Recent Researches in Circuits, Systems, Multimedia and Automatic Control
Cellular Automata Models for Cooperation in Multirobot Systems
RADU DOBRESCU*, DAN POPESCU*, GHEORGHE FLOREA** *"Politehnica" University, Faculty of Control and Computers, 313 Spl. Independentei, Bucharest **Systems Engineering Society - SIS SA, 22 Sos. Electronicii, Bucharest ROMANIA
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[email protected] Abstract. In order to describe the technological problems of the coordination of groups of mobile minirobots, a biologically-inspired control framework for multi-agent tasks that is based on cellular automata models is discussed. This framework allow to study the behaviour of the robot platforms as collaborative agents in a multi-agent system. The case study proves that the CA model is an useful tool that can be exploited in various multiagent coordination tasks where there is a common goal among the agents. Keywords: cellular automata, wireless sensor networks, multi-agent system, multi-robot system, sensor fusion. cooperative decision
and second dedicated strategies for coordination of a group of MMRs. Due to its size, the capabilities of a single unit are limited and, consequently, minirobots need to work in groups, or swarms (when the groups are very large), to significantly sense or affect the environment. The clusters of MMR can be considered as Multiagent Systems (MAS), and in the same time they are very similar with some biological systems which show orderly patterns emerging from seemingly random low level activities. Biological collective behaviors, where coordinated global behavior emerges from local interactions, have inspired decentralized approaches in various types of multiagent systems, e.g., swarm robotics [3], modular robots [4], and sensor networks [5]. A central challenge for these systems is designing local agent control rules that will lead to desired global behaviors. In the control theory community, there has been some success in analyzing bioinspired rules related to distributed consensus, e.g., in flocking [6] and multi-robot formation tasks [7]. Rules proposed for these problems have similar algorithmic properties and their convergence and performance have been analyzed for arbitrary topologies. Inspired by a recent biological studies [8, 9], we propose and analyze a cellular automaton framework that can capture such scenarios and achieve fast decision-making.
1 Introduction With the development of telecommunication miniature devices, embedded computing and sensing technologies, new possibilities for the design and use of minirobots, based on wireless sensor networks (WSN) has appeared [1, 2]. Due to the limited computing power, sensing range, and transmission range of individual sensors, the Wireless Sensor Networks (WSNs) are formed for real-time detection, sensing and collection of various environmental parameters or information of the target under surveillance. Clearly the integrity and accuracy of the collected information depend on the coverage ratio of the surveillance region. Different applications may have different requirements of the coverage. Among them the coordinated control of a group of mobile minirobots presents specific requirements. In the field of robotics, a minirobot is defined as a miniaturized robotic system, making use of advanced sensing, control and communication tehnologies. The aim of the paper is to solve some technological problems of the coordination of groups of mobile minirobots, designed as remote oriented platforms, named in the following MMRs (Mobile Mini-Robots). Two main objectives can be realized with this platform: first, research and development of new procedures for deployment and data aggregation in an unknown environment,
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large-scale multi-agent systems are the classical cellular automata [11]. Cellular automata (CA) were originally introduced as an abstract mathematical model that can capture the behavior of biological systems capable of selfreproduction. Subsequently, CA have been extensively studied in a great variety of application domains, but mostly in the context of simulation of complex physical, biological and/or socio-technical systems and their dynamics. Our aim is to use these complex system models as an abstraction for autonomously executing local processes that are coupled to, and interact with, one another. As particular features of the basic CA model which must be to provide appropriate abstractions for the large scale multi-agent systems , the following four seems to be the most relevant: heterogeneity of the generalized cellular automata in terms of the individual agent behaviors; inter-agent communication; adaptability of the individual agents; dynamic changes of the MAS network topology. In a similar manner, when considering a group of MMRs, defined as a Multi Robot Systems (MRS), we must focus on their cooperative capabilities. Following the approach in [12], we consider a taxonomy based on a top down approach, where four different levels are individuated: a Cooperation Level, a Knowledge Level, a Coordination Level and an Organization Level. At the first level we define by cooperation the situation in which several robots operate together to perform some global task that either cannot be achieved by a single robot, or whose execution can be improved by using more than one robot, thus obtaining higher performances. In this work we are interested only in those MRS which present many MMRs agents (we also call them a group) having, as a whole, a common global goal to achieve. Therefore, in the following, the term MRS will refer to a group of cooperative robots. A design choice that must be taken into account for developing a MRS is the type of robots composing the system. We can distinguish two different system compositions: homogeneous (when all members of the group of robots are exactly the same both in the hardware and in the control software) and heterogeneous (when the members of the group have a difference either in the hardware devices or in the software control procedures). The homogeneity or the heterogeneity of the members can influence the way in which robustness is achieved. In a homogeneous system every agent can execute the same actions as the other team members with the same results, so that a failure of
2 Description of sensor networks based multirobot systems as multiagent systems It is rather difficult to make equivalences between a group of MMRs and a WSN, then between a WSN and a MAS, and then to adopt a specific model for such collective inspired by a biological system, but there are a lot of arguments for that approach. The devices (nodes of the network) that can combine short range wireless communication with sensing, actuation and on-board processing capabilities and are connected in sensor networks become useful for a large range of applications, having as common characteristics some encountered in the collective behavior of entities from the living world. From this perspective, sensor networks need to have: dynamic networking, to be flexible enough to respond to frequent topological changes; selfcalibration, to adapt independently in their environment, reconfiguration capability, to deal with the loss or gain of a system resource and peer to peer communication. One can conclude that sensor networks are self-organized systems of nodes that co-ordinate themselves autonomously but their development is hindered by the constraints of the devices used. Implementing sensor networks will involve methods that allow the devices to make decisions based on their local environment and their own individual state. This, in fact, occurs in many biological systems. The behaviour of these biological systems can be emulated by computer simulations called cellular automata which consist of a geometric array of minimalist computing elements, each of which contains a finite state machine that is updated in discrete time steps [10]. The cells determine their next state by examining its’ present state and that of its’ neighbours and carrying out a set of simple rules. The fact that simple rules can generate complex outputs means that it possible for emergence to be an additional consequence and can be applied to technical systems, such as sensor networks. In a similar manner Multiagent Systems (MAS) are commonly viewed as a research area where (distributed) artificial intelligence and distributed computing overlap. Hence, research in MAS heavily draws on the existing theories, tools and methodologies from both AI and distributed computing. Among many abstract mathematical models of discrete dynamical systems, the one class that we find particularly appropriate and useful for addressing many fundamental issues in
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Recent Researches in Circuits, Systems, Multimedia and Automatic Control
geometric. Behavior emergence, cooperation, task allocation, herding, etc., are the issues related to multiple robotic systems. Cooperative behavior needs association with other robots for a mutual benefit and it increases the total utility of the system [14]. The research on multi agent/robotic systems relate to the mechanism of coordination, negotiation, cooperation and competition among agents/robots. Efforts are now being made to allow them to emerge adaptively through learning and interaction. Automatic development of cooperative strategies for teams of distributed autonomous robots, or software agents can be studied using cellular automata models.
a member can be easily compensated by another robot in the system, in such a way that fault tolerance is guaranteed. On the contrary adaptivity is weakly ensured because there is no differentiation among the robots. Therefore, homogeneous systems are typically used in the so called swarm-type approach, where a large number of autonomous robots are utilized to realize a distributed system. On the other hand, for assuring adaptivity without giving up fault tolerance, heterogeneous MRS are preferred. Heterogeneous robots allow the MRS to adapt more easily to the different situations which could emerge in a dynamic environment, since they offer a better chance to deal with new and unpredicted needs.
3.2. A general stochastic cellular automata model
3 Modeling multiagent systems with cellular automata
As already mentioned, a common thread in all multiagent systems is the issue of coordination of a large number of sparsely coupled agents in order to produce a coherent global behaviour using simple rules. It can be argued that cellular automata (CA) are the simplest example of a multiagent system. Unless explicitly stated (for example stochastic cellular automata (SCA)), the term cellular automata implies determinism. Cellular automata were categorized by the work of Wolfram [15], in which four universality classes were identified. All rules were shown to belong to one of class I (fixed point), class II (oscillatory), class III (chaotic), or class IV (long transient). Langton has argued that natural computation may be linked to the universality classes [16]. It was shown that by tuning a parameter to produce different CA rules, a phase transition was exhibited. It was found that class IV behaviour appeared in the vicinity of the phase transition. A most appropriate model for cooperative actions in MASs is the stochastic cellular automata (SCA). In deterministic cellular automata there is an alphabet of symbols, one of which may be adopted by each cell. The combination of all incoming symbols uniquely determines which symbol the cell will display as output. SCA work in the same way except at the output level. Instead of being a single unique symbol which is adopted with certainty, there can be multiple symbols adopted with probability less than 1. Based on this outgoing probability distribution over the K symbols, a single unique symbol is drawn to be the output of the cell. This is done for all cells simultaneously. It should be noted that a deterministic CA is a special case of a SCA, so the model presented below can
3.1. Cooperation in multi-agent systems A multi-agent system (MAS) is a distributed computing system with autonomous interacting intelligent agents that coordinate their actions so as to achieve its goal(s) jointly or competitively, either they have homogeneous or heterogeneous structures. Behavior emergence takes place through cooperation which can make use of the individually acquired intelligence as well. Agent based architecture offers modularity, robustness and separation of concerns in addition to other advantages of a distributed system. The two general types of designs seen among the multiagent system structures are the hierarchical and behavior structures. They differ on the type of information they process and in their interconnections [13]. In a hierarchical structure, the control issue is divided along functional lines into progressive levels of abstraction of data. It uses computational functions for system decomposition. In case of the behavior structure, the control problem is broken into behaviors without any central intelligent agent present. Through interaction between the competing constituents, emergent behaviors result. Cooperation among agents can be explicit or implicit. In case of the explicit information exchange, the agents perform actions to benefit other agents. In the implicit case, agents carry on with their own goal-seeking process and these actions will be beneficial to others. In the particular case of MRS, the MAS deals with special subjects like group architecture, resource conflict, origin of cooperation, learning and
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Recent Researches in Circuits, Systems, Multimedia and Automatic Control
on-board memory. Memory and its use to change state or rules are considered learning, operation that implies a level of cognition. Just as with living organisms, successful changes in behaviour or other capabilities must be based on experience and learning. Random changes would be highly likely to result in death (i.e., failure) of the node of the network of MMRs and consequently a damage of the network. We use cellular automata as a viable model for the deployed sensor networks having MMR as nodes considering them operating as organisms in an ecosystem. A cellular automaton model can represent a distribution of sensor nodes throughout a geographic zone. As illustrated in fig. 2, eight neighbor cells surround each internal cell. Border cells have three or five neighbors. Neighbor cells represent those nodes that can receive a transmission from a cell. Thus, the regularity of the grid represents a logical indication of physical proximity.
be considered general. The model is defined as follows: Let us consider a system of N cells, each of which is connected to a number of other cells. Let A represent an alphabet of K symbols. The state of celli at time-step i is xi [t ] ∈ A . The input probability distribution, pin, for celli is given by pin[t]=σi(x1[t],…,xN[t]) where σi accounts for the connections of celli to the other cells. The output probability distribution pout is given by the map µ: pout[t+1]=µ[pin(t)]. The probability distributions pin and pout are stochastic columns. The new state xi[t+1] of celli at time-step t+1 is randomly drawn according to the distribution pout[t+1]. The connections are described through the σi functions, and we assume that each cell has the same µ-map, limited to a parameterized subset called µsub. If we consider pin=[pin1,…,pinK] T and the unnormalized output probabilities given by 1 1 1 if K + β ( pinj − K ) ≥ 1 1 1 poutj = 0 if + β ( pinj − ) ≤ 0 K K 1 1 + β ( pinj − ) otherwise K K where β is derived from the tunable parameter β as follows:
2λ if 0 ≤ λ < 0,5 β = −1 if 0,5 ≤ λ < 1 0,5(1 − λ )
a) Cellular Automaton b) Sensor Network (MAS)
Fig. 1: Illustrating the neighborhood of a cell
Different values of λ determine the behavior of the CA. It easy to see that in a simple case, K=2, when λ=1 we have a completely deterministic rule, while when λ=0 we have a completely random rule. When 0
