Spatial Behavior of Individuals and Groups: PreliminaryFindings from a Museum Scenario

Dylan Shell1* Shivakumar Viswanathan3 Jing Huang1,2 Rumi Ghosh2 Jie Huang3

Maja Mataric1 Kristina Lerman1,2 Robert Sekuler3

1Department of Computer Science

University of Southern California

Los Angeles, CA USA 90089

2Information Sciences Institute

University of Southern California

Marina del Rey, CA USA 90292

3Volen Center for Complex Systems

Brandeis University

Waltham, MA USA 02454

Abstract— In order to better understand human navigation,way-finding, and general spatial behavior, we are conductingresearch into the effects of social interactions among individualswithin a shared space. This paper describes work in the inte-gration of instrumentation of active public areas, macroscopicmodeling, microscopic simulation, and experimentation withhuman subjects. The aim is to produce empirically groundedmodels of individual and collective spatial behavior. We describethe challenges and lessons learned from our experience withdata collection, construction of tractable models, and pilotexperiments.

I. INTRODUCTION

Whether it be shopping malls, parks, communal gardens oreven corridors, significant portions of our daily lives arespent moving through spaces intended for groups of people.Ideally, shared spaces should permit people to achieve theirvaried goals with minimal inconvenience. Furthermore, inthe event of an emergency, the space should enable effectivemanagement of crowds so as to minimize injury and lossof life. Well-designed spaces could do more than merelypromote efficiency—they can shape the experience and socialinteractions within the occupying groups. The successfuldesign of such spaces requires an understanding of thecollective spatial behavior of groups of people.

A predictive theory of human navigation and way-findingwithin a social context has applications beyond architectureand building design. Models of such behavior could beused within robots and smart-spaces in order to reasonabout the collective properties of groups and crowds. Asyet, few researchers in human-robot interaction have appliedmacroscopic models in an online sense, despite the fact thatrobots are increasingly expected to locomote naturally inareas with numerous moving people.

We have formed a multi-institutional collaboration tostudy this problem of characterizing the dynamics of humanspatial behavior. The ultimate goal is to provide principledmodels and tools to inform the architectural design of spacesoptimized for shared use, and develop technologies thatcan enable the accurate detection of life-threatening over-crowding scenarios for effective intervention. Furthermore,the data collected and models developed by this effort

* To whom correspondence should be addressed. Email: dshell@usc.edu

have much promise for use in on-line autonomous systemsintended to interact with large numbers of people.

Our specific focus is on the development of practicallytestable quantitative models that are based on human be-havioral data collected through the long-term deploymentof sensors in active public spaces and from controlledexperiments using VR-simulations of such spaces. To thisend, we have a partnered with the California Science Center(CSC) in Los Angeles. The CSC is a public museum in whichscience and technology are made accessible to children. Themuseum provides a wide spectrum of environmental featuresranging from small areas with high topological complexity(e.g., cafeteria, museum shop), to wide open spaces (e.g.,large exhibit halls), to junctions, corridors, etc. The museumattracts visitors in a variety of group sizes, boasting anaverage of 4,000 visitors per day. The result is a range of lo-cal (e.g., exhibit watching, following, walking together)andglobal (e.g., lanes, queuing, potential evacuation) collectivebehaviors. The museum has graciously provided floor plansand extensive access to the premises, including permissionto instrument areas with sensors.

This CSC environment is being used as the basis for threeconverging lines of inquiry: (1) how can high fidelity dataon crowd behavior be effectively collected and analyzed; (2)how can the observed patterns of crowd behavior be modeledand predicted using macroscopic mathematical models; and(3) what are the characteristics of individual behavior inpopulated spaces and how can they explained using cognitivemodels. This paper presents preliminary findings from theseinvestigations and identifies some of the key challengesencountered.

Section II describes the instrumentation, models and theirinterplay in macroscopic modeling of peoples’ movementin an area in the museum called the Life Tunnel and CellTheatre exhibit. This is a permanent museum exhibit essen-tially comprising of corridor space with structured branchesat which navigational choices are made. Section III describesour use of a virtual reality model of the CSC first floorto conduct controlled laboratory experiments to study howhuman subjects perceive and navigate crowded spaces whenroute planning is under-constrained and many potential pathsare feasible.

(a) The Life Tunnel and Cell Theatre exhibit with labelling of regions used in the models.

(b) Initial camera placement (c) Cameras for human annota-tions

(d) People and cameras for real-time observation

(e) Laser ranging devices

Fig. 1. Maps of the Life Tunnel exhibit showing details of sensor placement.

II. SENSING AND MACROSCOPIC MODELING OFGROUP BEHAVIOR: LIFE TUNNEL EXHIBIT

We have instrumented a part of the museum with sensorsto enable individuals and groups to be tracked, and aredeveloping a model of how the distribution of museumvisitors changes over time. The Life Tunnel and Cell Theatreare permanent exhibits that form part of the CSC’s interac-tive display on life forms in the north west corner of themuseum’s second floor. Figure 1(a) shows the layout of theexhibit, the entire space is approximately 20 meters longfrom the west door to the east door. The curved northernwall has several interactive displays, microscopes and televi-sions describing bacteria, viruses, and similar demonstrationsinvolving organisms. The area marked “Cell Theatre“ hasa central circular display in which both video and livedemonstrations are presented periodically.

A. Data collection and instrumentation

Our primary interest is in understanding the collectivedynamics of people as they move through the exhibit. Dueto the difficulties involved in identifying individuals forthepurposes of tracking (particularly due to occlusions), wedecided to focus on obtaining estimates of the aggregatenumbers of visitors for windows on the order of severalseconds. We have attempted to use a variety of sensors inorder to gain such estimates. This is a weaker formulationof the general tracking problem since one need not identifyand associated data from individuals across multiple frames,and consequently the solution will not generate trajectoryestimates.

The first attempt to monitor the entire exhibition spacewas through two ceiling-mounted cameras. The exhibit’slow ceilings meant that cameras needed to be fitted withfish-eye lenses to ensure complete visibility. We decidedthat the placement of more than two cameras would be

infeasible due to the infrastructure required, and the desireto interfere with the exhibit as little as possible. Figure 1(b)shows the placement of the cameras on the occasions inwhich we recorded data for several hours. We initially hopedthat automated processing could provide estimates for thenumbers of people at the regions delineated with dashed linesin Figure 1(a).

The video stills in Figure 2 show the output produced byone of the cameras. The images show that museum visitors atthe either end of the exhibit are reduced to only a few pixelsand have minimal contrast differences between them. Weconcluded that human annotation would be the most success-ful method for processing this video. In order to annotate thevideo, the two video streams were first synchronized using amarker event while collecting the data. The flow of visitorsmoving between each exhibit was counted for a ten secondwindow. For example, we estimated the number of peopleinside the Cell Theatre by comparing the number enteringand exiting in the time window. Similarly, for the entranceswe counted both direction of flow entering and leaving theexhibit as source data. In areas that are completely visible,the number of people can be counted directly rather thancalculating it on the basis of the flux. Figure 3 shows theresulting data.

Fig. 3. Time series of the number of people in sub-regions of the LifeTunnel. (From annotated video, coarse grained model with four sub-regions.)

(a) (b) (c) (d)

Fig. 2. Video stills from a ceiling mounted fish-eye camera and the simultaneous laser range reading.

Next, we experimented with the placement of cameraswith standard lenses. Figure 1(c) shows an arrangementwhich failed to give sufficient coverage of the exhibit, butwas very useful for accurately counting people crossing aparticular threshold. Unfortunately counting people by handis extremely tedious; in our experience, in an hour of videocan take up to two hours to annotate. Since multiple camerasare needed to give reasonable coverage, the total annotationtime must be multiplied by the number of cameras. Weattempted a real-time annotation by employing a groupof student volunteers spread so as to increase the spatialresolution of the data. Figure 1(d) shows the division oflabor: the lines separating the modeling sub-areas of theexhibit were marked on the floor. Seven people took up thepositions shown in figure and counted the visitors crossingthe line in either direction. This was done in a synchronizedfashion with a lead timer signaling each period of 10 seconds.

This counting task is quite challenging, as evidenced bythe fact that annotating video footage typically takes longerthan real-time. In order to address this, a second stage ofdata rectification was performed. The east camera was simplyused to measure movement through that doorway,but thewest camera was positioned so as to cover the same areaas one of the counters. We used it to estimate the error inreal-time annotation in order to give some measure of thedifference in reliability between collecting statistics fromvideo and in real-time. The collected data have a naturalsanity check in that no area should ever have negativepedestrians. In cases where an anomaly was detected, laserdata (described in detail below) were used to crosscheckand repair the annotation. The most common error appearsto have been switching the east-to-west and west-to-eastcolumns at page boundaries. Additionally, we now believethat the differences in real-time counting ability are ex-tremely large. Any estimate of error rate of one individual,based on a video ground truth, does not generalize to theremaining six counters. Figure 4 shows the resulting countswithin each region, constructed by adding and subtractingthe counts at each edge. For example, if there aren peoplein area E1a at timet0, then at timet1 = t0 +10 seconds onehasn+P1ws+P2sw−P1sw−P2ws people whereP1ws is thenumber of people crossing the line of position 1 from west toeast,P1sw the number of people crossing from east to west,

P2wsthe number of people crossing the line of position 2from west to east, andP2sw the number of people crossingfrom east to west. Some unresolved negative counts remain,although are not shown in the figure.

With each use of the video cameras two laser rangingdevices were deployed in the Life Tunnel. These are timeof flight devices that measure distance to an obstacle (towithin ∼2mm) at an angular resolution of2◦ at about50Hz. Figure 1(e) shows their positions, the shaded regionrepresenting the area in which sensor readings are received.The infrastructure, transport overhead, and space taken bythedevices mean that only two such devices can be convenientlydeployed in the Life Tunnel without severely interfering withthe visitor’s experience. The lasers’ readings are indepen-dently logged to disk, with the two computers maintainingsynchronized clocks.

Several standard Bayes’ filter techniques for trackingindividuals (e.g., [3, 4]) were applied to the captured data.Each failed due to severe and frequent occlusions. Figure 2shows laser data from the single west laser for each videostill. Notice that people are easy to distinguish from the back-ground, but that it is extremely challenging to estimate groupsize simply from the area of sensor readings. In particular,the data association component is extremely challenging. Asingle person may produce multiple readings, while a singlereading may represent multiple people. This noisy many-to-many relationship proves to be a major challenge for softwarepackages that have been designed and evaluated in sparseenvironments often with several independent readings fromoverlapping laser sensing fields.

In keeping with the original observation, initially we hadbelieved that tracking would be unnecessary so long asreasonable estimates of the occupancy of each location could

Fig. 4. Time series of the number of people in sub-regions of the LifeTunnel. (From real-time counts, fine grained model with seven sub-regions.)

Fig. 5. Model based on transitions to neighboring areas.

be ascertained. Experiences with our data have highlightedseveral tracking challenges. In the Life Tunnel scenario,people may move rapidly and then stop for long periodsof time to read or listen to the exhibit. This can requirea noisy action model. Such models typically mean thatprobability mass is lost extremely rapidly when occlusionsoccur. As a result, one of the core functions of the trackinginfrastructure, namely maintaining belief through time, fails.Furthermore, because the lasers have few readings in the CellTheatre itself, the only way to estimate the number of peopleoccupying the space is to count people who enter and exitat each door. Tracking software has a far greater success intracking people leaving the sensing area than just entering.In the former case, the belief function (particles, grids,Kalman filters) has converged and is doing a reasonable jobof predicting and following the observed trajectory. In thelatter case, no prior history helps to distinguish the readingfrom spurious noise, and consequently it may take severaltime steps to detect that the readings are in fact a visitor.The result is the position of the lasers and the shape of theenvironment mean that people moving into the Cell Theatreare more easily tracked than those leaving. When run onhours of data, this difference manifests itself in estimates forvisitors well beyond the Theatre’s capacity.

B. Modeling

First we constructed a simple phenomenological modelof how the distribution of museum visitors in the exhibitchanges over time by modeling the collective behavior ofan homogeneous group of visitors, each of whom can berepresented as a Markov process [5]. The diagram in Figure 5shows the one-way flow condition which can be easilytranslated into a set of coupled differential equations thatdescribe the dynamics of collective behavior. In one-wayflow, visitors enter from the west (left of the figure) andexit to the east (right side).

The variables of the model areNi(t) the average numberof visitors at exhibiti at time t. This number changes overtime due to transitions between the exhibits. These transi-tions, represented diagrammatically by arrows, are given bywij , the rate of making a transition from exhibiti (or source)to exhibit j (or sink) at timet. And the model assumesthat transition rates do not change in time. Moreover, aconstant number of visitors enter the exhibit in unit time.

Fig. 6. Model constructed based on the empirical transitionrate data.

The mathematical model is given by the equations below:

dN1(t)

dt= ws1s − w12N1(t)

dN2(t)

dt= w12N1(t) − w23N2(t)

dN3(t)

dt= w23N2(t) − w3kN3(t)

dN4(t)

dt= ws4s − w4kN4(t)

The transition ratewij is the probability a visitor will movefrom exhibit i to exhibitj in unit time. In this simple modelwij =

1−θ(Nj−Cj)τi

, whereτi is the mean exhibit viewingtime of the exhibiti, Cj is the capacity of the exhibitj, andθ(·) is a step function. The meaning of the transition ratesis as follows: an agent decides to transition from the currentexhibit i to the next exhibitj with a probability that dependsboth on how long it takes to view the current exhibit andhow crowded the next exhibit is. If the number of people atexhibit j is at, or exceeds, the capacity of the exhibit, agentsat i will wait until it becomes less crowded. This formulationallows us to take into account the effect collective behavior(crowding) has on the individual. The sink and source haveessentially infinite capacity and no associated viewing times,the transition rates leading to and from them have simplerforms:

ws1 = 1 − θ(N1 − C1), w3k = 1

τ3

ws4 = 1 − θ(N4 − C4), w4k = 1

τ4

Modeling museum visitors behavior as one-way flow maybe appropriate for special exhibitions, where there is usuallya single entrance, a single exit, and agents are encouraged(via recorded guides, museum docents, or simply pressurefrom behind) to move in a single direction through theexhibits. One-way flow, however, is not appropriate for theCSC, where people can enter the Life Tunnel exhibit fromeither end. We can take this into account by describing theflow between the exhibits as two-way flow. This is done byreplacing the arrows in Figure 5 with bidirectional arrows.New arrows introduce new terms into equations describinghow the numbers of agents at each exhibit change in time.Equations for this two way model are as follows:

d N1(t)

dt= ws1s1 − w12N1(t) + w21N2(t) −

N1(t)

τ1

d N2(t)

dt= w12N1(t) − w23N2(t) + w32N3(t) − w21N2(t)

d N3(t)

dt= w23N2(t) − w32N3(t) + ws3s2 − w3kN3(t)

d N4(t)

dt= ws4s1 − w4kN4(t) + ws4s2

This initial model simplified the condition by aggregatingeach pair of exhibits, so it only contains 4 exhibits whichcannot represent the real exhibits scenario which contains7 exhibits. In other words, these models of one-way andbi-directional flow operate at a spatial resolution equivalentto the data collected from the overhead cameras (shown inFigures 1(c) and 3). Note also that this model used idealizedtransition rates. We address these problems in the followingsection.

C. Transition Rates

The initial model used constant transition rates whichcannot explain the fluctuations existing in the experimentaldata. After working with the initial model, we decided toadd a stochastic term to the transition rates. Letτ∗

i be arandom variable which is normally distributed with meanτi and varianceσ2 where σ is a constant. Then the formchanges to:

wij =1 − θ(Nj − Cj)

τ∗

i

, τ∗

i ∼ N(τi, σ).

We can estimate qualitative transition rates between dif-ferent exhibits from the video data.1 This gives us a way toconstruct a dynamical model that is based on empirical data.The results of transitions collected from the data Figure 4are shown in Figure 7. The number of people transitioningbetween exhibits within the data was averaged to yield theempirical transition rates in Table I.

D. Current model

From Table I, we find a very high transition rate from thewest entrance to exhibits 1a and 1b. Similarly, there is a hightransition rate among neighboring exhibits. These featuresobserved in the empirical data resulted in the constructionof a new model. Figure 6 shows a model with edges addedto reflect the observations made on the empirical data.

Using the same modeling methodology, we translate thediagram Figure 6 to equations describing how the averagenumber of visitors at each exhibit changes in time.

The refined model can be applied to the initial coarse-grained data by using visitor counts exhibits1a and 3b asvalues for the west and east sources, respectively. Figure 8shows the results with parameters1 representing the numberof visitors entering from the west entrance, ands2 represent-ing visitors entering the east entrance.

It is most natural to apply this model to the data collectedat the same spatial resolution. Figure 9 shows the model’ssolutions for initial conditionsNi(t = 0) = 0 for all i;and using parameterss1 equal to the flow entering fromthe west, ands2 equal to the flow entering from the eastentrance. The mean viewing times for the exhibits wereτi = {2, 2, 2, 2, 2, 2, 9} and exhibit capacities were chosento bec = {10, 10, 10, 10, 10, 10, 50}, same as before.

1We could similarly estimate the quantitative values for thetransitionrates, but doing so would require us to track individual visitors, in orderto compute the distribution of exhibit viewing times, whichis beyond thescope of the project.

(a) West entry & exit (b) Area E1a

(c) Area E1b (d) Area E2a

(e) Area E2b (f) Area E3a

(g) Area E3b (h) Cell Theatre

Fig. 7. Transition rates from data collected for each exhibit area by directreal-time observation.

Fig. 8. Predicted occupancy of each sub-region of the refinedmodel oncoarse grained data of Figure 3.

The models predictions shown Figure 8 appear qualita-tively similar to the data shown in Figure 3, while thesame cannot be said for Figure 9 and the respective datain Figure 4. We attribute this to three factors: First, the datain Figure 4 are of a much lower density than that shown inFigure 3. Second, the quality of the Figure 4 data, becauseof the collection methodology used, depends critically on thecounting skills of each and every individual counter, and asingle failure devalues the estimates at neighboring locations.As noted above, the existence of negative values is evidenceof such errors in this data set. Third, while the inflow ofpeople into the exhibit is directly measured, the flow ofpeople exiting was simply calculated from the model ratherthan measured.

III. COGNITIVE MODELING OF INDIVIDUALBEHAVIOR IN A VIRTUAL POPULATED SPACE:

MUSEUM FIRST FLOOR

The work described earlier focused on the behavior ofgroups of people in a relatively simple and navigationallyconstrained environment. Here our attention turns to large

To \ From West Entrance Area 1a Area 1b Area 2a Area 2b Area 3a Area 3b Cell Theatre East EntranceWest Entrance 0.667 0 0 0 0 0 0.394 0

Area 1a 0.727 0.242 0.091 0.061 0.030 0 0.333 0

Area 1b 0.182 0.212 0.273 0 0.155 0 0.394 0

Area 2a 0.061 0.242 0.212 0.091 0.091 0 0 0

Area 2b 0 0 0 0.212 0.091 0.030 0.030 0

Area 3a 0 0.030 0.152 0.061 0.152 0.182 0.061 0

Area 3b 0 0 0 0.152 0.061 0.061 0 0

Cell Theatre 0.061 0.212 0.152 0.061 0.182 0.242 0.030 0

East Entrance 0 0 0 0 0 0 0 0.030

TABLE I

AVERAGED TRANSITION RATES FROM COLLECTED DATA.

Fig. 9. Predicted occupancy of each sub-region of the refinedmodel onfine grained data of Figure 4.

spaces with medium-to-high levels of topological complexityand several open areas. Additionally, instead of consideringmacroscopic models, the focus here is on understandingthe cognitive determinants of how an individual’s spatialbehavior is affected by others.

A. Approach

Architects and urban planners have long studied how anenvironment’s spatial configuration affects the difficultyofway-finding, i.e. going from a locationA to a desired goal-locationB. Here, we consider an extension of this problem,namely, how does spatial configurationand the distributionof people in the space influence way-finding difficulty. Desk-top Virtual Reality (VR) models are a useful and widely usedtool in spatial navigation research [1, 2, 6, 7]. We exploitedthis approach to conduct controlled laboratory experimentson human subjects. VR has the useful (and unique) propertythat it allows different subjects to interact with the same setof agents, thereby producing repeatable “social” experiments.

The first floor of the CSC was chosen as the preliminarytest-bed for our empirical, VR investigations. Figure 10shows the blueprint of CSC’s first floor. To emulate thissetting, we developed a VR setup that (i) had features andlayout complexity comparable to those of the actual museum,and (ii) could be populated with artificial agents (or “bots”)capable of exhibiting scripted behavior to emulate the socialsetting of a museum. Our VR setup enables subjects tonavigate freely through the environment using a joystick.

The customized VR system was developed by DigitalArtefacts Inc using the DI-Guy engine2. It has basiccollision detection capabilities that prevent a subject frommoving through walls or through agents in the museum.This constraint effectively makes the agents into obstacles.The VR system also has a large collection of different agent

2Digital Artefacts Inc., 119 Technology Innovation Center,OakdaleCampus, Iowa City, IA. DI-Guy is a product of Boston DynamicsInc.,78 Fourth Avenue, Waltham, MA

Fig. 10. Layout of first floor of California ScienceCenter. Photographs of this floor can be seen athttp://robotics.usc.edu/interaction/nsfhsd/csc-recon.php.The rectangular bounding box of the floor is approximately 115m × 60min size.

“personalities” (i.e. old woman, policeman, child, man in awheelchair, etc.) that are used to populate the museum, andeach agent has a variety of readily interpretable naturalisticmotions (e.g. talking, standing and waiting, sitting, andeating, etc.).

B. Experiment

In a familiar environment where both the current locationA and the goal-locationB are known, finding a path fromAto B that, say, minimizes the distance or time taken is a route-planning problem. This can be non-trivial problem dependingon the geometry of the space. However, the difficulty of thisproblem is significantly increased when either of both thefollowing is true: (1) the space is unfamiliar; and (2) the goal-location is unknown or uncertain. When the goal-location isunknown, one would expect that a person familiar with theenvironment would have a distinct performance advantage ineffectively searching the space to find it over a person whois unfamiliar with the space.

Here, we investigated if this advantage would hold truein a populated space as well. We hypothesized that theadded cognitive load associated with navigating through apopulated space could impact this performance advantage.The motivation for posing this question is that in museums,visitors often vary in their extent of familiarity with thespatial layout or with the location of particular goals.

To test this hypothesis, we designed a task that forcessubjects to pay attention to each of the agents in the museum

Fig. 11. Sample screenshot of what the subject sees while performing thesearch task. The the image in the upper right hand corner shows the currenttarget, who in this case is also present in the scene.

and to their locations in order to achieve high performancelevels. The basic protocol is as follows. The subject isrequired to perform a series of nested way-finding tasks.The overall task occurs in a series ofn rounds. At the startof round i, the subject is shown an image of an agent ortargetTi that is maintained for the duration of the round.The subject’s task is to find the location of this target and hasto verify that they have indeed found the target by actuallygoing to the location from their current location. The subjectis deemed to have successfully found a target if they come upwithin a predefined distance of the target. When successfulverification occurs, the round ends. The next round followingthis same protocol begins immediately. This continues tillthesubjects have successfully found alln targets. The subjectsare instructed to perform this task as rapidly as possible, i.e.minimize the overall time taken.

A screen shot of what a subject sees while doing the taskis shown in Figure 11.

This task was used to compare the performance of twogroups of subjects, one consisting of subjects who werefamiliar with the layout and the other having naive subjects.

C. Methods

We ran a pilot experiment to test this hypothesis with asmall number of subjects (8 subjects - 5 male, 3 female).

Each subject completed a “sense of direction” question-naire followed by a practice session in a virtual maze, whichwas meant to familiarize them with the task and with the useof the joystick. Following this, the main task was explainedto them. Subjects were divided into two groups. One groupreceived a virtual “flythrough” tour of the empty museumbefore performing the task while the other group did not.This second group is referred to as the “online” group asthey had to make decisions about where to search for thetargets as they performed the task as the layout was unknown.Each subject in the flythrough group received either a tourthat went clockwise or counterclockwise along the entireperimeter of the museum.

All subjects were placed in the populated museum at themain entrance, and were instructed to find each of the8targets as rapidly as possible. Which of these agents wouldbe the targets was not known to the subject beforehand. Oncompletion, the subjects were asked to recall the description

0 Online Flythrough0

2

4

6

8

10

12

14

16

Condition

Tim

e (m

inu

tes)

Fig. 12. Total time taken by each subject to find8 targets.

of the eight targets seen and the order in which they wereseen. Following this, they were asked to draw a sketchmapof the museum with as much detail as they could remember,and mark the locations of each of targets on the map.

The museum was populated by66 agents in all, of which8 were targets. The locations of7 of the 8 targets weresuch that they were not directly visible from the positionof the previous target or from the starting location, in thecase of the first target. The remaining agents were distributedpseudo-uniformly around the museum with each being aloneor in small groups of less than4. A small fraction of theagents constantly moved through the museum, but the targetsremained static. The use of small group size and limitedmovement of the agents was done to reduce the need forroute-planning around crowds.

D. Results

The predictions for the experiment were that we wouldexpect all subjects to perform a systematic sweep of the spacefor the first few targets as they had not been seen before,but the behavior would transition into a more dominantlymemory-guided search for the later targets. Furthermore, asthe “online” group was not familiar with the space before-hand, we predicted that this would lead to comparatively lesssystematic search patterns for this group.

The results of seven of the eight subjects were analyzedas one subject was excluded for very poor performance. Thetime taken is shown in Figure 12. The minimum time toperform this task when the layout of the museum is knownas well as the locations of all the targets is approximately4.5 minutes. As expected, it took the subjects significantlylonger,≈ 8 to 15 minutes, to find all8 targets.

When the distance taken by each subject is consideredper target as shown in Figures 13(a) and 13(b), we see thatthe first two targets are associated with large differencesin performance between subjects both within and betweengroups. However, there is a substantial reduction in thisvariability for targets3 to 8. Notably, the length of theshortest paths between the starting location and Target1,and between Targets1 and2, are comparable to that betweentargets6 and7 and targets7 and8.

However, with respect to the search pattern, the prelim-inary data show little or no difference. Importantly, mostsubjects exhibit search patterns that differ significantlyfroma systematic sweep of the space. For example, compare thepath of a subject in the “flythrough” group shown in Figure14 corresponding approximately to a systematic sweep of the

0 Online Flythrough0

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400

600

Target1

Dis

tanc

e(m

)

0 Online Flythrough0

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0 Online Flythrough0

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(a) Searching for1 to 4 targets

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(b) Searching for5 to 8 targets

Fig. 13. Distance covered by subjects in searching for targets

200 400 600 800 1000 1200 1400 1600 1800

100

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700

800

900

1000 Start

TARGET 1

Fig. 14. An example of the path data available from the subject’sexplorations in the museum. The blue dots indicate the locations of theagents.

space, with the path of another representative subject fromthe same group shown in Figure 15.

The results reported above are from very coarse measurescalculated on the data. However, the small number of sub-jects is not a reflection of the quantity of data from suchexperiments. Here, each subject generated about 3000 data-values on average in terms of path information. Currently,we are developing more detailed measures to exploit the hightemporal resolution of this kind of information. Specifically,we are current focusing on analyzing the spatial relationshipof the agents visible the subjects at every instant to predictwhat the subjects will do next and which agents they willremember; and the changes in the visibility polygon betweentime-steps to quantify how subjects survey the premises.

IV. OUTLOOK AND FUTURE WORK

This paper describes ongoing work aimed at producingpredictive models of navigation in social circumstancesacross a range of environmental conditions. The work consid-

200 400 600 800 1000 1200 1400 1600 1800

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Fig. 15. Path of another subject from “flythrough” group

ers three issues: collection of data on crowds and collectivespatial behavior, development and refinement of mathemati-cal models, and controlled experiments with human subjectsto understand the effects of social interaction on navigationand way-finding. Our approach is to focus on two scenarios:(1) the Life Tunnel exhibit is a relatively structured spacein which we aim to understand the collective behavior; (2)the California Science Center first floor is a large space,including both non-line of sight topology and open areas,in which navigational choices related to explicit tasks canbesystematically studied.

Ongoing Work

We are currently working on several problems including:(1) identifying a suitable bridging scenario, which couldpotentially be based on a emergency evacuation in orderto consider both important way-finding and macroscopic ef-fects; (2) implementation and evaluation of batch algorithmsin order to estimate position and density more effectively;(3) experiments and models to detail the role of attentionbiases and memory induced by the distribution of agents onnavigation decisions and search strategy.

V. ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of the NationalScience Foundation. This work was supported in part by awardnumbers BCS-0527725 and BCS-0527689, and Research Experi-ence for Undergraduates (REU) supplements for summers 2006and2007.

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