IQ-ASyMTRe: Synthesizing Coalition Formation and Execution forTightly-Coupled Multirobot Tasks

Yu Zhang and Lynne E. Parker

Proc. of IEEE International Conferenceon Intelligent Robots and Systems, Taipai, Taiwan, 2010.

Abstract— This paper presents the IQ-ASyMTRe architec-ture, which is aimed to address both coalition formation andexecution for tightly-coupled multirobot tasks in a single frame-work. Many task allocation algorithms have been previouslyproposed without explicitly enabling the sharing of robot ca-pabilities. Inspired by information invariant theory, ASyMTRewas introduced which enables the sharing of sensory and com-putational capabilities by allowing information to flow amongdifferent robots via communication. However, ASyMTRe doesnot provide a solution for how a coalition should satisfysensor constraints introduced by the sharing of capabilitieswhile executing the assigned task. Furthermore, conversionsamong different information types1 are hardcoded, which limitsthe flexibility of ASyMTRe. Moreover, relationships betweenentities (e.g., robots) and information types are not explicitlycaptured, which may produce infeasible solutions from the start,as the defined information type may not correspond well to thecurrent environment settings. The new architecture introducesa complete definition of information type to guarantee thefeasibility of solutions; it also explicitly models informationconversions. Inspired by our previous work, IQ-ASyMTRe usesmeasures of information quality to guide robot coalitions tosatisfy sensor constraints (introduced by capability sharing)while executing tasks, thus providing a complete and generalsolution. We demonstrate the capability of the approach both insimulation and on physical robots to form and execute coalitionsthat share sensory information to achieve tightly-coupled tasks.

I. INTRODUCTION & RELATED WORK

Tightly-coupled multirobot tasks (MTs) [3] refer to tasksthat require the cooperation of multiple robots. The under-lying assumption is that individual robots may not haveall the capabilities required to accomplish a task; instead,multiple robots need to share their capabilities. In order todetermine appropriate coalitions of robots from the robotteam, many architectures [2] [9] [4] reason about coalitionsby dividing tasks into subtasks or roles that individual robotscan perform. For example, in a robot insertion task [8], asupervisor robot provides visual information to guide theimplementor robot to execute the insertion. One issue withthis approach is that subtasks or roles have to be predefinedfor different tasks, as it is not feasible to define all possiblesubtasks or roles for arbitrary tasks. Another issue is thatrobots sometimes need to share sensory and computationalcapabilities in order to accomplish a task. Defining robot

This material is based upon work supported by the National ScienceFoundation under Grant No. 0812117.

Yu Zhang and Lynne Parker are with the Distributed IntelligenceLaboratory in the Department of Electrical Engineering and ComputerScience, University of Tennessee, Knoxville, TN 37996-3450, USA,{yzhang51,parker}@eecs.utk.edu.

1Information types differ from data types (e.g., integer) in that they havesemantic meanings (e.g., a robot’s global position).

capabilities in terms of subtasks or roles is often too coarse,and is often not helpful for enabling capability sharing.

The work of [2] achieves fault-tolerant task allocationwith uncertain task specifications using a cooperative backoffadaptive scheme. It defines robot capabilities in terms ofbasic high-level tasks and allows robots to use task executionhistories to detect and adapt to device imperfections andmalfunctions. However, it does not explicitly enable capa-bility sharing among robots and hence the flexibility of theapproach is limited. The work of [4] introduces a market-based framework for tight coordination in multirobot tasks.Passive coordination is used to quickly produce solutionsfor local robots, while active coordination is used to pro-duce complex solutions via coordination among teammates.Although the robots need to tightly coordinate throughcommunication, robot capabilities are still not shared. Thework of [9] adapts a multiagent coalition formation algorithmto the multirobot domain and aims at maximizing the overallutility of the system. Again, robot capabilities are not sharedamong the robot team members. Inspired by informationinvariant theory [1], ASyMTRe [5] was proposed whichdivides robot capabilities into sensory and computationallevel schemas and motor schemas, and forms coalitionsby reasoning about the information required for activatingthese schemas. Connections among communication schemasenable information to flow through the system to whereit is required and capability sharing is implicitly achieved.The ASyMTRe architecture enables a finer resource sharingamong heterogeneous robots through communication and ishence more flexible. Thus, we build upon this approach inthe research described in this paper.

Another issue with tightly-coupled multirobot tasks is howto physically execute the tasks while sharing capabilities.This is especially challenging when the sharing of capabil-ities within the coalitions introduces sensor constraints. Ina cooperative robot navigation task for example, the leaderrobot shares its localization capability by communicating itsglobal position to the follower robot. In order to localize,the follower robot is constrained to keep the leader withinits field of view (FOV) so that it can compute the relativeposition of the leader. Only with both pieces of informationwould the follower be able to compute its own globalposition and then navigate to a desired goal position. Ourprevious work [10] develops an information quality basedapproach that provides a flexible way for maintaining sensorconstraints within the coalitions while executing tasks.

In order to achieve a complete solution for tightly-coupledmultirobot tasks, we need both ASyMTRe for forming coali-

tions as well as our previous approach for sensor constraintsatisfaction to physically execute the task. However, thecombination of the two approaches is not a simple addition.Several links are missing and challenging. First of all, thedefinition of information type in ASyMTRe is not suffi-cient for task execution. Knowing that a robot can sensethe relative positions of other robot teammates and that ateammate has a localization capability does not necessarilyimply a solution, since the two robots may not be withinthe line of sight of each other. The definition of informationtype has to be complete in the sense that the presence ofcertain information types guarantees a solution. This requiresan extended architecture in which the reasoning processcan distinguish among different environment settings (e.g.,where the robots are located) and provide feasible coalitionsolutions accordingly. Furthermore, information conversion,which is one of the key points of information invarianttheory, is not explicitly modeled. Without explicit modeling,application-specific code needs to be designed in advance fordifferent tasks. Moreover, during the task execution, whenthe information quality model identifies the situations inwhich the satisfaction of sensor constraints may potentiallyfail for certain coalitions, the robots must be able to searchand reform coalitions in a timely manner. Thus, dynamicenvironments should also be taken into account.

This paper presents a new architecture that combinesASyMTRe and our previous information quality based ap-proach into a complete solution for tightly-coupled multi-robot tasks. This approach, which we call IQ-ASyMTRe,introduces the capability of dynamic-environment reasoningfor dynamic coalition formation. To the best of our knowl-edge, this is the first attempt to create a complete and generalsolution for tightly-coupled multirobot tasks addressing boththe formation of coalitions, as well as the execution ofthose coalitions to address a specific task. After a review ofASyMTRe and our previous work (Sections II and III), weexplain the new IQ-ASyMTRe architecture in detail (SectionIV). Afterwards, we present experiments in simulation andwith physical robots to demonstrate some aspects of the newarchitecture (Section V). Finally, we conclude with somediscussion and plans for future work (Section VI).

II. ASYMTRE

The ASyMTRe architecture [5] defines basic buildingblocks of robot capabilities to be collections of environmen-tal sensors (ESs), perceptual schemas (PSs), motor schemas(MSs), and communication schemas (CSs). A robot, Ri, canbe represented by Ri = (ESi, Si), where ESi is a set ofenvironmental sensors installed on Ri, and Si is the set ofschemas that are pre-programmed into Ri. According to aset of rules, connections are created among the schemas onthe robots to allow information to flow through the system.A set of information types F = {F1, F2, ...} is introducedto label the inputs and outputs of each schema. A schemacan be activated if its inputs are satisfied either by sensorsor the outputs of other schemas with the same information

types. The ultimate goal is to activate the required MSs onthe robot coalition team members to accomplish the task.

For reasoning about coalitions, ASyMTRe uses an anytimealgorithm to search the entire solution space and return thebest solution found so far according to predefined cost mea-sures. One of the most important contributions of ASyMTReis that it enables a finer resource sharing by dividing robotcapabilities into smaller chunks (i.e., schemas), and reasonsabout how these schemas can be connected. Information canflow through the system to where it is required such thatcapability sharing is implicitly enabled through communica-tion. ASyMTRe has been shown to provide more flexibilityfor achieving tightly-coupled multirobot tasks. (Please referto [5] for more details of ASyMTRe.) However, severallimitations of ASyMTRe prevent its application to arbitraryphysical multirobot tasks. One of the most obvious limita-tions is that ASyMTRe does not provide a solution for howa coalition should satisfy the sensor constraints introducedby the sharing of capabilities while executing the assignedtask. This issue has been addressed in our prior work [10],which introduces an information quality based approach thatmodels sensor constraints explicitly and provides a generalmethod for satisfying the constraints, such that the coalitionscan be maintained during the execution.

III. THE INFORMATION QUALITY APPROACH

In order to flexibly control robots while maintainingsensor constraints through the environment, a mechanismis needed to quantify the utility of these constraints beingsatisfied. For this purpose, inspired by [6], our previous work[10] uses measures of information quality to describe thefitness for using the information in the current environmentsettings, including the retrievability and usefulness of theinformation. We divide the computation of the informationquality measurement into two parts. First, the sensor qualitymeasurement is used to describe the retrievability and/orusefulness of the information using the sensor based onsensor characteristics; second, environmental influence ismodeled as a weight to the sensor quality measurementto capture how the environment affects the retrievabilityand/or usefulness of the information. For example, in a robottracking task, the information quality for tracking is higherwhen the target is in the center of the tracker robot’s FOVthan if the target is on the edge of the FOV; in a box pushingtask, when the box is pushed too close to an obstacle, theinformation quality for tracking the box is reduced since theobstacle can potentially block the view of the box. To handlethe application-specific environmental influence, instead ofexact geometric reasoning, we compute the influence basedon environment samples. To compute a motion command forexecution, we sample the motion space into motion vectorsusing a motion model. Then for each motion vector, wepredict the information quality measurement for the robot’spredicted configuration after executing the vector. After-wards, we simply choose the motion vector that leads to thebest information quality (for more details, please see [10]). Aconstraint model is also implemented to provide alternative

coalitions when certain sensor constraints are unsatisfiable.For example, in a cooperative robot navigation task, when theview of the leader robot is blocked, the follower robot canrelax the original constraint to follow another robot whichis also following the leader. The relaxation of constraintsenables robot coalitions to dynamically change formations.This capability is important for robots to execute tasksin different environment settings. For example, to navigatethrough narrow hallways, the robots need to change from theoriginal formation into a line formation while maintainingthe relaxed constraints for achieving the same task.

Experimental results have illustrated that this approachworks for applications such as robot tracking and cooperativenavigation tasks. However, one obvious limitation of thisapproach is that the constraint model has to be designed inadvance to control how the constraints should be relaxed foralternative coalitions. The dynamic coalition formation capa-bility of ASyMTRe can reason about alternative coalitionsbased on the information required; the alternative coalitionscan be used to control the constraint relaxation process.Hence, a general solution for constraint relaxation is achievedby combining the two approaches.

IV. THE IQ-ASYMTRE ARCHITECTURE

We next describe the IQ-ASyMTRe architecture, includinga discussion of the incorporation of information quality. Wethen present the solution space for the new architecture anddiscuss the advantages and disadvantages of this approach.Coalition formation and execution are discussed afterwards.

A. Extensions of Representation

The incompleteness of the definition of information typein ASyMTRe is due to the fact that the relationships betweenentities and information types are not specifically captured.Entities can be locations, agents or anything that can beidentified in the environment. Intuitively, information mustbe specified with a set of referents. For example, the in-formation of rA’s global position is meaningless withoutspecifying rA. Furthermore, ASyMTRe does not explicitlymodel conversions among information types. Our approachto overcome these limitations is discussed in the following.

1) Referents for Information Types: For a particular infor-mation type Fi ∈ F (see section II), there are Ni referentsassociated with it. We represent the information type byFi(Ref1:Ni), where Refj is used to refer to the jth referentfor the information type Fi. Each referent, Refj , can beinstantiated to a particular entity or remain uninstantiatedfor future instantiations. Fully instantiated instances of in-formation types represent actual information that can beused. Partially instantiated instances of information typesrepresent a class of information. For example, FG(X) canbe the global position information of any entity that Xis instantiated to. Specifying referents for the informationtypes makes the definition of information type complete. Forexample, the relative position information type FR has tworeferents. After instantiating the two referents to robot rAand rB respectively, the reference of information FR(rA, rB)

TABLE IRULE PS USED IN COOPERATIVE ROBOT NAVIGATION TASK

Rule PS Description

FG(X) + FR(Y,X) → FG(Y ) global + relative → global

FR(Y,X) → FR(X,Y ) relative → relative

FR(X,Z) + FR(Y, Z) → FR(X,Y ) relative + relative → relative

has a unique meaning (i.e., rA’s position relative to rB), nomatter how the information is retrieved or used.

The advantage of a complete definition for informationtype is that infeasible coalitions can be excluded fromconsideration. For example, one way for robot rA to computeits own global position is to acquire another robot’s globalposition and the relative position of the robot to itself. Giventhat rA has a camera to detect robot teammates and robotrB has a localization sensor, ASyMTRe would believe that acoalition with rB is a solution even though rB is not in rA’scamera’s FOV. IQ-ASyMTRe would exclude the coalitionwith rB since the information FR(rB , rA) is not retrievable.

2) Information Rule PS: Information rule PS is a specialkind of perceptual schema that specifically models the con-versions among information types. ASyMTRe handles theconversions by hardcoding them into different perceptualschemas. The introduction of these rule PSs is especiallyuseful when information types are specified with referents.With referents instantiated to different entities, two instancesof the same information type represent two different piecesof information, while they are considered to be the samein ASyMTRe. This distinction is important when multiplepieces of information of the same information type can beused in the conversions to create other information. For ex-ample, from the relative position of robot rB to robot rA androbot rC to robot rA, we can compute the relative positionof rB to rC . The rule PS representation for this conversionis FR(rB , rA) + FR(rC , rA) → FR(rB , rC). ASyMTRecannot represent such conversions, which may lead to theloss of possible solutions. Table I shows some basic rulePSs. The conversions are general since the referents can beinstantiated to different entities. However, we require that thesame referent labels be instantiated to the same entities.

B. Incorporation of Information Quality

Our previous work [10] introduces measures of informa-tion quality to describe the fitness for using the informa-tion in the current environment settings. Information qualitymeasurements are used to guide motion selections such thatthe robots can execute tasks through the environment whilemaintaining certain levels of information quality for sensorconstraints within the coalitions. To incorporate informationquality, a function is defined for each information typethat a sensor can produce, which returns the informationquality measurement with respect to the current environmentsettings in the sensor’s FOV. Qi(Conf1:Ni

) represents theinformation quality measurement for Fi given the currentenvironment settings (i.e., work space settings and the currentconfigurations for entities Ref1:Ni

) in the sensor’s FOV,

whereas Confj is the current configuration of the entity thatRefj is instantiated to. The information type must be fullyinstantiated for the measurement to return non-zero values.

C. Solution Space and Potential Solutions

Potential solutions represent the possible alternative waysthat schemas can be connected to achieve a certain task.Potential solutions can be extracted from the solution space.In order to create the solution space, the IQ-ASyMTRereasoning algorithm starts from the goal motor schemas(MSs) and checks all schemas that can provide inputs for theMSs. The algorithm then checks recursively for the inputsof those schemas until the path either ends in a conflict state(i.e., the same referent is instantiated to different entities)or in a terminal state (i.e., communication schema (CS)or environmental sensor (ES) that can be the source ofthe required information). One important difference betweenour IQ-ASyMTRe reasoning algorithm and the reasoningalgorithm in ASyMTRe is that we allow multiple activationsof the same schemas for individual potential solutions. Thisis due to the fact that in IQ-ASyMTRe, information canbe different for the same information types with differentinstantiations of the referents. Hence, the same schemas canbe used to accept and produce different information havingthe same information types. This may seem at first to lead toa clumsy representation of the solution space. However, thefact that the information types can be partially instantiatedenables us to represent the space more concisely; meanwhile,instantiations of the information types can also be specificenough to exclude infeasible solutions.

As an example, Figure 1 shows a typical solution space forcomputing the global position information. Each schema orsensor acts as a connection node in the solution space. Thealgorithm processes from left to right, from top to bottom;while information flows from right to left, from bottom totop as the arrows indicate. Two special connection nodesare created to indicate the AND and OR relationships amongnodes in different levels. This solution space encodes twopotential solutions. While the ASyMTRe architecture needsto introduce two schemas that distinctly work for thesetwo scenarios, the rule PS we introduce in IQ-ASyMTReprovides a more comprehensive and extensible approach.Figure 1 also demonstrates the representation power of thepartially instantiated information types. In this figure, thereferent X can be instantiated to any entity as long as allreferences of X are instantiated consistently.

A solution space is usually composed of more than onepotential solution. The potential solutions can be extractedand represented as:

PoSkh = (Sk

1 , Sk2 , ..., F

k1 , F

k2 , ...,Mapk) (1)

where PoSkh is the hth potential solution for robot rk.

Sk1 , S

k2 , ... are the schemas that need to be activated and

F k1 , F

k2 , ... are the pieces of information that need to be

communicated. Mapk records the current instantiations forhow the referents are instantiated to entities, and is used todetermine whether future instantiations are valid or not.

Fig. 1. A typical solution space for a robot to obtain its global positionwith only a camera sensor. The referent local refers to the robot itself. Thesolution space encodes two solutions. One solution is to have another robotsend over its global position (CS: FG(X) ⇒ FG(X)) and (AND) usethe camera sensor to sense the relative position of the robot to itself (PS:Camera ⇒ FR(X, local)). A rule PS (PS: FR(Y,X) ⇒ FR(X,Y )) isused to convert FR(X, local) to FR(local,X). The other solution (OR)is to have both pieces of information (CS: FG(X) ⇒ FG(X) and CS:FR(local,X) ⇒ FR(local,X)) sent over by another robot.

In order to simplify the solution space, apart from thebasic connection constraint that the inputs and outputs ofthe connecting schemas must have the same informationtypes, additional constraints are created. First, we requirethat information of the same type appearing further tothe right of a reasoning path must not have fewer or thesame uninstantiated referents than the set of uninstantiatedreferents from the information further to the left. Secondly,the Localness in Reasoning constraint states that no schemaconnection except for CS should be created if none of thereferents for the information type of concern is instantiated tothe local entity. Given this constraint, for example, robot rAwould not directly provide the relative position of robot rB torobot rC , even though rA can compute the information fromthe relative positions of rB and rC to itself. However, therequired information for the computation would be availableupon request. The External Communication constraint statesthat a CS can be used only when not all referents are instanti-ated to the local entity for the information type. For example,if robot rA needs its global information, FG(rA), it cannotrequest it directly. Instead, it must first seek other ways (e.g.,computing it from another robot’s global position and therelative position of the robot) to obtain the information.

D. Coalition Formation & Execution

Coalition formation is performed in a distributed manner.We use the same request-and-wait negotiation protocol forcoalition formation as the distributed version of ASyMTReuses. However, this method often comes with latency. (Anal-ysis of the latency will be performed in our future work.)For robots to maneuver through dynamic environments,this latency is especially hazardous since environments canchange unexpectedly and rapidly. When sensor constraintsare unsatisfiable in certain situations, the robots must reactin real time to search for alternative coalitions. The fact thatthe IQ-ASyMTRe architecture enables dynamic-environment

reasoning by eliminating infeasible coalitions may alleviatethe problem, since the delay for processing these infeasiblecoalitions is avoided. Dynamic-environment reasoning isnot possible in ASyMTRe since entities related with theinformation types are not specified. Upon request, if the robotbeing requested has the information, it will notify the requestsender of the availability. When there are multiple possiblecoalitions for a potential solution, the possible coalitions canbe sorted by the quality of the coalitions (which we callcoalition quality henceforth), which can be computed usingthe information quality measurements for the informationtypes related to the coalitions. After the coalition is deter-mined, the requesting robot would send a request to set up thecoalition (for details, see [5]). During the execution, in casesthat the coalition quality drops continuously due to changesin the environment that may potentially lead to unsatisfiablesensor constraints, the coalition formation process can beactivated dynamically to search for alternative solutions.

For every robot in a certain coalition, a goal commandvector is computed. When the coalition quality is above arisk threshold, the robots directly execute the goal commandvector. When the coalition quality falls below the riskthreshold, the robots would try to improve the quality. If thecoalition quality deteriorates below a danger threshold, thecoalition formation process would be re-activated to searchfor alternative solutions.

E. The Algorithm

The overall algorithm for IQ-ASyMTRe is shown inAlgorithm 1. The algorithm starts with collecting sensoryinformation related to the current potential solution andinformation communicated to it. It then checks the currentpotential solution against the information collected and setsup a coalition when possible. If the information is not suf-ficient, then the robot will send out requests for the missingpieces of information and check the solution again later.One important characteristic of the algorithm, which differsfrom ASyMTRe, is that the information collected usingsensors and through communication is used in the planning(coalition formation) phase to exclude infeasible coalitionswhen relevant information required is not retrievable.

V. SIMULATION & EXPERIMENTAL RESULTS

In simulation, we first show the solution spaces for differ-ent robot configurations in a cooperative robot navigationtask. Afterwards, we present the capability of dynamic-environment reasoning enabled by the IQ-ASyMTRe archi-tectue and explain how such a capability is used to eliminateinfeasible coalitions. We then show the architecture in actionfor a robot navigation task. Physical robot experiments areprovided afterwards. For all the following experiments, un-less specifically mentioned, we use only the first and secondrule PSs given in Table I.

A. Simulations

In a robot navigation task, each robot needs to localizein order to navigate to the goal position. For this purpose,

Algorithm 1 The Algorithm for IQ-ASyMTReReason about the MSs required for the task and create thesolution space using the reasoning algorithm.Extract potential solutions and order solutions accordingto the predefined cost measures for schemas.while true do

COLLECT: collect sensory information related to thecurrent potential solution.Collect information communicated by other robots.Process requests from other robots.Share requested information when available.if a coalition is set up then

goto EXECUTION.end ifRetrieve the next solution from the ordered list.Check the solution against all information collected.if the information collected is sufficient then

if some information needs to be communicated thenRequest to set up a coalition with related robots.if the coalition is set up then

Reset the next solution to be the first solution.goto EXECUTION.

elsegoto COLLECT.

end ifelse

Set up a coalition by itself and goto EXECUTION.end if

elseSend requests for the missing information and set thenext solution to be the current solution and wait forsome time, then go to COLLECT.

end ifEXECUTION:if coalition quality is below the danger threshold then

Break the coalition and goto COLLECT.else if coalition quality is below the risk threshold then

Execute the motion vector produced by the informa-tion quality model and goto COLLECT.

elseExecute the goal command.

end ifend while

robots can use sensors onboard and/or request help fromother more capable robots. The robot can also help otherrobots upon request. We next show the solution spaces inthe robot navigation task for different robot configurations,and using different rule PSs as listed in Table I. To orderthe potential solutions in the solution space, we assign coststo schemas that reflect the complexity of using particularschemas. Due to space limitations, we omit the listing ofperceptual schemas that are required for each solution. Weassign a cost of 0.5 to PSs (including rule PS) since theysolely involve computation. The costs of ES and CS are

TABLE IISOLUTION SPACE USING FIRST TWO RULE PS’S IN TABLE I

Fiducial Only Fiducial & Laser

1. ES:FG(local)

1. CS:FG(X), ES:FR(X, local) 2. CS:FG(X), ES:FR(X, local)

2. CS:FG(X), CS:FR(local,X) 3. CS:FG(X), CS:FR(local,X)

3. CS:FG(X), CS:FR(X, local) 4. CS:FG(X), CS:FR(X, local)

4. CS:FG(X), CS:FR(local,X) 5. CS:FG(X), CS:FR(local,X)

TABLE IIISOLUTION SPACE USING ALL RULE PS’S IN TABLE I

Fiducial & Laser

1. ES:FG(local)

2. CS:FG(X), ES:FR(X, local)

3. CS:FG(X), CS:FR(local,X)

4. CS:FG(X), CS:FR(X, local)

5. CS:FG(X), CS:FR(local,X)

6. CS:FG(X), CS:FR(local, Y ), CS:FR(X,Y )

7. CS:FG(X), CS:FR(X,Y ), CS:FR(local, Y )

assigned to 1 and 2 respectively. The cost of a CS is sethigher to discourage the robots from requesting help.

Tables II and III list the ordered potential solutions forrobots with different configurations and using different rulePSs in the robot navigation task. In these tables, ES rep-resents the use of environmental sensors. Fiducial sensorscan sense the relative positions to special markers andare often used to retrieve the relative position informationbetween robots, while laser sensors can support localizationusing a Monte Carlo method. CS represents the use ofcommunication schemas to transfer information from onerobot to another. The ultimate goal in such tasks is toobtain the global position, FG(local), such that the robot canlocalize and navigate to the goal. Table II shows the potentialsolutions for robots with a fiducial sensor only and with alaser and a fiducial sensor. Table II shows that the reasoningprocess generates different solution spaces for different robotconfigurations. ASyMTRe needs to build a PS for each po-tential solution listed in the tables, since conversions amonginformation types are not specifically modeled and must behardcoded into different PSs. Such an approach would workfor cases with few potential solutions as in Table II. However,for cases with more complicated solution spaces or morepotential solutions, as in Table III, a more flexible solutionas our approach is required. One note is that the ASyMTRearchitecture actually cannot be used to produce solutions6 and 7 in Table III. This is because ASyMTRe cannotdistinguish information of the same information type, whichis due to the lack of referents associated with the informationtypes. One of the disadvantages of the new solution space,however, is that there can potentially be duplicate solutions.Notice that solutions 3 and 5 (as well as solutions 6 and 7)in Table III represent the same solution even though theyare generated from different branches in the solution spaceand have different costs. In future work, we will analyze the

(a) (b)

(c) (d)

Fig. 2. (a) No robots are within the FOV of the red robot. (b) Only the bluerobot is within the FOV of the red robot. (c) Both the blue and yellow robotsare within the FOV of the red robot. (d) The same robot configurations asin (c) with an obstacle, shown in black.

impact of the duplicates on the searching performance. Toresolve the issue, we can always design a post-processingalgorithm to remove the duplicates.

To illustrate the capability of dynamic-environment rea-soning for coalition formation, we provide four scenarios fora robot in a cooperative robot navigation task to determinewhich coalitions to set up, as shown in Figure 2. In allscenarios, we assume that the red robot has only a fiducialsensor for sensing relative positions of other robots. Figure2(a) shows a scenario in which no other robot is within theFOV of the red robot. The reasoning algorithm searches thepotential solutions from the left column in Table II, from topto bottom, until it finds a feasible solution. For solution 1,the algorithm successfully reasons about the current situationand moves to solution 2, since no other robot is within itsFOV. ASyMTRe, on the other hand, cannot identify that onerelated entity (i.e., another robot) for the information typeFR is not available, as it does not associate entities withthe information types. (Actually, ASyMTRe would treat allfour scenarios equally, assuming that all other robots arewithin the red robot’s FOV.) Solution 2 then requires therobot to broadcast a message requesting the information ofFG(X) + FR(rred, X). The referent local is instantiated tothe red robot itself. In Figure 2(b), the blue robot is withinthe FOV of the red robot and the reasoning process identifiesthe feasibility of solution 1 and broadcasts a request forFG(rblue). In Figure 2(c), the red robot understands thatboth the blue and yellow robots are within its FOV, so itbroadcasts a message requesting FG(rblue) or FG(ryellow).If both the blue and yellow robots reply with their globalpositions, the red robot would choose the one with thebetter coalition quality (refer to section IV.D). The robots inFigure 2(d) are in the same configurations as in Figure 2(c),except that an obstacle is added such that the blue robot canpotentially be blocked. The reasoning process ignores the

coalition with the blue robot due to the low coalition qual-ity and requests only FG(ryellow). This experiment showsthe dynamic-environment reasoning capability for coalitionformation enabled by the combined approach.

We next show in simulation a cooperative robot nav-igation task that combines the previous perspectives anddemonstrates how IQ-ASyMTRe completely solves a tightly-coupled multirobot task from the beginning to end. In thisexperiment, three robots are to navigate to the same goalposition. Among them, only the red robot can use the lasersensor to localize. The other two robots have a fiducial sensorto sense the relative positions of other teammates and alaser sensor for environment sampling. They cannot use thelaser sensors for localization since the perceptual schemafor localization (i.e., software for Monte Carlo localization)is disabled. Figure 3 shows snapshots from the experimentwith the execution time shown in seconds. The robots startwith the initial configurations as in Figure 3(a). Both followerrobots search for solutions from the left column of Table II,from top to bottom. As they both can sense the leader robot’srelative position using the fiducial sensors, they both set upa coalition with the leader using solution 1. The coalitionsnavigate through the environment in a triangle formationas shown in Figure 3(b). When the environment becomesnarrower due to obstacles on both sides of the corridor, thereis risk of collision for the yellow robot to navigate throughwithout adjusting its moving direction. Furthermore, theobstacle nearest to the yellow robot also reduces its coalitionquality with the leader due to potential blocking risk. Theblue follower robot goes through first as the obstacles arefurther away. The yellow robot, on the other hand, first triesto improve the coalition quality after it drops to below therisk threshold, while avoiding obstacles. However, as thecoalition quality deteriorates due to the potential blockingrisk from the blue robot and obstacles, the yellow robotbreaks the coalition with the leader robot and searches thesolution space from the start again. It then realizes that theblue robot is in its FOV and tries to set up a coalition withit. Since the blue robot knows that it can localize with thehelp from the leader robot, the coalition is confirmed andthe blue robot becomes the leader of the yellow robot asFigures 3(c) and 3(d) show. One interesting note is that theyellow robot does not need to know how the blue robotachieves localization. The rest of the snapshots show that therobot coalitions navigate through the environment in a lineformation and reach the goal position successfully. Noticethat after they start navigating in a line formation, unless theyellow robot’s coalition with the blue robot is at risk and itregains sight of the leader, the yellow robot would not trynor is it necessary to rebuild coalition with the leader robot.A supplementary video file for this entire task execution isalso available for downloading.

This experiment presents an important capability whichwe name dynamic-environment reasoning for dynamic coali-tion formation. Our previous work [10] achieves dynamiccoalition control by hardcoding the alternative coalitions inthe constraint model. The IQ-ASyMTRe architecture uses

the dynamic coalition formation capability of ASyMTRe forreasoning about alternative coalitions based purely on theinformation required, hence providing a more general andflexible solution. The information quality model is essentialsince it helps the robots maintain the sensor constraints anddetermines when a coalition needs to be reformed.

B. Physical Experiments

To demonstrate the flexibility and robustness of the IQ-ASyMTRe architecture with physical robots, we design twoscenarios for the cooperative robot navigation task in whichtwo robots have the same goal position. Both robots havea camera sensor pointing forward to determine the relativeposition of other robots and only one of them (the helper,labeled ‘1’ in Figures 4 and 5) has a localization capability.The motivation is that the helper robot may be in front of therequesting robot (i.e., the robot that needs help), or the helperrobot may be behind the requesting robot, in which case therequesting robot cannot detect the helper in order to computeits relative position. ASyMTRe would consider these twocases equal and hence would provide the same coalitionsolution, which is for the helper robot to communicate itsglobal position to the requesting robot. However, in thelatter case, even with the helper robot’s global position, therequesting robot cannot compute its global position sincethe helper’s relative position is not retrievable, as the helperrobot is behind it. The snapshots for the execution of thesetwo scenarios are shown in Figures 4 and 5. To show that therobots can set up coalitions in a timely manner, we start thetwo robots without delay for the initial coalition setup. Forboth scenarios, the helper robot starts execution first since itis self-sufficient for this task. In Figure 4, the helper startsin the front and the coalition is set up for the helper robot tocommunicate its global position to the requesting robot. InFigure 5, the helper starts at the back and the IQ-ASyMTRearchitecture successfully reasons about the situation; thecoalition is set up for the helper robot to communicate bothits global position (via laser) and the relative position (viacamera) to the requesting robot. After the coalitions are setup, the robots execute the coalitions while maintaining thesensor constraints and successfully reach the goal positions.The elimination of infeasible coalitions through dynamic-environment reasoning makes the coalition formation morerobust to various situations. The coalition formation and ex-ecution are all performed dynamically and in real time. Thisexperiment shows that the dynamic-environment reasoningcapability can distinguish among different environment set-tings (including robot configurations) and provide feasiblecoalitions accordingly.

VI. CONCLUSIONS AND FUTURE WORK

This paper presents the IQ-ASyMTRe approach, whichis aimed for a complete solution for tightly-coupled multi-robot tasks in which robots share capabilities. This approachcombines an extended ASyMTRe architecture and our pre-vious information quality based approach such that coalitionformation and coalition execution are accomplished within

(a) t = 2.5s (b) t = 25.5s (c) t = 35.5s

(d) t = 49.0s (e) t = 65.5s (f) t = 89.5s

Fig. 3. (a) Initial configurations. (b) Both follow robots set up a coalition with the leader (red) and robots navigate in a triangle formation. (c) Theenvironment becomes narrower due to obstacles and influences the yellow robot. The yellow robot breaks the coalition with the leader and sets up acoalition with the blue robot. (d) Robots navigate through the environment in a line formation. (e) and (f) Robots navigate around the corner and reachthe goal position.

(a) (b) (c)

Fig. 4. (a) Initial configurations with the helper robot (labeled ‘1’) in thefront. (b) The helper robot goes to the goal while the requesting robotis trying to set up a coalition with the helper. (c) The coalition is setup and the robots navigate through the environment with the helper robotcommunicating its global position to the requesting robot at the back.

(a) (b) (c)

Fig. 5. (a) Initial configurations with the helper robot (labeled ‘1’) at theback. (b) The helper robot starts first while the requesting robot is trying toset up a coalition with the helper. (c) The coalition is set up and the robotsnavigate with the helper robot communicating both the global informationof itself and the relative position to the requesting robot in the front.

the same architecture, with sensor constraints introducedby capability sharing within the coalitions. This approachintroduces the capability of dynamic-environment reasoningfor dynamic coalition formation and demonstrates how sucha capability enables autonomous and dynamic cooperativecontrol. To the best of our knowledge, this is the first attemptto create a complete and general solution for tightly-coupledmultirobot tasks that involves capability sharing.

In future work, we plan to apply IQ-ASyMTRe to morecomplex tasks and with more robots, in order to further provethe feasibility and show the scalability of this approach.The properties of the new architecture will be analyzed indetail to include the real-time computational requirements

of this approach. We will also provide a formal analysisof the performance of coalition formation and compare itwith other approaches. Other interesting aspects includedeveloping more complete definitions of information quality,as well as addressing sensor fusion [7].

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