Example of coalition specifics, b) Coalitions in a Usarsim arena.
test the capabilities of coalitions with many robots without the common costs of
multi-robot experiments. We performed preliminary experiments with extremely
heterogeneous MRS, which show that the coalitions formed with our approach
can successfully perform in basic USAR arenas (see Fig.4(b)).
5
D i s c u s s i o n and f u t u r e w o r k s
In this paper we addressed the problem of coalition formation in MT-MR-IA
contexts. Our approach aims at computing the best possible solution that each
robot can adopt to give its contribute for the success of the missions. In particular, we consider the problem of distributing the resources among different types
of missions. Once the algorithm is executed, robots are suitably subdivided and
grouped in order to favor the correct execution of the requested missions. In addition, each robot receives coordination constraints for the correct cooperation
with the other robots. In our experiments, we noticed that the offiine configuration procedure allows for a solutions of more complex multi-task problems with
the same run-time constraints.
As future work, we would like to consider a distributed version of the presented approach in order to increase the overall robustness of the system. Furthermore, it is interesting to investigate the possibility of integrating the presented approach with [19] in order to deal with MT-MR-TA contexts in the
USAR scenario.
An additional issue to be further investigated is the definition of metrics and
experiments for evaluation of robot capabilities and coalition formation effectiveness.
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