Assessing Information Utility in Cooperation-basedRobotic Systems

Rui Rocha (1, 2), Jorge Dias (1) and Adriano Carvalho (2) ∗

(1) Institute of Systems and Robotics, University of Coimbra, PORTUGAL(2) Faculty of Engineering, University of Porto, PORTUGAL

AbstractIn this article we propose a measure of information

utility that can be used to enable more effective co-operation in multi-robot systems (MRS). After givingsome background in the area and making some refer-ences to the state of the art, we present an observationmodel for a MRS, based on which we devise a formalmethod to assess the information utility. The methodputs on emphasis the optimization of the balance be-tween performance gain and cost increasing due to re-sources usage, including communication. Then, theproposed method is used to simulate and assess infor-mation utility on a MRS performing a consume mis-sion. We conclude with a discussion and directionsfor future research.

1 IntroductionMulti-robot systems (MRS) have been widely in-

vestigated for the last decade [1, 2]. These systemsemploy teams of cooperative robots to carry out mis-sions that are either inherently distributed in time,space, or functionality, and cannot be achieved by asingle robot, or where a multi-robot solution is moreefficient, cost effective, reliable and robust than a sin-gle robot solution. Most of the work in MRS hasbeen devoted to the definition of different architec-tures, mostly behavior-based, that rule the interactionbetween the behaviors of individual robots [3, 4].

Communication is a central issue of MRS becauseit determines the possible modes of interaction amongrobots, as well as the ability of robots to build suc-cessfully a world model, which serves as a basis to rea-son and coherently act towards a global system goal.Communication may appear in three different formsof interaction [1]: (1) via environment, using the en-vironment itself as the communication medium (stig-mergy); (2) via sensing, when an agent knowingly usesits sensing capabilities to observe and perceive the ac-tions of its teammates; and (3) via communication,using a communication channel to explicitly exchangemessages among the agents, thus compensating per-ception limitations.

∗E-mails: {rprocha, jorge}@isr.uc.pt, asc@fe.up.pt

Arkin [5] demonstrated that sometimes coopera-tion between robotic agents was possible even in theabsence of communication, however this is a weakform of cooperation and it may me very inefficient.Mataric [6] showed that the ability to distinguishother robots from the rest of other objects providessufficient power to overcome interference. Balch etal. [7] made simulation studies of three typical multi-agent tasks, using the three basic communicationtypes referred above, and found that communicationimproves performance significantly in tasks with littleimplicit communication and that more complex com-munication strategies (goal-oriented) offer little bene-fit over basic communication (state). Within CEBOTframework, Fukuda et al. [8] studied methods thatseek to reduce communication requirements, by in-creasing the awareness level of individual cells. Parker[9] investigated the impact of awareness on a MRS andconcluded that it improves performance, regardless ofteam size. Tambe presented STEAM [10], a generalmodel of teamwork, which includes a heuristic thatattempts to follow the most cost-effective method ofattaining mutual belief in joint intentions, by man-aging a tradeoff between communication and teamincoherence costs. Stone and Veloso [11] proposeda method for inter-agent communication, which as-sumes that agents alternate between periods of lim-ited and unlimited communication. Although previ-ous work on communication structures for MRS hasled to some useful conclusions and design guidelines,there is no a principled formalism that can be system-atically used to assess information utility and supportthe efficient use of communication in MRS. Currentarchitectures (e.g. [3, 4]) extensively use explicit com-munication, not taking care, giving low emphasis, orusing no principled heuristics to avoid the communi-cation of redundant information. As communicationis always limited, either in resources applied to per-ceive the world or in bandwidth of a communicationchannel, using efficiently those resources is crucial toscale up cooperative architectures for teams of manyrobots, without limiting them to simple reactive andloosely-cooperative systems, with very limited or noawareness. This paper starts to bridge this gap.

Proceedings of ICAR 2003 The 11th International Conference on Advanced Robotics Coimbra, Portugal, June 30 - July 3, 2003

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Section 2 presents a discrete event dynamic obser-vation model for a MRS. Section 3 uses this modelto introduce a method to assess the information util-ity, which is viewed as a balance between performancegain and cost increasing (resources usage), where com-municated information is measured through the con-cept of information entropy [12]. Section 4 thenpresents a simulation model of a MRS performing aconsume mission, in which the proposed method isused to assess information utility. Section 5 discussesthe simulation results and gives some future researchdirections.

2 Observation model

This section presents an observation model for amulti-robot system (MRS) composed of n robots,which are controlled in order to cooperatively performa given mission.

Notation. The finite set F = {1, . . . , n} ⊂ N isthe fleet of n robots forming a MRS. Each robot ismodeled as a discrete event system, i.e. an event-driven system [13]. The finite discrete state set Xcontains all the possible and relevant states x ∈ Xfor a robot ri ∈ F , when performing a given mis-sion. State transitions are synchronized with the oc-currence of events at discrete points in time. Thetime instant associated with the occurrence of the k-th event is tk, k ∈ N. The finite event set E con-tains all the events ek ∈ E that are relevant to themission execution. The triple ok = (ek, tk, rk) ∈ Odenotes the occurrence of an event ek ∈ E at t = tk,detected by the robot rk ∈ F , where O = E × R ×Fis the countable set of all possible triples. The stateof robot ri ∈ F at t = tk is denoted by xi(k) ∈ X .The MRS’s state at t = tk is the n-dimensional vectorx(k) = [x1(k), . . . , xn(k)]T , x(k) ∈ Xn. The instanttime t = t0 (k = 0) denotes the initial time and x(0)denotes the corresponding initial state. The countablesequence x∗(k) = {x(0), . . . ,x(k)}, x∗(k) ∈ Xn∗, isthe MRS’s state trajectory up to time t = tk, k ∈ N0,being Xn∗ the space of countable sequences of ele-ments in Xn. The countable sequence

o∗(k) = {o(1), . . . , o(k)}, o∗(k) ∈ O∗, (1)

is the MRS’s list of events up to time t = tk, k ∈ N,being O∗ the space of countable sequences of elementsin O, obeying the condition ∀oi,oj∈E , ri = rj ⇒ ti �=tj , which means that a robot can detect and processno more than one event at a given instant time.

A MRS is viewed here as a event-driven dynamicsystem, where events are the inputs to the system andstate transitions are synchronized with the occurrenceof events [13]. Time is included in our model in or-der to be able to keep track of system’s performance.

Since the last event occurrence, and until the nextevent occurrence, i.e. for tk−1 ≤ t < tk, the MRS’sstate has been x(k − 1) ∈ Xn. When an event occursat t = tk, we have a triple ok = (ek, tk, rk) ∈ O thatcan be used, in conjunction with the current state,to compute the new MRS’s state vector, through thestate transition function

f : Xn ×O → Xn. (2)

A mission is viewed as a set of goals, representingphysical and logical restrictions that must be fulfilled.Physical resources that are used to execute a givenmission – a fleet F of n robots and a communicationchannel – are important to assess cost. In order to as-sess performance, the resource concept must be gen-eralized. We define resource as any phenomena thatis physically observable. When specifying a mission,we have to define a set of such resources, in order tobe able to measure performance. Some examples ofthese resources are: space (e.g. coverage area), en-ergy, time, number of robots, etc. Performance met-rics are generally relative metrics, such as: number oftasks per robot, number of tasks per time unit, en-ergy per robot, etc. Let R = {1, . . . , m} be a finiteset of resources that are required to assess the MRS’sperformance when executing a given mission, and letm be the cardinality of the set R. Let H denote aspace of resources measuring functions of the formh : Xn∗ × O∗ → R, h ∈ H. Such functions measureresources given the MRS’s past history, i.e. the statetrajectory and the list of events up to current instanttime. Let hi ∈ H be the measuring function of the re-source i ∈ R and ai(k) = hi(x∗(k),o∗(k)) be the mea-sure of the resource i at t = tk. The m-dimensionalvector of resources measures (positive real numbers)at t = tk is a(k) = [a1(k), . . . , am(k)]T ∈ R

m.The MRS’s performance can be evaluated through

a function p : Rm → R

+. It is assumed that p(a(k)) isa (linear or non-linear) combination of the resourcesmeasures a(k) and that it always computes to posi-tive real numbers. The function is also assumed to bemonotonous increasing with performance, i.e. highervalues mean better performance. Hereafter, p(a(k))will be abbreviated as pk. Given the MRS’s currentstate x(k) and the current vector of resources mea-sures a(k), the accomplishment of the mission is eval-uated through a function

g : Xn × Rm → {success, fail, ongoing}, (3)

where success means mission accomplished, failmeans mission failed and ongoing means that mis-sion still can be accomplished at a future instant timetj > tk. The mission is successful iff

∃j∈N : g(x(j), a(j)) = success. (4)

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If it exists such an index j, the mission execution timeis tmission = tj .

3 Information utilityWhen an event ek ∈ E occurs, we may say that

it is associated with some kind of information. Ina MRS, events may be classified along three classes,depending of type of conveyed information: (1) in-ternal events, concerning the robot’s own activitiesand information gathered internally by the robot (e.g.end of an internal processing task, reaching some po-sition, etc.); (2) external events, concerning changeson the mission execution environment and informa-tion obtained through the robot’s sensors (e.g. de-tection of an obstacle, finding an object relevant tothe mission execution, observing the movements ofanother robot in the team, etc.); and (3) received mes-sages, concerning information provided by other teammembers (e.g. detection of an environmental condi-tion, individual state information, a negotiation bid,synchronization-related information, etc.). The firsttwo classes of events convey information about theenvironment (sensing, perception) and through theenvironment (implicit communication and stigmergy)and are not controllable. The latter class of events isconcerned with information conveyed through explicitcommunication and are controllable. The occurrenceof an event may always be seen as some gain of infor-mation and is this information that enables the MRSto evolve in time through its state space X , using thefunction (2). The event set E is thus partitioned intotwo disjoint subsets: the subset Enc of non-controllableevents and the subset Ec of controllable events. Thus,E = Enc ∪ Ec and Enc ∩ Ec = {∅}. When it occurs anon-controllable event ok = (ek, tk, rk), ek ∈ Enc, therobot rk ∈ F gets some information. Then, it maydecide to communicate to other robots the informa-tion it has just acquired, by sending them a message.When a robot decides to send a message to anotherrobot, the former robot generates on the latter robota controllable event el ∈ Ec, l > k. The communica-tion cost associated with controllable events is mod-eled through a function en : Ec → R

+, and a commu-nication cost per information unit ccom. The func-tion en computes the entropy associated with a con-trollable event, i.e. the amount of information units(e.g. bits) that must be communicated [12]. Givenan event e ∈ Ec, the associated communication cost isen(e) · ccom. Each state x ∈ X is assumed to have anassociated constant cost per time unit, which is alwayspositive and is given by a function cstate : X → R

+.The mission execution cost during the time intervaltk−1 ≤ t < tk, k > 0 is given by

∆ck = ∆cck + (tk − tk−1)n∑

i=1

cstate(xi(k − 1)), (5)

where

∆cck ={

en(ek) · ccom , ek ∈ Ec,0 , ek ∈ Enc.

. (6)

The cumulative mission cost up to time t = tk is givenby the recursive function

ck ={

0 , k = 0ck−1 + ∆ck , k > 0 . (7)

Suppose that it occurs an event ok =(ek, tk, rk), ok ∈ O. Let v : O∗ → N0 be afunction that computes the time index of the verylast event occurrence detected by the robot rk ∈ F ,given the list of events (1) up to time t = tk. If theproposition

∃ow=(ew ,tw,rw)∈O∗ : rw = rk, tw < tk,

∀om=(em,tm,rm)∈O∗ , rm = rw, tm > tw ⇒ tm = tk.

is true, the function v returns the index w, w ∈ N0

that satisfies the proposition, otherwise it returns 0,i.e. ok is the first event occurrence detected by robotrk. The event occurrence ok is viewed as an informa-tion gain, but it has also an associated cost, given bythe function

∆ic : Xn∗ ×O∗ → R+, ∆ic ∈ H. (8)

Note that this function belongs to the space H ofresources measuring functions. The computation of∆ic(x(k),o∗(k)) = ∆ick depends on whether theevent is non-controllable or controllable. Let w =v(o∗(k)). If ek ∈ Enc,

∆ick = (tk − tw) · cstate(xrk(w)). (9)

If ek ∈ Ec,

∆ick = (tk−tw)·cstate(xrk(w))+en(ek)·ccom. (10)

The relative performance variation due to the eventoccurrence ok is given by

∆pk

pk=

pk − pk−1

pk, k > 0. (11)

The relative mission cost variation due to the eventoccurrence ok is given by ∆ick/ck, k > 0. The infor-mation utility associated with the event occurrence ok

is measured by the dimensionless ratio

uk =∆pk

pk

∆ick

ck

. (12)

The average information utility during the mission ex-ecution is

uk =1k·

k∑i=1

ui, k > 0. (13)

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Let l(k) be the number of controllable events up totime t = tk. The influence of explicitly communicatedinformation on the average information utility can beassessed by the quantity

uck =

0, l(k) = 0 ∨ uk = 0,

∑ ki=1

uk, ek ∈ Ec

0, ek ∈ Enc

l(k)·uk, otherwise.

, (14)

which we denote as communication utility. This quan-tity measures the average communicated informationutility relative to the average information utility in-cluding all event occurrences (all types of informa-tion). If the mission is successful, i.e. there is a timetj = tmission that verifies condition (4), the mission’sinformation utility index is uj , which can be used tocompare two different systems performing the samemission, or to compare the performance of a givensystem when performing different missions. For thesame mission, the communication utility is ucj .

4 Case study and results

In this section, we use the functions presented inthe previous section to assess information utility dur-ing the execution of the multi-robot mission describedbelow.

4.1 Case study descriptionThe case study we have chosen to demonstrate the

usage of the information utility measure is the con-sume mission, which is somewhat similar to the con-sume task described in [7]. The state space X for thismission contains states Wander, Acquire, Consume,Move To Help, Acquire To Help and Help Consume.The event set E contains events detect, attach, com-plete, detect bc, help rq, help compl and timeout. Thestate transition graph for a robot is depicted in Fig.1. This graph can be used to compute the state tran-sition function (2) for this mission. The mission ofa team of n homogeneous and non-holonomic robots(differential drive robots) is to wander about a 2D en-vironment, looking for static items of interest. Oncea robot encounters one of these items (event detect),it acquires the item (state Acquire), attaches itselfto the item (event attach) and consumes it (stateConsume), i.e. performs some work on the item. Therequired time to consume the item is tc. When a robotencounters a new item, it can request help for otherrobots (event help rq), in order to reduce the item’sconsume time to tc/n2

c , where nc is the number ofrobots consuming an item. The event detect bc mod-els the situation in which a wandering robot finds anitem that is already being consumed by other team-mate(s). When a robot is moving to help anotherrobot (state Move To Help), if it could not reach theitem within a predefined time, a timeout event occurs

Figure 1: State transition graph for a robot (it iscommon to all teammates).

and the robot jumps to state Wander. The 2D en-vironment is populated with static obstacles, whichmust be avoided by the robots. Robots must alsoavoid colliding each other. The goal of the mission isto find and to consume b items before t = tmax. Theunique controllable event is help rq. It is assumedthat this event models the reception of a message withthe 2D coordinates of a requesting help robot. Thus,its associated entropy is en(help rq) = 32 bits if weassume that each coordinate is coded through a 16bits binary code. The number of resources for thismission is m = 4. Table 1 presents the meaning of theresources measuring functions we have modeled in or-der to assess the mission performance. The vector ofresources measures at t = tk is

a(k) = [a1(k), a2(k), a3(k), a4(k)]T

= [h1k, h2k, h3k, h4k]T ,(15)

where hik = hi(x∗(k),o∗(k)), i ∈ R. The missionaccomplishment function gk = g(x(k), a(k)) can becomputed by

gk =

success , a3(k) = b ∧ a1(k) ≤ tmax,ongoing , a3(k) < b ∧ a1(k) < tmax,fail , a3(k) < b ∧ a1(k) ≥ tmax.

(16)

Table 1: Measured resources for assessing perfor-mance of the consume mission.

i ∈ R h ∈ H Meaning1 h1 Elapsed time since the beginning of the

mission.

2 h2 Number of detected items (eventsdetect, detectbc and helprq) for everyrobots.

3 h3 Number of consumed items (eventscomplete) for every robots).

4 h4 Average time spent in state Consumefor every robots.

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Table 2: Simulation parameter values for the con-sume mission.

Parameter ValueWorkspaceLength x Width 50 m x 50 mRobotsNumber of robots {1, 2, 3, 4}Axle length 0.5 m

Velocity (maximum) 1.4 m.s−1

Acceleration (linear) 0.9 m.s−2

Sensor range 2 mCommunication range {0, 20} m

Communication cost (ccom) 0.3125 bit−1

ItemsNumber of items 30Ray 0.5 mConsumption time (tc) 100 sSpacing 2 mMinimum distance to initial pose 10 mObstaclesWorkspace coverage {0, 5, 10} %Ray 1 . . . 4 mSpacing 3 mx ∈ X cstate(x){Wander, Move To Help} 1 s−1

{Acquire, Acquire To Help} 0.8 s−1

{Consume, Help Consume} 2 s−1

Performance weights

{α, β, γ, δ} {10−10, 0.4, 0.2, 0.4}

The performance function pk = p(a(k)) can be com-puted by

pk =

{α , k = 0,

α + β a2(k)a1(k) + γ a3(k)

b + δ tc

a4(k) , k > 0,

(17)where α, β, γ and δ are weights, such as α, β, γ, δ > 0,α � β, α � γ and α � δ. The constant α guaran-tees that the performance function always computesto positive real numbers.

The robots’ behavior along their possible stateswere modeled through potential field techniques andfollowing an approach very similar to the one that isdescribed in [7]. There were implemented five basicbehaviors: noise, avoid obstacles, avoid robots,move to goal and consume. The robots’ behavior foreach state is a linear combination of those basic behav-iors, with predefined weights. For example, in stateWander, the active basic behaviors are noise,avoid obstacles and avoid robots. The basic behaviornoise is active for all robot’s states in order to avoid lo-cal minima and maxima. Table 2 presents the missionparameters, whose values were selected empirically.The maximum mission time was tmax = 11000 s.

4.2 Results and discussionThe simulation model described above was used

to gather results with different combinations of threevariables: team size, obstacles’ coverage and commu-nication range. Fig. 2 shows the simulation resultsthrough some representative graphics. The graphs onthe left show the simulation results with the robots’

Figure 2: Simulation results: a) on the left, withoutexplicit communication; b) on the right, with commu-nication range configured to 20 m.

communication range configured to 0 m, i.e. withevent help rq disabled. In this situation, a robot cannever reach the state Move To Help. Conversely,the graphs on the right show the simulation resultswith robots’ communication range configured to 20m, i.e. with event help rq enabled. In the simula-tions performed to get these graphs, the multi-robotsystem (MRS) always accomplished the mission withsuccess, i.e. it always consumed all the 30 items be-fore tmax = 11000 s. Observing the graphs of tj ,we can see that the mission execution time reduction,due to team size increasing and/or due to obstacles’coverage decreasing, is more significant when we gofrom the single robot case to teams of two robots,than we go from two robots to three or four robots.This means that the benefit of increasing redundancyis significant for small teams and less important formore populated teams. The reduction in tj is alsomore significant for teams that are allowed to use ex-plicit communication. Obviously, obstacles’ coverageinfluences the mission execution time, because obsta-cles must be avoided by the robots, thus condition-ing their progression along the workspace. Observingthe graphs of the ratio pj/cj, we can identify a lo-cal maxima in the same point (a team of 2 robotsand 0% of obstacles’ coverage), whether robots are al-lowed to communicate or not. It is also noticeable avery significant influence of explicit communication inthe ratio pj/cj , denoting its utility for this mission.On average, communication resulted in an improve-ment of 35% on its value. For a team of four robots

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Figure 3: Graph of communication utility.

working in an environment with 10% of obstacles’ cov-erage, that increase was much higher (about 94%).This increase was generally higher for combinationsof teams with more robots and lower obstacles’ cover-age values. Now comparing the graphs of pj/cj ratiowith the corresponding graphs of information utilityuj , we can observe some correlation between the twomeasures, which means that optimizing the balancebetween performance and cost seems to be equivalentto optimize the information utility. That correlationis particularly noticeable in the absence of communi-cation. Notice, for example, in the graph of uj with-out communication a local maxima in the same pointwhere the ratio pj/cj has also a maxima. Observingnow the graph of communication utility (Fig. 3), wecan observe that this measure has also a strong corre-lation with the ratio pj/cj, though that correlation isnot so evident for the information utility measure.

5 Summary and conclusions

Although communication plays a crucial role inMRS and some authors have already concentratedon this issue, there is no a principled formalism thatcan be systematically used to assess information util-ity and support efficient communication. This paperstarted to bridge this gap by presenting a discreteevent observation model and devising a formal methodto assess the utility of information and communicationfor a MRS. The proposed measures of utility were usedto perform a simulation study on a consume mission,whose main conclusions were: the benefit of increas-ing redundancy is more significant for small teams;explicit communication allows to get higher values forthe ratio between performance and cost, specially inmore populated teams working in environments withlower obstacles’ coverage values; in the case of non-communicating teams, there is an evident correlationbetween the performance versus cost ratio and theinformation utility measure; in the case of communi-cating teams, communication utility is correlated with

the performance versus cost ratio.

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