A FORMATION BEHAVIOR FOR LARGE-SCALE MICRO-ROBOT FORCE DEPLOYMENT. Donald D. Dudenhoeffer Michael P. Jones

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1 Proceeings of the 2000 Winter Simulation Conference J. A. Joines, R. R. Barton, K. Kang, an P. A. Fishwick, es. A FORMATION BEHAVIOR FOR LARGE-SCALE MICRO-ROBOT FORCE DEPLOYMENT Donal D. Duenhoeffer Michael P. Jones The Human-System Simulation Laboratory Iaho National Engineering an Environmental Laboratory P.O. Box 1625 Iaho Falls, ID , U.S.A. ABSTRACT Micro-robots will soon be available for eployment by the thousans. Consequently, controlling an coorinating a force this large to accomplish a prescribe task is of great interest. This paper escribes a flexible architecture for moeling thousans of autonomous agents simultaneously. The agents behavior is base on a subsumption architecture in which iniviual behaviors are prioritize with respect to all others. The primary behavior explore in this work is a group formation behavior base on social potential fiels (Reif an Wang 1999). This paper extens the social potential fiel moel by introucing a neutral zone within which other behaviors may exhibit themselves. Previous work with social potential fiels has been restricte to moels of perfect autonomous agents. The paper evaluates the effect of social potential fiels in the presence of agent eath (failure) an imperfect sensory input. 1 INTRODUCTION This paper examines multi-agent moeling an simulation for a large-scale number of autonomous agents. Specifically, the paper examines the evelopment of a simulation program to moel the interaction an collective behavior of micro-robotic task forces consisting of 1000 or more entities. The objective of the research presente in this paper is twofol. The first objective is to evelop a viable simulation tool for stuying autonomous agent behavior an collective interaction. The secon is to examine behavioral moels for group formation an coorinate motion. Technology will soon make possible the practical eployment of micro-robots on the size orer of 2.5cm square. The ispersion of thousans of these micro-robots represents a tremenous capability for application in surveillance an remote sampling. However, many issues, beyon technical feasibility still nee to be examine. Notable research papers by Reynols (1987), Gage (1992), Hogins an Brogan (1994), Kenney an Eberhart (1998), Reif an Wang (1999), an Suzuki an Yamashita (1999), examine one of these issues, namely that of interaction an coorinate motion among autonomous agents. This paper extens an avances previous research efforts by examining the issues of imperfect perception an entity eath. The simulation framework evelope for this project encapsulates the robots as autonomous entities in which capability is ae or reconfigure by the aition of objects (behaviors, sensors, physical characteristics, etc.). The simulation escribe in this paper was evelope using Exten. The paper begins by presenting a vision for future micro-robotic eployments. Some of the issues involve in coorinating the group s behavior are also ientifie. Next the paper iscusses the evelopment of the agent moel an construction of the simulation. Thirly, movement coorination is emonstrate using a force function between neighboring entities. Finally, experimental results an future work are iscusse. 1.1 Research Motivation Technological avances in micro-robotics, remote sensors, an artificial intelligence continue to increase the capabilities of micro-robots while ecreasing the size of such units. It is easy to imagine proucing an eploying thousans of inexpensive, essentially isposable micro-robots in the near future. Although possibly limite in iniviual capability, eploye in large numbers their cumulative ability represents a tremenous force. Given the proper social behavior set, the agents form a collective; much like a colony of ants or swarm of bees. Importance shifts from the actions of iniviual agents to the collective behavior. A complex system evelops. A complex system is efine as one whose component parts interact with sufficient intricacy that they cannot be preicte 972

2 by stanar linear equations; so many variables are at work in the system that its overall behavior can only be unerstoo as an emergent consequence of the holistic sum of all the myria behaviors embee within. (Levy 1992). The autonomy, social interaction an system complexity elevate the robots from mere mechanical agents to a point where they approach a semblance of artificial life (AL). A key element of micro-robot eployment is the construction of behavior sets that facilitate group formation an coorinate motion of micro-robotic forces. This paper examines the utility of Social Potential Forces in maintaining spatial relationships in the face of micro-robot eaths an sensor imperfections. Aitionally, this paper introuces an aaptation, which promotes preferential expansion of the collective in a specific irection. 1.2 Application Scenario To unerstan the complexities of micro-robot eployment an the nee for coorinate control, consier the following scenario. A train with several cars containing hazarous material (HAZMAT) has eraile. A subsequent explosion has scattere ebris aroun the crash site. The extent of the area contamination an the status of the cars carrying the HAZMAT are not known. Due to the angerous nature of the scattere material, a task force of micro-robots is selecte for site evaluation prior to human entry into the area. An Unmanne Aerial Vehicle (UAV) rops a group of 2000 micro-robots equippe with chemical sensors over the ebris fiel an in the vicinity of the overturne cars. As the robotics coorinator, your mission is to utilize the micro- robots to map the contamination levels in the area an assess the hazars before humans enter. This scenario represents a practical an seemingly simple application of micro-robots. However, it reveals many of the technical challenges involve in eploying large numbers of micro-robots. These challenges inclue the following questions. 1. Given a ranom or batch istribution of the 2000 micro-robots, how o you organize them into a nearly equiistant formation to maximize sensor coverage of the suspect area? 2. Once, the pattern is forme, how o you irect the masses in coorinate motion in the irection of interest? 3. During the formation an sensor sweep, how o you ientify an then ajust for the inevitable eaths (unit failures) in orer to ensure complete coverage? This example illustrates the nature of some of the collective tasking an coorinate motion issues that still face large-scale micro-robot force eployments. These issues of autonomous behavior an comman an control are also face when using larger robots, but the problem is much more complex for several reasons. First, the iminutive size of the units severely restricts their capability in terms of computational power, memory storage, sensor coverage, etc. Secon, the sheer size of the collective, one thousan or more, makes iniviual control of the units by an operator unfeasible. This project raws inspiration from observations of social communities in nature, i.e. bees, ants, birs, fish. The approach taken is to assign each unit a simple set of iniviual behaviors. Within this framework, each unit senses an reacts to its environment an other units within the group. The units together form a collective behavior. The moel presente in this paper encapsulates a behavior set that promotes group formation builing an coorinate motion. These capabilities aress some of the eployment issues illustrate in the HAZMAT scenario by giving the iniviuals some autonomous behavior that helps accomplish the prescribe mission. 2 PROJECT DEVELOPMENT Simulation unfortunately is a necessary evil. (Arkin 1995) Simulation, although accepte in many isciplines as an essential tool for gaining insight into system operation, has many skeptics among researchers in the robotics fiel. The prevailing thought is that the only true test of a new system esign is to implement that system on an actual robot an evaluate the robot in a real worl environment. No one can eny that this is inee the ieal metho for complete evaluation. However, costs, resources, time an even technology often limit the feasibility of conucting real worl testing. In these instances, simulation plays a valuable role in evaluating avance concepts an esigns. Likewise, when resources become available for fieltesting, maximum benefit can be achieve by focusing tests on the critical elements ientifie through prior simulation. 2.1 Simulation of Micro-Robots Many concerns of the robotics community are the result of prior simulations that have unrealistically represente the challenges of real worl robotic system eployment. Many of these concerns are vali an have reuce the usefulness of simulation as a evelopment tool. The following list etails some of the specific concerns raise regaring previous robotics moeling an simulation. The list was 973

3 compile from the literature an personal iscussions with several prominent roboticists. 1. Simulate robots live forever. (immortality) 2. Simulate robots see everything. (perfect sensing) 3. Simulate robots possess unlimite computational ability. 4. The computer coe use to rive the simulation oes not resemble the same program coe use to rive the actual robot. (Arkin 1995) A simulation shoul take into account the realistic performance of sensors an the effects of environmental conitions. The level of realism shoul be relate to the focus area an goals of the experiment. Concept exploration may not require a complete worl moel in terms of exact uplication of the environment, but it shoul aequately reflect the capabilities of the components in question. Micro-robotic prouction is not to a point where full-scale eployment is possible, but the simulation escribe later tries to aress the above issues in terms of estimate capabilities. The capabilities of the simulate micro-robots are easily ajuste within the simulation to increase realism as more accurate information becomes available. 2.2 Founations of Micro-Robotic Agent Moeling The moeling an simulation of large-scale forces (1000 or more units) of autonomous agents is a relatively new area of research. The roots of such simulation can be trace back to the concept of cellular autonoma (CA) first conceive by John von Neumann an his colleague Stanislaw Ulam when they were exploring the realm of Artificial Life an self-reproucing automaton. Accoring to Levy (1992), Arthur Burks actually coine the phrase Cellular Autonoma while eiting von Neumann s papers on the subject. In the late 1960s, a University of Cambrige mathematician, John Horton Conway, took the concept of CA an evelope the game of Life. This game inspire an influence generations of researchers in the realm of AL an autonomous agent research. The game of Life consists of a two imensional gri on which entities exists within iniviual cells. The entities have one of two states, alive or ea. The game traces the generations of entities as they are born, live an ie. The state of an entity in the next generation is base solely on the number an states of the neighboring entities in the eight cells ajacent to the entity in question (Levy 1992). The game of Life illustrates some of the key concepts use for autonomous robot moeling an multi-agent simulation. These core concepts inclue: 1. Ientification of an focus on iniviual entities. 2. A efine rule set governs iniviual behavior. 3. Iniviual entities are irectly affecte by neighboring entities. These concepts establish the principles for multi-agent moel evelopment an they serve as the basis for the esign of our micro-robot simulation. Throughout the remainer of the paper the terms agent an micro-robot are use interchangeably. The reason for this is twofol. First, we wish to shift focus away from any preconceive mental moels an the associate limitations that arise when picturing a robot. The main focus is on the agent s behavior or psyche. Secon, we want to avoi limiting the simulation principles iscusse to just micro-robotic applications. The principles an metho iscusse in this paper can be aapte easily to other moeling applications. For example, an automate highway system might employ autonomous automobiles that implement similar group spacing behavior. 3 SIMULATION MODEL CONSTRUCTION The multi-agent simulation was evelope using Exten by Imagine That, Inc. Exten is primarily known as a process simulation language an has not been use to a great egree for multi-agent simulation. However, Exten offere a means to evelop a prototype system without the overhea of eveloping a complete simulation environment. The C-like nature of Exten s MODL language also supports the project goal of eveloping simulation coe that coul be porte rather than re-written when programming real robots for evaluation. 3.1 Environment Moel The simulation is similar to the game of Life iscusse earlier. The simulation runs in a two imensional plane represente by a global gri (x, y coorinate system). Aitional gris may be layere with the global gri to represent obstacles, terrain, sensory objects, weather, an other environmentally significant elements. The gris may be static or ynamic an reflect changing elements in the environment. This layering of gris allows rapi manipulation of scenarios for elaborate What if? analysis. The current work oes not inclue any aitional environmental gris. Agents within the moel move within the spaces efine by the global gri. At each simulation step, an agent may move no further than a single block away from its present position. Thus, it may remain in position or move to one of the eight ajacent (horizontal, vertical an iagonal) spaces. A master status table contains agent position an state information. This table, couple with information from the global gri, is use to simulate sensing of neighboring 974

4 entities. The iniviual sensors moele on a particular agent can etermine the range an irection of other entities within their prescribe sensor range. A more etaile iscussion of the sensor moel is escribe in section Agent Moel In aition to the concepts from the game of Life, the principles of complex reactive systems influence the agent moel s construction. Arkin (1998) efines a reactive system as one that tightly couples perception to action without the use of intervening abstract representation or time history. Reactive systems place little emphasis on planning an utilize agent behavior sets as their core builing blocks. Simply speaking, reactive system an behavior base systems sense the worl an react Agent Moel Principles The agent simulation moel is base on the premise that in the near future technology will allow the prouction an eployment of large-scale masses of micro-robots. The robots will be small. They will likely possess only basic capabilities an mission specific sensors. Direct communication between agents may or may not exist. The maturity of this technology oes not yet exist. As a basis for moeling the capabilities of these future agents, the acaemic experimental robot GrowBot by Parallax, Inc. was use. The GrowBot provies a goo test platform in that it was capable, but not too capable in terms of computational power an sensor configuration. Specific assumptions about iniviual capabilities will be escribe in the corresponing iscussion of those capabilities. The simulation esign is very object oriente in its approach to agent construction. Sensors an behaviors are encapsulate when possible. This approach allows iniviual components to be ae an remove from the moel as if the corresponing physical component were being ae to or remove from a real agent. This moular esign permits rapi capability reconfiguration uring concept exploration. Aitionally, a very conscious effort was mae to separate the simulation artifacts from the logic coe being evaluate. For example, we attempte to account for the real-time parallel nature of iniviual entity behavior while running in a sequential simulation environment. Furthermore, the bounaries between the true state of the environment an that which can be perceive by an agent are clearly maintaine. The goal was to create simulation coe that coul be porte rather than re-written when programming real robots for evaluation Basic Agent Moel The moel of an autonomous micro-robot is constructe by builing upon a base autonomous agent object. The basic moel of the agent can be thought of as simply a physical shell. In abstract programming terms it may also be thought of as an object with general capabilities. The basic agent possesses only locomotion as an innate capability. The agent exists in one of three states: ea, alive or ormant. The only core capability possesse by the agent is motion, which is further restricte by spee an enurance limitations. We make a istinction between the agent s motion capability an a behavior esigne to irect or use that capability of motion. This basic agent serves as the platform on which aitional capabilities (i.e., sensors) an iniviual behaviors are layere. Sensors are ae to the agent moel by plugging in sensor moels. The sensors query the environment moel to perceive objects or conitions of interest. The agent receives input from these sensors to increase its basic capabilities. Similarly, new behaviors may be ae to take avantage of aitional sensory capability. However, it shoul be note that sensors an behaviors are not the same thing nor is it necessary to have a one-to-one corresponence between sensors an behaviors. Sensors provie a means for perceiving environmental states or conitions while behaviors are the actions the agent takes base on the perceptions it makes. Behaviors may rely on multiple sensory input (stimuli). For example, a robot s next move may be base on the input it receives from multiple neighbor etection sensors. Similarly an iniviual stimulus is not necessarily unique to one behavior. Neighbor position information may be use in both a group formation behavior an a collision avoiance behavior. When behaviors conflict or compete for resources, an arbitrating mechanism usually ictates the agent s reaction. In this way behaviors are layere. Section escribes the behavior arbitration moel. 3.3 Sensor Moel Sensors are moele as encapsulate object classes. The agent uses a fixe set of input an output parameters to communicate with each sensor. Consequently, multiple types an qualities of sensors may be evaluate with complete transparency to the agent moel. The agents presente in this moel possess two types of sensors, a Nearest Neighbor sensor an an Object Detection sensor. This project istinguishes itself from much of the past research in this area by the attention eicate to moeling realistic sensor capabilities. The premise behin agent interaction is that one agent can see his neighbor. The ability to etect an ientify neighboring agents cannot be taken for grante. Ajacent agents can be ientifie via two methos. The first metho consists of an active broacast in which agents broacast position information. Neighbor position may be erive from a relative coorinate system or by strength an irection of the signal. Omni-irectional position ata is possible. 975

5 The secon metho involves passive etection without open communication between agents. Neighboring agents are etecte through passive sensors. Infrare sensors are an example of this type of sensor. Sensor coverage is irectly tie to the number an arrangement of sensors. Detection is further epenent on the sensor s accuracy. The agent moel uses passive etection. Each agent possesses an array of five sensors for etecting neighboring agents. Each sensor has a coverage sprea of 45 egrees. Figure 1 illustrates the sensor configuration use in the moel. Three aitional sensors coul have been ae for complete 360-egree coverage. This was not one to conserve the resources that woul have been consume by each aitional sensor. These resources inclue power consumption, physical space, an computing (CPU) time. For this stuy s purposes, 360-egree coverage was not necessary because an agent oes not care who is behin it. The sensors etect the nearest agent within the sensor s coverage area. The sensor returns the relative bearing, range an type of the neighbor agent etecte. Neighbor type is important because neighbor type will etermine the agent s reaction to the etection. Figure 1 represents the neighborhoo of the agent. The perceive neighborhoo, represente by the black ots, consists of only those neighbors correctly etecte by the agents. Note that only the nearest neighbor is etecte if multiple neighbors exist within the same sector. The Object Detection sensor etermines whether an obstruction exists along the intene path of the agent. Specifically, an obstruction is etecte only if it is immeiately in front of the agent. This sensor returns a signal inicating an obstacle was etecte. Within the moel, no errors are associate with this sensor. 3.4 Behavior Moel The most important element of agent construction is the behavior set. In eveloping concepts an moels for iniviual agent an collective behavior schemas, biological entities an examples from nature were examine for insight. Important to this research project were the relationship that birs an fish exhibite in flocking an schooling behaviors. Birs an fish have the ability to form an maintain collective patterns. These patterns are forme by the animal s ability to balance the esire to remain close to the flock (or school) an also to avoi collision (Shaw 1975). Within the flock, the bir oes not possess universal knowlege (i.e., knowlege of the position of all others in the flock), but it ajusts its position base on the perception on its immeiate neighbors. Reynols use this framework to evelop his groun breaking animation work on Bois (Reynols 1987). These two principles of flocking an local perception provie the basis for the evelopment of the agent s behavior Subsumption Architecture Figure 1: Agent Sensor Arrangement an Neighborhoo Two types of errors are moele for each sensor, an inherent offset error an a etection error. The offset error accounts for the imperfect angular alignment of a sensor with respect to the intene relative positioning. This error is constant. The etection error represents the imperfection of the sensor an the egraation of the etection probability as a function of the etection range. The etection function is base on an exponential istribution with a mean etection range of forty inches. Once a set of iniviual behaviors has been evelope, a framework or architecture must be constructe to initiate behavioral responses an coorinate multiple behaviors. The subsumption architecture (Brooks 1986) provies the basis for behavioral coorination within the micro-robot agent moel. In simplistic terms, the subsumption architecture is base on layering reactive behavior sets on top of each other. These behaviors concurrently react to the perceive environment. A key tenet is that reaction is base on perception an not on planning. Coorination among behaviors involves a hierarchical scheme where higher level behaviors suppress or inhibit lower level behaviors. In this same way, successively more complex behaviors can seamlessly be layere onto the existing behavior set (Arkin 1998). Figure 2 illustrates the micro-robot agent s behaviors in orer of their priority. The priority goes from Collision Avoiance (highest) to Wanering (lowest) Wanering Behavior The Wanering Behavior reflects the agent s esire to move about when not uner other influences. The 976

6 wanering may be a ranom walk or motion in a preetermine irection. In the experimental results presente in Section 4, the Wanering Behavior has a preefine preference to irect the agent towar the east (i.e. right). etermine the slope an equilibrium point of the force function. The equilibrium point is efine as the istance in which the combine effect of the repelling an attracting forces is zero. This force function has the following characteristics: 1. Attraction is controlle by the c 2 / α2 term. 2. Repulsion is controlle by the c 1 / α1 term. 3. The equilibrium point where the combine effect is zero is given by =(c1/c2) (1/(α1 - α2)). Figure 2: Behavior Architecture Group Formation Behavior The Group Formation Behavior seeks to establish a specific spatial relationship between ajacent neighbors. The work by Reif an Wang (1999) on Social Potential Fiels provies the basis for establishing an maintaining this spatial relationship between agents within the moel. In aition to the work by Reif an Wang, this paper introuces the concept of a neutral zone within the social potential fiel. The neutral zone permits the Wanering Behavior to activate an promotes expansion of the collective in a specific irection. Social Potential Fiels have as an unerlying concept that an agent is influence by his immeiate neighbors. A force vector is use to represent the influence exerte by an agent s neighbors. The nature of the force can be attracting or repelling epening on the istance between agents. The sign an magnitue of the force is represente by the force function (Reif an Wang 1999). Equation (1) is the force function use in the Group Formation Behavior moel f ( ) = c1 1 α where c 1, c 2 0, α 1 > α 2 > 0. This function creates a repelling force if a neighbor is close an an attracting force if the neighbor is far away. If a neighbor is too close, the agent tens to move away an gain further separation. If the neighbor is too far away, the agent moves towar the neighbor to close the istance between them. The efinitions of what is too close an too far away are arbitrary an represent flexibility in configuring the behavior epening on the mission an esire sensor coverage. In Equation (1), represents the range between neighboring agents. The constants, c 1, c 2, α 1 an α 2 + c2 2 α (1) Note that this function represents the force applie by a single neighboring agent. In practice, all perceive neighbors apply forces. The resulting force is the vector summation of all the forces applie by all neighbors. Another moel parameter that may be set is to have neighbors of ifferent types that exert forces using ifferent force functions. However, the simulation results presente in the next section use a homogenous set of agent types an hence, a single force function. To unerstan the effect of multiple force vectors on a single agent, consier agent A with perceive neighbors N 1, N 2,..., N k with istances 1, 2,..., k. The iniviual forces applie by the neighbors is given by: fa( i) = c1i 1i α i c2i 2i α i The combine force applie to agent A enote by F(A) is: F( A) = i= 1 Equation (3) represents the force magnitue. It oes not represent behavior. Behavior is the reaction to the forces applie an is realize in the agent by either the esire for motion in a certain irection or the esire to remain in place. As state earlier, this paper introuces an aaptation to Reif an Wang s presentation of Social Potential Fiels. The aaptation is the introuction of a critical force. The critical force is efine as the magnitue of force below which the agent feels no effect. As an example, a critical force set at 5 implies that a cumulative force, F(A), woul require a magnitue greater than 5 to cause a reaction by the agent. By careful selection of the force function f(x) an the critical force, a neutral zone between repelling an attracting forces is create. Within this neutral zone, no force effect exists. This neutral zone accomplishes two purposes. First, it minimizes movement oscillations aroun the equilibrium point where the sign of the force changes. Secon, it provies an opportunity for aitional behaviors previously k + ( fa i ) (2) (3) 977

7 subsume by the force effect an Group Formation Behavior to have an effect on the agent. In the agent moel, uring perios the agent resies within the neutral zone, the Wanering Behavior ictates the esire motion of the agent. In our moel, the Wanering Behavior irects the agent to hea east. The agent waners east until the critical force is again reache. At this point, the Group Formation Behavior is activate. This combination of both behaviors working in conjunction not only promotes a uniform spatial relationship between neighbors, but it also causes the entire formation to preferentially expan an move in an easterly irection. This type of behavior reaily supports a scenario in which the agents are batch roppe or are ispense from a canister an are taske with establishing a uniform sensor net across a specifie area Collision Avoiance Prior to repositioning, an agent will look ahea at the position of his next intene move. If another agent or obstruction is etecte, the agent will evaluate a position 90 egrees to the right of the intene position. Again the agent evaluates this position. If occupie, the agent will turn 90 egrees right an repeat the process. If after turning in a circle, no move is evaluate as safe, the agent will remain in place for that simulation step. On the next simulation step, the process begins again. 4 SIMULATION RESULTS This paper presents the initial evelopment an research into behavior-base comman an control for autonomous micro-robots. A primary goal of the project was to evelop a simulation framework that permitte us to explore autonomous agent esign an the emergence of collective behaviors. A simulation framework was evelope using Exten. At the time of this paper, the simulation is capable of moeling the interactions of over one thousan autonomous agents. Figure 3 shows the simulation moel an the basic screen. The ots isplaye represent 350 ranomly isperse agents. Animation is not a project focus at this time an the agents are simply represente as an oval icon occupying a pixel on the screen. The simulate worl represents each pixel as an inch. Thus the istance represente between consecutive gri lines is 100 inches or just over eight feet. The iniviual agents are rawn a little larger than they woul be if rawn exactly to scale so that they can be seen in the isplay. 4.1 Moel Assumptions One of the important aspects of this simulation project was to create a creible moel of agent performance. In reality, Figure 3: Initial Dispersion 350 Agents technology has not reache the point of eveloping microrobots capable of fiel eployment. Performance capabilities are therefore base on miniature robot capabilities an on reasonable approximations of expecte future performance. The moel facilitates capability moification to incorporate new performance ata, as it becomes available. The following assumptions are mae about agent an sensor capability: Agent Size one inch in length. Agent Spee one inch per secon (maximum). Agent Failure failure equate with agent eath, follows an exponential istribution with an average agent life span of 17 minutes. Mean range of neighbor etector 40 inches. Maximum offset error of neighbor etector two egrees. 4.2 Force Function an Critical Force Selection The force function, f(), use for the examples in this paper is given by Equation 4. 30,000 f ( ) = Selection of c 1 = 30000, implies that the equilibrium point is locate at a istance of 30 inches. Figure 4 is a graph of the function. Note the slope of the function. The shape or slope of the function has a large effect on the transition between repulsing an attracting force, particularly in the combination of competing forces exerte by multiple neighbors. The repulsion force (represente by the portion of the graph below the x-axis) is larger than the attraction force. Also, the attraction force flattens out quickly such that its effects o not get too large as the istance between agents increases. (4) 978

8 Social Potential Force 10 Force Distance from Neighbor Figure 4: Social Potential Force Function The critical force use in the simulation run is set at 5. This implies that a force magnitue, F(A), of at least 5 is require to initiate a reaction by the agent. While F(A) is less than the critical force, the Wanering Behavior ominates motion irection (subject to the Collision Avoiance Behavior). When the critical force is exceee, the Group Formation Behavior takes over. Selection of the force function parameters an the critical force is base on the neighbor etection capability an esire spacing between agents. In the moel, esire average spacing is set at 30 inches with a +/- six-inch tolerance. 4.3 Simulation Runs The major thrust of this project was to evaluate the robustness of Social Potential Fiels in maintaining spatial relationships between agents when confronte with imperfect sensing an agent failure. Aitionally, the project introuce the concept of a critical force which, when couple with a Wanering Behavior, promotes coorinate motion. The following iscussions illustrate the project finings. All simulation runs are initiate from the ranom ispersion illustrate in Figure 3. The simulation time step is set at one secon. Each illustration shows the collective after 500 time steps or 8.3 minutes (simulate time) The Perfect Worl Figure 5 represents the ispersion pattern for the case in which sensing is perfect an agents o not fail. Note the nearly uniform spatial relationship between agents. Aitionally, note the preferential expansion of the collective in an easterly irection. This perfect worl represents a performance baseline for comparison. Note that the rightmost agents have move about 500 units (inches). The trailing agents have also progresse though a little more slowly as they are concerne about also proviing complete coverage of the area being swept. Figure 5: Moel of a Perfect Environment Agent Death In this run (shown in Figure 6) sensors work perfectly, but the agents are subject to eath. Death inclues har mechanical failures of the agent an estruction by environmental factors (i.e. falling in a hole or being crushe by an animal). The eath follows an exponential istribution with an average agent life span of 1000 time units (secons). The agents that have ie are no longer isplaye in the figure so the ensity of the collection has ecrease. Figure 6: Moel of Agent Death (Failure) Imperfect Sensing This simulation run (Figure 7) represents the case in which a sensor offset error an a sensor etection probability are incorporate into the agent moel. Agent failure is not moele in this execution of the simulation. The sensor offset error is ranomly istribute between +/- two egrees from the sensor s intene main axis alignment. The sensor etection probability is exponential istribution with an average neighbor etection range of 40 inches. 979

9 Figure 7: Moel Using Imperfect Sensors Combine Death an Imperfect Sensing The combine effects of both agent eath an imperfect sensors are illustrate in the simulation run presente in Figure 8. Figure 8: Moel of Agent Failure an Imperfect Sensors Discussion These simulation runs emonstrate three important results. First, the social potential fiel metho is robust for maintaining spatial relationships when use in the presence of agent eath an imperfect sensors. The ispersion patterns are similar for both perfect sensor an imperfect ones. When agents fail, the collective ajusts its shape to fill in the gaps. This behavior prouces a fairly uniform coverage of the area being swept by the agents. Secon, the introuction of the critical force permits the collective to waner. That is, without the critical force, the group formation behavior always ominates the wanering behavior an the collective oes little more than simply space itself out. When the wanering behavior is allowe to have an effect, the collective can be move in a preefine irection. This result is particularly apparent in Figures 5 an 6. The final conclusion is that motion efficiency uner social potential force control is highly epenent on accurate neighbor etection. Motion efficiency is efine as the ratio of net istance travele to total motion. The introuction of imperfect sensing reuces motion efficiency. For example, the average easterly istance travele in the imperfect sensors case is only inches as compare to inches achieve with perfect sensing (see Table 1). Intuitively, one woul assume that the Wanering Behavior woul ominate with imperfect sensor performance. The simulation showe, however, that the agents oscillate between positions significantly more in the case of imperfect sensors. The agents were constantly reajusting their position epening on neighbor etection, lost etection an regaine etection. Table 1 illustrates average agent motion. Easterly motion is the total motion east. X motion is the total movement, east an west, along the x coorinate. The ratio of Easterly motion an X motion is equal to motion efficiency. The lower efficiency of the two simulations with imperfect sensor configurations inicates movement oscillations back an forth with minimal avancement. Agent Config. Table 1: Average Agent Motion Agent Motion (Average istances in inches) Easterly Motion X Dist. X Motion Y Dist. Y Motion Total Dist. Perfect Death Imperfect Sensors Death & Imp. Sensors Future Research This paper represents part of a continuing effort to evelop behavior an control concepts for micro-robots, but also for autonomous agent constructs. Social potential fiels are shown to provie robust coorinate behavior for ealing with agent eath an sensor imperfections in a simulate environment. The next step is to conuct an evaluation on actual robotic platforms. This paper an Reif s research explore social potential fiels in terms of a force function that is uniform an not affecte by the relative position of the neighboring agent. Further research is planne to examine the effect of sector epenent force functions which not only epen on the istance from the neighboring agent, but also on the relative angle of the neighbor s position. The use of a sector-base force function may have potential in the formation of intricate patterns with the agents. The concept of resiual forces that ecay over time may be a way to aress the inefficiencies an reuce 980

10 motion oscillations. In this manner, the agent possesses a ecaying memory of previous forces. The resiual force woul ampen the oscillation effect by creating some memory of a previously etecte agent that was not etecte uring the current etection cycle. Another interesting concept that must be explore further is the effect of the agents initial istribution on their subsequent behavior an group formation. This paper examines the case of a batch istribution in which all agents are initially bunche in a small area. Future stuy involves reviewing the relationship between initial ispersion an the force function in constructing the esire spatial relationship an coorinate motion. 5 CONCLUSIONS In this paper, we have escribe a flexible architecture for moeling thousans of autonomous agents. The agents behavior is base on a subsumption architecture in which iniviual behaviors are prioritize with respect to all others. The architecture use to moel iniviual agents permits specific capabilities to be quickly plugge in an teste. Of primary interest in this research was the use of social potential fiels as a mechanism for coorinate group behavior. This paper introuce the concept of a neutral zone in the social potential fiel an emonstrate its effect on the agents ispersion. Furthermore, the ispersion patterns illustrate the interaction between the social potential fiel an a wanering behavior operating within a subsumption architecture. Simulation has been criticize frequently by members of the robotics community ue to the too common use of moels that assume perfect performance of agent an sensors. We presente the results of moeling an testing some of the real-worl limitations of small-scale microrobots. The research escribe here specifically investigate the effects of agent eath an imprecise sensors. Initial simulation results suggests that group coorination base on social potential fiels is robust to these types of real-worl imperfections, but motion efficiency is relies on sensor performance. Future efforts will explore coorinate behaviors for other mission objectives such as those outline in the initial HAZMAT scenario. These objectives inclue forming a perimeter aroun a region an perioic, operator-inuce moifications to the mission. ACKNOWLEDGMENTS A special thanks is extene to the following people who provie valuable insight into robotic system moeling an evelopment: Dr. Lynne Parker of Oak Rige National Laboratory, Dr. Douglas Gage of SPAWAR, Mr. Alan Schultz of the Naval Research Laboratory an Mr. Mark McKay of the Iaho National Engineering an Environmental Laboratory. This work is supporte through the INEEL Long-Term Research Initiative Program uner DOE Iaho Operations Office Contract DE-AC07-99ID REFERENCES Arkin, R. C Behavior-Base Robotics. Cambrige, Massachusetts: The MIT Press. Arkin, R. C Just what is a robot architecture anyway? Turing equivalency versus organizing principles. ftp://ftp.cc.gatech.eu/pub/people/arkin/webpapers/stanfor3.ps.z, Georgia Tech Mobile Robot Laboratory. Brooks, R A robust layere control system for a mobile robot. IEEE Journal of Robotics an Automation 2 (1): Gage, Douglas W Comman an control for manyrobot systems. In Proceeings of AUVS-92. Reprinte in Unmanne Systems 10 (4): Hogins, J. K. an D. Brogan Robot hers: group behaviors for systems with significant ynamics. In Artificial Life IV: Proceeings of the Fourth International Workshop on the Synthesis an Simulation of Living Systems. Cambrige, Massachusetts: The MIT Press, Kenney, J. an R. Eberhart Particle swarm optimization. In Proceeings of the IEEE International Conference on Neural Networks IEEE Service Center, Piscataway, NJ, Levy, S Artificial Life A report from the Frontier Where Computers Meet Biology. New York: Vintage Books. Reif, J. H. an H. Wang Social potential fiels: a istribute behavioral control for autonomous robots. Robotics an Autonomous Systems 27: Reynols, C. W Flocks, hers, an schools: A istribute behavior moel. In Proceeings of SIGGRAPH 87. Reprinte in Computer Graphics 21 (4): Shaw, E., Fish in schools. Natural History 84 (8): Suzuki, I. an M. Yamashita Distribute anonymous mobile robots: formation of geometric patterns. SIAM Journal of Computing 28 (4): AUTHOR BIOGRAPHIES DONALD D. DUDENHOEFFER is research scientist for the Iaho National Engineering an Environmental Laboratory (INEEL) in Iaho Falls, ID. He receive his Masters of Science egree in Operations Research from the Naval Postgrauate School in His research interests 981

11 inclue simulation, robotics, human performance moeling, military operations an comman an control. Prior to working at the INEEL, he serve 12 years on active uty as a submarine officer an currently hols the rank of LCDR in the U.S. Navy Reserves. His aress is <ue@inel.gov>. MICHAEL P. JONES is a Distinguishe Engineer for WhizBang! Labs in Provo, UT. He receive a B.S. egree in Computer Science from Brigham Young University in 1990 an M.S. an Ph.D. egrees in Computer Science from the University of Colorao, Bouler in 1992 an 1997 respectively. His current research interests inclue autonomous agents, speech an language unerstaning an machine learning. His aress is <mjones@whizbang.com>. Duenhoeffer an Jones 982