Co-Fields: A Physically Inspired Approach to Distributed Motion Coordination

Transcription

1 Co-Fields: A Physically Inspired Approach to Distributed Motion Coordination Marco Mamei 1,2, Franco Zambonelli 2, Letizia Leonardi 1 1 Dipartimento di Ingegneria dell Informazione Università di Modena e Reggio Emilia 2 Dipartimento di Scienze e Metodi dell Ingegneria Università di Modena e Reggio Emilia {mamei.marco, franco.zambonelli, letizia.leonardi}@unimo.it To Appear in IEEE Pervasive Computing, 2004 ABSTRACT This paper focuses on the problem of orchestrating the movements of mobile autonomous agents and proposes an approach that takes inspiration from the laws of physics. Our idea is to have the movements of agents driven by locally perceived computational force fields ( Co-Fields ), generated by the agents themselves and propagated via some embedded infrastructure. A globally coordinated and adaptive behavior in the agent s movements can then emerge due to the interrelated effects of agents following the shape of the fields and the dynamic fields re-shaping. Keywords: Mobility, Coordination, Agents, Adaptive Systems, Context Awareness. 1. INTRODUCTION As computing is becoming pervasive, autonomous computer-based systems are going to be embedded in all our everyday objects and in our physical environment. In such a scenario, mobility too, in different forms, will be pervasive. Mobile users, mobile devices, computer-enabled vehicles, as well as mobile software components, define an open and dynamic networked world, in which large set of autonomous components should be enabled to interact with each other and to orchestrate their activities. Here we specifically focus on the problem of coordinating the movements of a large set of autonomous agents in a distributed environment (distributed motion coordination). The term agent can refer not only to software components, but also to any autonomous real-world entity with computing and networking capability (e.g., a user carrying on a Wi-Fi PDA, a robot, or a modern car). The goals of agents coordinated movements can be various: letting them to meet somewhere, distribute themselves accordingly to specific spatial patterns, or simply move in the environment without interfering with each other and avoiding the emergence of traffic jams. 1

2 Any type of coordination there included motion coordination requires some sort of context awareness. In fact, an agent can coordinate with other agents only if it is somehow aware of what is around, i.e., its context. Starting from these considerations, we focus on the problem of dynamically providing agents with simple, easy to be obtained, and effective contextual information, supporting and facilitating their motion coordination activities in a robust and adaptive way. To achieve our goal, we take inspiration from the physical world, i.e., from the way particles in our universe move and globally self-organize accordingly to that contextual information which is represented by potential fields. In particular, in our approach, contextual information is expressed in the form of distributed computational fields (Co-Fields). Each agent of the system can generate and have propagated by the network infrastructure specific fields, conveying application-specific information about the local environment and/or about itself. Agents can locally perceive these fields and move accordingly, e.g. following the fields gradient. The result is a globally coordinated and adaptive movement, achieved with very little efforts by agents. 2. CASE STUDY SCENARIO AND MOTIVATIONS What types of motion coordination activities do we intend to support and why do they need a novel approach? To answer these questions, we introduce a simple case study and show that current coordination models are, form a software engineering point of view, inadequate to effectively address motion coordination problems. 2.1 Case study scenario Our case study involves the problem of providing support for tourists visiting a museum. Specifically, we focus on how tourists can be supported in planning their movements across a possibly large and unfamiliar museum and in coordinating such movements with other, possible unknown, tourists. Such coordination activities may include scheduling attendance at specific exhibitions occurring at specific times, having a group of students split in the museum according to teacher-specific laws, helping a tourist to avoid crowd or queues, letting a group of tourist to meet together at a suitable location, and even helping to escape accordingly to specific emergency evacuation plans. To this end, we assume that: (i) tourists are provided with a software agent running on some wireless handheld device, like a palm computer or a cellular phone, in charge of giving her/him suggestions on 2

3 how and where to move; (ii) the museum is provided with an adequate embedded computer network. In particular, embedded in the museum walls (either associated to each artistic items or to each museum room), there will be a network of computer hosts, each capable of communicating with each other and with the mobile devices located in its proximity via the use of a short-range wireless link. The number of the embedded hosts and the topology of the network may depend on the museum, but the basic requirement is that the embedded network topology mimics the topology of the museum plan (i.e. no network links between physical barriers, like walls); (iii) both the devices and the embedded hosts are provided with a localization mechanism to find out where they are actually located in the museum. This localization mechanism could be implemented by some kind of GPS-like device or with cheaper local mechanisms relying on the properties triangulating radio or acoustic signals [HigB01]. The above scenario and the associated motion coordination problems are of a very general nature, being isomorphic to scenarios such as, e.g., traffic management and forklifts activity in a warehouse, where navigators equipped vehicles hint their pilots on where to go, or software agents exploring the Web, where mobile software agents coordinate distributed researches by moving on various Web-sites. Therefore, also all our considerations are of a more general validity, besides the addressed case study. 2.2 Inadequacy of current approaches In the last few years, several middleware and coordination models, addressing among the others the problem of coordination and interaction in a multi-agent system (more generally, in a distributed multi-component system), have been proposed. Models based on direct communication promote designing a distributed application by means of a group of components that are in charge to communicate with each other in a direct and explicit way. Systems like Jini, UPnP and FIPA-based agent systems [BelPR01] are examples of middleware infrastructures rooted on a direct communication model. The problem of this approach is that agents are placed in a void space: the model, per se, does not provide any contextual information, agents can only perceive and interact with other components/agents, and the middleware support is mostly reduced to helping in finding communication partners. Thus, each agent has to manually become context aware by discovering and explicitly interacting with the other entities in the environment. For instance, in the case study, an agent would have to explicitly retrieve and communicate with some services providing the 3

4 museum map, it would have to discover which other tourists are currently populating the museum, and explicitly negotiate with them to agree on a specific motion coordination policy (e.g., to move avoiding the formation of queues or to meet each other at a suitable place). From a software engineering perspective, this imposes a notable burden in the agent code and typically ends up with ad-hoc, not scalable, and not adaptable solutions. Models based on shared data-spaces support inter-agent interactions through shared localized data structures. These data structures can be hosted in some data-space (e.g., tuple space), as in JavaSpaces [FreHA99], or they can be carried on by agents themselves and dynamically merged to enable interactions, as in Lime [PicMR01]. In these cases, agents are no longer placed in a totally void space, but live in an environment that can be modeled and described in terms of the information stored in the data spaces. Such information, typically referring to local conditions, can provide some sort of contextawareness to agents without forcing them to directly communicate with each other. For instance, in the case study, one can assume to have, at each room and corridor, a local data-space storing both local map information and messages left by the other agents about their presence and possibly about their intended next position. Still, to enforce a specific motion coordination pattern, agents may have to access several data-spaces to access all the required information (e.g., which agents are in which rooms), to build an internal representation of the current situation (e.g., where crowds and queues are) and then decide the next movements by (again) negotiating with other agents or accordingly to a predefined, non adaptable, set of rules. In other words, the contextual information can express only raw local data that it is still up to the agents to understand and exploit for the achievement of a specific motion coordination tasks. Event-based models relying on publish/subscribe mechanisms make agents interact with each other by generating events and by reacting to events of interest, without having them to interact explicitly with each other. Typical infrastructures rooted on this model are: Jini Distributed Events and UPnP General Event Notification Architecture (GENA). Without doubt, event-based model promotes stronger contextawareness, in that components can be considered as embedded in an active environment able of notifying them about what s happening around. For instance, in the case study, a possible use of this approach would be to let each agent notify its movements across the museum, update (accordingly to other agents notified movements) its internal representation of the crowd distribution in the museum (i.e. context-awareness) and then move properly by continuously adapting its plans accordingly to the 4

5 newly received events. However, from a software engineering perspective, the information conveyed by events tends to be too low-level to be effectively used by agents, forcing them to catch and analyze a possibly large number of inter-related events to achieve a specific motion coordination pattern. This process is of course a big burden in the agent code, making also such kind of middleware unsuitable from a software engineering point of view. 3. THE CO-FIELDS APPROACH The Co-Fields proposal is mainly driven by the above analysis and aims at providing agents with abstract simple yet effective representations of the context. To this end, Co-Fields delegates to the infrastructure the task of constructing and automatically updating an essential distributed view of the system situation possibly tailored to application-specific motion coordination problems that tells agents what to do (i.e., how to move to implement a specific motion coordination patterns). Agents are simply let with the decision of whether to follow such a suggestion or not. To achieve the above goals, the Co-Fields approach is centered on a few key concepts: 1. Contextual information is represented by computational fields, spread by agents and/or by the infrastructure, diffused in the infrastructure, and locally sensed by agents; 2. A motion coordination policy is realized by letting the agents move following the local shape of these fields, the same as a physical mass moves in accord to the locally sensed gravitational field. 3. Both environment dynamics and agents movements may induce changes in the fields surface, automatically propagated by the infrastructure, thus inducing a feedback cycle (point 2) that can be exploited to globally achieve a global and adaptive motion coordination pattern. Of course, Co-Fields can be implemented using existing coordination model, but this is not the point: rather, the point is in how we could exploit middleware and coordination models to facilitate application-level management of complex (motion) coordination policies 3.1 Computational Fields A computational field is a distributed data structure characterized by a unique identifier, a locationdependent numeric value, and a propagation rule identifying how the field should distribute in the network and how its value should change during the distribution. Fields are locally accessible by agents depending on their location, providing them a local perspective of the global situation of the system. 5

6 For instance, with reference to the case study, the guide of the museum can spread in the museum network infrastructure a computational field (let s call it PRESENCE field) whose value monotonically increases as it gets farther from his/her. Such field implicitly enables any tourist, from wherever in the museum, of sensing the presence of the guide and its distance. Also, by sensing the local gradient of the PRESENCE field, the tourist could also know in which direction the guide can be found (Figure 1). Fields can be generated by the agents or by the environment, and their existence must be supported by a proper distributed network infrastructure. In the case study, such a network is assumed to be part of the museum infrastructure, but in general any type of network, even ad-networks of mobile nodes, can be used to support Co-Fields [MamZL03]. When a field is injected in the network by a specific source node, it is propagated breadth-first, hop-by-hop through the network as specified by its propagation rule. The propagation rule specifies how the field s value should change during propagation and the extent (i.e., global versus spatially-confined) of the propagation. The final shape of the field surface is determined both by the field s propagation rule and by the network topology. This enables the same field to adapt and be suitable to different museum floor-plan. 3.2 Motion Coordination In Co-Fields, the simple principle to enforce motion coordination is to have agents move following the local shape of specific fields. For instance, a tourist looking for a guide can simply follow downhill the corresponding PRESENCE field. Dynamic changes in the environment and agents movements induce changes in the fields surface, producing a feedback cycle that consequently influences agents movement. For instance, should the museum guide be moving around in the museum, the Co-Field infrastructure would automatically update the corresponding PRESENCE field and would have any agent/tourist looking for a guide re-adapt its movement accordingly. Should there be multiple guides in the museum, they could decide to sense each other s PRESENCE fields so as to stay as far as possible from each other to improve their reachability by tourists. In general, a Co-Fields based system can be considered as a simple dynamical system and can be effectively modeled as that (see [MamZL02] for details on Co-Fields modeling): agents are seen as balls rolling upon a surface, and complex adaptive movements are achieved not because of the agents wills 6

7 and skills, but because of dynamic re-shaping of this surface. Of course, such a physical inspiration and the strictly local perspective in which agents act promote a strictly greedy approach in agents movement: agents act on the basis of their local viewpoint, disregarding if a small sacrifice now (i.e., climbing a Co-Fields hill instead descending it) can possibly lead to greater advantages in the future. In a circular track for example, a tourist looking for a guide that is moving clockwise, instead of greedily follow downhill the PRESENCE field (as the Co-Fields approach promotes), could better decide to move uphill to meet the guide counterclockwise. However, this is a general drawback of distributed problem solving, where efficiency reasons often rule out the possibility of globally informed decisions by distributed agents. 3.3 Application-Specific Coordination The achievement of an application-specific coordination task is rarely relying on the evaluation, as it is, of an existing computational field (as in the case of a tourist looking for a guide and simply following the specific field of that guide). Rather, in most cases, an application-specific task relies on the evaluation of an application-specific coordination field, as a combination of some of the locally perceived fields. The coordination field is a new field in itself, and it is built with the goal of encoding in its shape the agent s coordination task. Once a proper coordination field is computed, agents can achieve their coordination task by simply following (deterministically or with some probabilistic rule) the shape of their coordination field uphill or downhill (depending on the specific problem) as if they were walking upon the coordination field associated surface (see Figure 1). For instance, in the case study, for guides to stay as far as possible from each other, they can follow uphill a coordination field CF resulting from the combination (the sum) of all the computational fields of each guide: CF = n i= 1 PRESENCE i At the moment, we still have not identified a general methodology to help us identify, given a specific motion pattern to be enforced, which fields have to be defined, how they should be propagated, and how they should be combined in a coordination field. We are confident some methodology to help in that direction can be found in the future, and would possibly make Co-Fields applicable to a wider class of distributed coordination problems even beyond motion coordination. Nevertheless, independently of that, the immediate applicability of Co-Fields is guaranteed by the possibility of getting inspiration from 7

8 (and of reverse engineering) a wide variety of motion patterns found in Nature. Phenomena such as diffusion, birds flocking, ants foraging, bee dances [BonDT99], to mention a few examples, can all be easily modeled with Co-Fields (i.e., in terms of agents climbing/descending a coordination field as the composition of some computational field), and all have practical application in mobile computing scenarios. X X Y Y (a) (b) Figure 1. The PRESENCE field. Agent Y senses the PRESENCE field generated by the agent X to: (a) get farther away from the agent X; (b) approach agent X. 3.4 Implementation Issues Co-Fields can potentially be implemented on any distributed middleware providing basic support for data storing (to store field values), communication mechanisms (to propagate fields) and eventnotification mechanisms (to update fields and notify agents about changes in fields values). The above considerations apply both to the case in which Co-Fields can rely on a fixed network infrastructure (where a set of Co-Fields servers can be made in charge of fields propagation and to which mobile devices may connect) as well as to the case of mobile ad-hoc networks (where each device will act as a Co-Field server and will propagate fields in an ad-hoc way in the wireless media [MamZL03]). For both cases, some sort of localization mechanisms must be enforced for mobile devices [HigB01]. From our side, we have implemented a prototype of Co-Fields upon a fixed network infrastructure exploiting MARS programmable tuple spaces acting as Co-Fields servers [CabLZ02]. MARS tuple spaces have been allocated on IP nodes acting as wireless access points. Users, carrying on Linux IPAQ with wireless card, can access the MARS tuple spaces of the nodes to which they are connected. Moreover, to enforce the strict locality in connections required by Co-Fields: each tuple space contains a tuple identifying its spatial location; each IPAQ can dynamically determine in its turn 8

9 its own location (i.e., for the sake of testing, we have implemented a simple localization mechanisms based on RF-ID tags). Thus, an IPAQ can select which tuple space to actually interact (i.e., that of the room in which the user is currently located) with by comparing its own location and those of all the inrange tuple spaces. The nodes of the infrastructure are virtually connected with each other, according to a topology resembling the museum floor-plan. Different topologies mapping different floor-plans can be realized simply by providing each node with only the IP addresses of its virtual neighbors in the intended topology, and have the communication between nodes being restricted to the provided virtual neighbors. To implement fields propagation in the virtual topology in a hop-by-hop way, we have exploited the fact that MARS tuple spaces can be programmed to react to any access event with arbitrary computations. As an example, each MARS tuple space can been programmed to react to the income of a tuple like (TYPE= Presence, NAME=any, VAL=any) with a computation that access neighbor tuple spaces and inserts (avoiding loops and backward propagation) the same tuple with the VAL-field increased by one. The overall result of this process is a field-like distributed data structure (implemented by means of tuples) spread across the virtual network and having its VAL-entry reflecting the hop distance form the source, as the PRESENCE field should be. Similar processes apply for other types of fields as well as for dynamically updating the distributed shape of a field upon agents movements. The reactivity of MARS tuple spaces has also been exploited to notify agents about changes in fields values. In addition, MARS tuple spaces have also been programmed to periodically read tuples stored in its neighbor tuple spaces, cache them locally, and enrich them with an entry specifying the coordinates of the server from which the tuple has been read. In this way, agents are enabled to locally evaluate the direction in which a field increases/decreases, and use this information to direct its movements. In addition to the prototype implementation, we have developed a simulation environment for Co- Field, the test the effectiveness of our approach in large-scale scenarios. Such simulation environment has been developed using the Swarm toolkit for multi agent system simulations [ The Co-Fields simulation enables us to model: any specific museum map; the presence in such environment of any needed number of Co-Field servers connected accordingly to the museum plan; and the presence of any needed number of agents each with a specific plan of visit to the museum. 9

10 As far as the practical scalability of a Co-Field implementation is concerned, two considerations are worth reporting. One the one hand, because local values of fields can be stored by each Co-Fields server in terms of simple tuples of a few bytes, Co-Fields does not introduces storage scalability problems: a very large number of different fields can be locally stored even by node with low storage capabilities. On the other hand, the speed at which an agent is expected to move (e.g., tourists in the museum) is extremely low if compared to the speed at which fields in a network can propagate. Thus, the inevitable delay at which fields propagation/update occur does not significantly affect, even in large systems, the behavior of agents. 4. EXAMPLES OF THE USE OF CO-FIELDS To clarify the usage of Co-Fields, we detail here some specific motion coordination problems that tourists and other persons in a museum may be in need to face. In all these example, we assume that the topology of the museum network mimics the museum map with an infrastructure node in each room and corridor, and that the nodes of the infrastructure can locate the room in which a tourist currently is (and so the total number of tourists in a room). 4.1 Exploiting the PRESENCE Fields: Meetings and Predations We have previously shown how the PRESENCE field can be exploited to detect where a person (e.g., a tourist or a guide) is in the museum and how it can be reached. Moreover, the PRESENCE field can be exploited to enforce a variety of other interesting motion patterns. As a first example, let s consider a meeting service to help a group of tourists or museum guides to dynamically meet with each other (a very general service that could be of great use also in other scenarios, e.g., emergency evacuation situations and distributed gaming). Although different policies can be though related to how a group of tourists should meet (e.g., a specific point or by a specific tourist), here we concentrate on having a group of tourists collaboratively walk towards each other and eventually meet in some dynamically determined intermediate point. If each member i of the group generate a PRESENCE i field, then each tourist i of them can evaluate its coordination field by taking the maximum PRESENCE field of all the other tourist: CFi = max( PRESENCEx ), i = 1,.., n 10

11 and then follow such coordination field downhill. While the coordination fields continuously change due to the concurrent movements of all the members of the group each following its own coordination fields, the result is that the members of the group gradually approach towards each other, until collapsing in a single point. In other words, because agents actually attract each other, the system naturally converge to the situation in which all the agents are in the same point. Figure 2 shows the result of the Co-Field meeting process for two different simulations (performed with the already mentioned Swarm environment) on different museum maps. The key point to emphasize is that the meeting process, and Co-Fields in general, is adaptive: it work well even independently of the characteristics of the environment (e.g., of the museum plan), without having to change a bit in the code of agents or in the structure and propagation of computational fields. Figure 2. From left to right, different phases of the meeting process in two different simulated museums. Only the tourists in the meeting group are shown. As another example exploiting the PRESENCE fields, consider a group of security guards in charge of searching, surrounding, and catching a child that got lost and is wandering in a big museum. This is a peculiar instance of the more general problem of having a group of predator agents moving in an 11

12 environment with the goal of surrounding and capture a prey agent, a problem that, again, has several applications in other scenarios (e.g., military and police actions and collaborative mobile robots). By getting inspiration from the behavior of wolves, which succeed in collaboratively surround a prey using the simple strategy or approaching the prey while trying to stay as far as possible from each other, we can define the coordination field of a generic predator i in this way: CF pred i = PRESENCE prey n j= 1, j i PRESENCE expressing that the predators follow downhill the PRESENCE field of the prey (to reach it) and, at the same time, tries to stay far from all other predators. The result (Figure 3) is that predators, rather than simply approaching the prey, are able to effectively surround it. Of course, should the prey move much faster than the predators, the process would possibly never converge. pred j Prey Prey Predators Predators Figure 3. From let to right: three predators moving in a simulated museum to surround a prey. 4.2 The ROOM and CROWD Fields: Load Balancing Any tourist moving in the museum will definitely wish to avoid crowd while doing that. Co-Fields could be of help to that purpose. Let us assume that each of the rooms in a museum generates a ROOM field whose value increases with the hop-distance from the generating room (see Figure 4-a). ROOM fields are static, do not change over time, and depends only on the room location. Clearly, an agent following downhill a ROOM field will inevitably reach the source room. Accordingly, for an agent to visit a specific set of rooms in the most efficient way (we assume that the set of room one is interested in could be simply specified via, e.g., a graphical interface), it has simply to follow the coordination field a minimum combination 12

13 mcomb of all the ROOM fields (where ROOM fields are combined so as to take in each room the one with the minimum value) in its visit schedule: CF = mcomb ( ROOM, ROOM 2,..., ROOM 1 n If an agent follows downhill the above coordination field, it gets in the closest room of its visit schedule. Then, as the visit of that room is completed, it can simply remove the corresponding ROOM field from mcomb and continue to reach the other rooms. All of this still takes place without considering crowd conditions in rooms. To take into account crowd conditions, the nodes of the infrastructure could locally generate a CROWD value derived from the PRESENCE fields, to measures the amount of crowd in the museum rooms. This can be simply calculated, for each room, as the total number of local PRESENCE fields with value 1, normalized to the dimensions of the room, to better represent how much a particular room is crowded. The landscape of the resulting global CROWD field (see Figure 4-b) is dynamically varying depending on agents movements and expresses the global crowd conditions in the museum. Clearly, if all agents always follow the CROWD field downhill, the overall result is (as in a diffusion process) a global convergence towards a balance of the crowding conditions in the museum rooms. Museum Plan ) Room B Room C Room B Room C Room A Room A Room D Room D (a) Room Generated Field Crowd Field (b) Figure 4. (a) the ROOM field of room A; (b) the CROWD Field. The numeric values in the rooms indicate the local value of the fields. Putting all together, if an agents wants, at the same time, to visit the room in its schedule and to avoid crowd condition, it can use the following coordination field: CF = 1 w) mcomb ( ROOM, ROOM,..., ROOM n ) + w CROWD (

14 The first terms of the coordination field tends to attract the agents towards the rooms in its visit schedule, while the second tends to repel it from crowded areas. The weight w can be used to specifying the relevance of the crowd field, and we assume it can be specified by a tourist via the help of some user interface. For w=0, the load balancing mechanism is turned off and agents proceed towards their closest destinations in the greed path, disregarding crowded areas. If w is low, the agent will proceed towards their destinations rooms following a greed for most of the times, and being diverted to alternative paths only in the case of very crowded conditions. As w gets higher, alternative (possibly longer) paths are suggested more often, whenever the greed path will be a bit crowded. For w=1, agents ignore their visit schedule and simply move to balance the load in a diffusion process. Clearly, the expressed coordination field could with small adaptations be used for the sake of load balancing in a variety of other scenarios where a set of agents have to move according to their own plans in a crowded environment, e.g., forklift in a warehouse or cars in a city. To test the validity of our approach, we developed a set of simulations with agents being set up with a random visit schedule and an average of half the room of the museum to visit. Specifically, agents move to rooms they want to visit, stay there for a specific amount of time, then walk to the next room in the schedule according to the coordination field. Agents increases their staying in a room and decreases their walking speed proportionally to the local crowd conditions, i.e., the number of persons in their current room. The results of the experiments on two different museum maps are shown in Figure 5. As it can be seen, for both maps, the appliance of the Co-Field method for load balancing avoid the emergence in the museum of highly crowded zone, which are instead likely to appear when tourists visits the museum disregarding the Co-Fields fields. These results show an improvement of the average visit time for tourists, which applies for wide range of values of the weight w. However: on the one hand, for very small values of w, agents give very little importance to crowd conditions and are not able to get full advantage of the Co-Fields; for very high values of w, agents overestimate the importance of crowd and tends to select longer path to avoid even not-very-crowded rooms, with an overall worsening of the average visit time. 14

15 The comparison of the results for the two different maps (a,b,c versus d,e,f in Figure 5) confirms once again that the Co-Field approach is indeed adaptive. However, it is important to understand that the actual effectiveness of our approach may depend on the characteristics of the environment. Specifically, a museum where a small number of alternative paths are available to tourists to reach rooms, prevent them to take great advantage of Co-Fields load balancing (e.g., the performance improvement in the map of Figure 5-a is lower than in the more connected map of Figure 5-d). However, in general, a highly constrained environment necessarily constraints the extent of applicability of any motion coordination policy. Therefore, this cannot be considered a limitation of Co-Fields per se. normalized average visit time No Load Balancing Load Balancing w =0.2 Load Balancing w =0.4 Load Balancing w =0.6 Load Balancing w =0.8 (a) (b) (c) # of tourists in the museum (d) (e) (f) normalized average visit time No Load Balancing Load Balancing w =0.2 Load Balancing w =0.4 Load Balancing w =0.6 Load Balancing w = # of tourists in the museum Figure 5. Load balancing in two different simulated museums (a,b,c and d,e,f). (a,d) when agents do not exploit Co-Fields, crowded zones appear; (b,e) these crowded zones are mostly avoided when agents follow the proper coordination field. (c,f) overall, tourists take advantage of the Co- Fields approach by decreasing their average visit time over the case in which no load balancing is applied (normalized to the average visit time of a single tourist in an empty museum). 15

16 It is interesting to note that the same load balancing approach can be applied even to other motion coordination problems. For instance, turning back to the meeting problem, it is possible to consider a coordination field that, in addition to the evaluation of the PRESENCE field, also takes into account the CROWD field: CF ( x, y, t) = (1 w) max( PRESENCE ) + w CROWD i In that way, the movements of the agents as they move towards each will also consider the possibility of avoiding crowded rooms. A potential problem that may affect the load balancing and the meeting strategies (if the latter is modified to take into account crowd) relates to the possible emergence of spurious local minima (i.e., not associate to agents goals) in the coordination fields, trapping agents in unwanted locations. In general, whenever two fields expressing an attracting part (e.g., the ROOM fields) and a repelling one (e.g., the CROWD field) are combined by agents in a coordination field, it may be the case that such spurious local minima arise. However, the fact that the coordination field is computed internally by the agent, enables any agent to understand whether a minimum is a spurious one or not by simply analyzing the single components of the coordination field. For instance, in the case of load balancing, an agent can easily understand whether a minimum it has reached correspond to a room it wished to visit or, instead, it is a false minimum created by a peculiar combination of the ROOM and CROWD fields (Figure 6-a). In the latter case, the agent, depending on its internal policy, can decide either to temporarily ignore the CROWD field and proceed disregarding it (Figure 6-b) or to find alternate paths (Figure 6-c). Room R2 Room Ry 2+6= 8 Room R1 1 3 Coordination Field 4 Room R2 Room Ry Field of Room R2 x Room R Room R Room Ry 4 5 Alternative Path (Field of Room Ry) 2 Room R

17 Figure 6: (a) An agent willing to visit room R2, gets trapped in room R1 due to a local minimun of the coordination field; (b) the agents can analyze the components of the coordination fields (i.e., the ROOM fields only), discover the presence of the local minimum, and decide to proceed ignoring the CROWD field along R2; (c) Alternatively, it can evaluate the existence of alternate paths by looking for ROOM fields decreasing both towards R2 and towards another direction (e.g., the field of ROOM Ry). If such a field exists, the agent can follow the field of Ry and, once the minimum of Ry has been reached, it can switch back to the original coordination field. 5. RELATED WORKS (FOR THE EDITORS: THIS CAN BE MOVED IN A SIDEBAR) Several proposals in the last few years have been proposed to facilitate, among the others, distributed motion coordination. In robotics, the idea of potential fields driving robots movement is not new [Kha86]. For instance, one of the most recent re-issue of this idea, the Electric Field Approach (EFA) [JohS01], has been exploited in the control of a team of Sony Aibo legged robots in the RoboCup domain. Following this approach, each Aibo robot builds a field-based representation of the environment from the images captured by its head mounted camera, and decides its movements by examining the fields gradients of this representation. Although very close in spirit, EFA and Co-Fields are very different from the implementation point of view: in Co-Fields, fields are distributed data structure actually spread in the environment; in EFA, fields are just an agent internal representation of the environment and they do not actually exists. Co-Fields requires a supporting infrastructure to host fields data structures, but it completely avoids the complex algorithms involved in field representation and construction. Shifting from physical to virtual movements, the popular videogame The Sims [ exploits sorts of computational fields, called "happiness landscapes" and spread in the virtual city in which characters live, to drive the movements of non-player characters. For instance, if a character is hungry, it perceives and follows a happiness landscape whose peaks correspond to places where food can be found, i.e., a fridge. After having eaten, a new landscape will be followed by the character depending on its needs. Although sharing the same inspiration, Sims happiness fields are static and generated only by the environment. In Co-Fields, instead, fields are dynamic and can 17

18 change over time, and agents themselves are able to generate fields to promote a stronger selforganization perspective. The MMASS formal model for multi-agent coordination, described in [BanMS02], represents the environment as a multi-layered graph in which agents can spread abstract fields representing different kinds of stimuli through the nodes of this graph. The agents behavior is then influenced by the stimuli they perceive in their location. In fact agents can associate reactions to these stimuli, like in an eventbased model, with the add-on of the location-dependency that is associated to events and reactions. The main difference between the MMASS approach and the Co-Fields one is that, in Co-Fields, agents combine perceived fields and are constantly guided by the fields produced, while in MMASS fields are considered independent from each other and are exploited only to trigger one-shot reactions. Also, the application domain of MMASS simulation of artificial societies and social phenomena is quite different from that of Co-Fields. An area in which the problem of achieving effective context-awareness and adaptive coordination has been addressed via a field-based approach is amorphous computing [Nag02]. The particles constituting an amorphous computer have the basic capabilities of propagating sorts of abstract computational fields in the network, and to sense and react to such fields. In particular, particles can transfer an activity state towards directions described by fields gradients, so as to make coordinated patterns of activities emerge in the system independently of the specific structure of the network. Such mechanism can be used, among other possibilities, to drive particles movements and let the amorphous computer self-assemble in a specific shape. A very similar approach to self-assembly has been proposed in the area of modular robots, to let a robot composed by multiple, flexibly connected components to dynamically re-shape itself to meet specific purposes [SheS02]. Although serving totally different purposes, both approaches shares with Co-Fields the idea of having a single, physically inspired, mechanism to both diffuse contextual information and to organize adaptive motion coordination patterns. 6. CONCLUSIONS AND FUTURE WORKS While both a preliminary prototype implementation and the outcomes of our simulation shows the feasibility of the approach, a number of research directions are still open to improve its generality and its practical applicability. In addition to the already identified need for general methodologies to help 18

19 designing specific coordination patterns in terms of Co-Fields, it will be important to explore the potential of Co-Fields in encoding more general distributed coordination patterns, possibly not related to motion. ACKNOWLEDGEMENTS Work supported by the Italian MIUR and CNR in the Progetto Strategico IS-MANET, Infrastructures for Mobile ad-hoc Networks and by Nokia Research Center Boston. REFERENCES [BanMS02] S. Bandini, S. Manzoni, C. Simone, Space Abstractions for Situated Multiagent Systems, 1st International Joint Conference on Autonomous Agents and Multiagent Systems, Bologna (I), ACM Press, pp , July [BelPR01] [BonDT99] [CabLZ02] F. Bellifemine, A. Poggi, G. Rimassa, JADE - A FIPA2000 Compliant Agent Development Environment, 5th International Conference on Autonomous Agents, ACM Press, Montreal (CA), pp , May E. Bonabeau, M. Dorigo, G. Theraulaz, Swarm Intelligence, Oxford University Press (Oxford, UK), G. Cabri, L. Leonardi, F. Zambonelli, Engineering Mobile Agent Applications via Context-Dependent Coordination, IEEE Transactions on Software Engineering, 28(11):1040:1058, Nov [FreeHA99] E. Freeman, S. Hupfer, K. Arnold, JavaSpaces Principles, Patterns, and Practice, Addison-Wesley (Reading, MA), [HigB01] [JohS01] [Kha86] J. Hightower, G. Borriello, Location Systems for Ubiquitous Computing, IEEE Computer, 34(8):57-66, Aug S. Johansson, A. Saffiotti, Using the Electric Field Approach in the RoboCup Domain, RoboCup 2001, LNAI, Springer Verlag, pp , Seattle, WA, USA, O. Khatib, Real-time Obstacle Avoidance for Manipulators and Mobile Robots, The International Journal of Robotics Research, 5(1):90-98, [MamZL02] M. Mamei, F. Zambonelli, L. Leonardi, Co-Fields: An Adaptive Approach to Motion Coordination. Technical Report University of Modena and Reggio Emilia, No , March available at [MamZL03] M. Mamei, F. Zambonelli, L. Leonardi, Tuples on the Air: a Middleware for Contextaware Computing in Dynamic Networks, Proceedings of the Workshops at the 23rd International Conference on Distributed Computing Systems, IEEE CS Press, Providence (RI), pp , May

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