Cooperative Cleaners: a Study in Ant Robotics
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Israel A. Wagner Cooperative Cleaners: Computer Science Department Technion, Haifa 32000, Israel A Study in Ant Robotics [email protected] and IBM Haifa Labs, MATAM, Haifa 31905, Israel [email protected] Yaniv Altshuler Vladimir Yanovski Alfred M. Bruckstein Computer Science Department Technion, Haifa 32000, Israel Abstract of robots without a central supervisor, using only local inter- actions between the robots. When this decentralized approach In the world of living creatures, simple-minded animals often coop- is used, much of the communication overheads (characteristic erate to achieve common goals with amazing performance. One can of centralized systems) are saved, the hardware of the robots consider this idea in the context of robotics, and suggest models for can be fairly simple and better modularity is achieved. A prop- programming goal-oriented behavior into the members of a group of erly designed system should achieve reliability through redun- simple robots lacking global supervision. This can be done by con- dancy. trolling the local interactions between the robot agents, to have them Significant research effort has been invested during the last jointly carry out a given mission. As a test case we analyze the prob- few years in design and simulation of multi-agent systems lem of many simple robots cooperating to clean the dirty floor of a (Brooks 1990 Steels 1990 Levi 1992 Sen et al. 1994 Arkin non-convex region in Z2, using the dirt on the floor as the main means and Balch 1998 Wagner et al. 1998 Wagner and Bruckstein of inter-robot communication. 2001). Such designs are often inspired by biology (see Brooks 1986 Arkin 1990 Arkin and Balch 1997 for behavior-based KEY WORDS—robotics, covering, multirobotics, robustness, control models, Deneubourg et al. 1990 Drogoul and Fer- cooperative robotics ber 1992 Mataric 1992 for flocking and dispersing models or Benda et al. 1985 Haynes and Sen 1986 for predator–prey approach). Inspiration has also been found in physics (e.g. 1. Introduction Chevallier and Payandeh 2000) and the application of eco- nomics (see e.g. Smith 1980 Golfarelli et al. 1997 Wellman In the world of living creatures, simple-minded animals such and Wurman 1998 Rabideau et al. 1999 Thayer et al. 2000 as ants or birds cooperate to achieve common goals with sur- Gerkey and Mataric 2002 Zlot et al. 2002). prising performance. It seems that these animals are ‘pro- Tasks that have been of particular interest to researchers grammed’ to interact locally in such a way that the desired in recent years include synergetic mission planning (Alami global behavior is likely to emerge even if some individuals et al. 1997), fault tolerance (Parker 1998), swarm control of the colony die or fail to carry out their task for some other (Mataric 1994), human design of mission plans (MacKenzie reasons. We consider a similar approach to coordinate a group et al. 1997), role assignment (Stone and Veloso 1999 Can- dea et al. 2001 Pagello et al. 2003), multi-robot path planning The International Journal of Robotics Research (Lumelsky and Harinarayan 1997 Ferrari et al. 1998 Svestka Vol. 27, No. 1, January 2008, pp. 127–151 and Overmars 1998 Yamashita et al. 2000), formation gener- DOI: 10.1177/0278364907085789 ation (Arai et al. 1989 Fredslund and Mataric 2001 Gordon c SAGE Publications 2008 Los Angeles, London, New Delhi and Singapore Figure 16 appears in color online: http://ijr.sagepub.com et al. 2003), traffic control (Premvuti and Yuta 1990), forma- 127 128 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / January 2008 tion keeping (Wang 1989 Balch and Arkin 1998), exploration tolerance. Even if almost all the agents cease to work before and mapping (Rekleitis et al. 2003), target tracking (Parker and completion, the remaining agents will eventually complete the Touzet 2000) and target search (LaValle et al. 1997). mission. We prove the correctness of the algorithm as well as Unfortunately, the geometrical theory of such multi-agent an upper bound on its running time, and show how our algo- systems is far from being satisfactory, as has been pointed out rithm can be extended for regions with obstacles. in Beni and Wang (1991) and many other articles. A short The rest of the paper is organized as follows. In Section 3 discussion regarding the conceptual framework of intelligent the formal problem is defined as well as the aims and assump- swarms (or swarm intelligence systems) and the motivation be- tions involved. The algorithm is presented in Section 4, and an hind the use of such appears in Section 2. analysis of its time-complexity is described in Section 5. Sec- Our interest is focused on developing the mathematical tion 6 is devoted to the problem of exploring/cleaning regions tools necessary for the design and analysis of such systems. In with obstacles, and is followed by several experimental exam- a recent report (Wagner and Bruckstein 1994) we have shown ples (Section 7). We conclude the paper with a discussion and that a number of agents can arrange themselves equidistantly by highlighting several connections to related work, presented in a row via a sequence of linear adjustments, based on a sim- in Section 8. ple ‘local’ interaction. The configuration convergence is expo- This paper is a revised and extended version of the work nentially fast. A different way of cooperation between agents presented in Wagner and Bruckstein (1997). is inspired by the behavior of ant colonies, and is described by Bruckstein (1993). There it was proved that a sequence of ants engaged in deterministic chain pursuit will find the short- 2. Swarm Intelligence: Framework and est (i.e. straight) path from the anthill to the food source, using Motivation only local interactions. In Bruckstein et al. (1994) we investi- gate the behavior of a group of agents on Z2, where each ant- 2.1. Motivation like agent is pursuing his predecessor according to a discrete biased random-walk model of pursuit on the integer grid. We Robotics solutions to increasingly complex and varied chal- proved that the average paths of such a sequence of a(ge)nts lenges are growing in demand. Experience has dictated that a engaged in a chain of probabilistic pursuit converge to the single robot is no longer the best solution for many application straight line between the origin and destination, and this hap- domains. Instead, teams of robots must coordinate intelligently pens exponentially fast. for successful task execution. In this paper we investigate a more complicated question Dias and Stentz (2001) present a detailed description of concerning the behavior of many agents cooperating to explore multi-robot application domains and demonstrate how multi- an unknown area (for purposes of cleaning, painting, etc.), robot systems can be more effective than a single robot in where each robot/agent can only see its near neighborhood. many of these domains. However, when designing such sys- The only method of inter-robot communication is by leaving tems it should be noticed that simply increasing the number traces on the common ground and sensing the traces left by of robots assigned to a task does not necessarily improve the other robots. See Min and Yin (1998) Acar et al. (2001) But- system’s performance. Multiple robots must cooperate intel- ler et al. (2001) Koenig and Liu (2001) Polycarpou et al. ligently to avoid disturbing each other’s activity and achieve (2001) Batalin and Sukhatme (2002) Latimer et al. (2002) efficiency. Rekleitisy et al. (2004) for similar research. There are several key advantages of the use of such intelli- We present an algorithm for cleaning a dirty area that guar- gent swarm robotics. First, such systems inherently enjoy the antees task completion (unless all robots die) and prove an up- benefit of parallelism. In task-decomposable application do- per bound on the time complexity of this algorithm. We also mains, robot teams can accomplish a given task more quickly show simulation results of the algorithm on several types of re- than a single robot by dividing the task into sub-tasks and ex- gions. These simulations indicate that the precise time depends ecuting them concurrently. In certain domains, a single robot on the number of robots, their initial locations and the shape may simply be unable to accomplish the task on its own (e.g. of the region. carrying a large and heavy object). Second, decentralized sys- In the spirit of Braitenberg (1984), we consider simple tems tend to be, by their very nature, much more robust than robots with only a bounded amount of memory (i.e. finite- centralized systems (or systems comprised of a single com- state machines). Generalizing an idea from computer graph- plex unit). Generally speaking, a team of robots may provide a ics (see Henrich 1994), we preserve the connectivity of the more robust solution by introducing redundancy and by elim- ‘dirty’ region by allowing an agent to clean only so-called inating any single point of failure. While considering the al- non-critical points: points that do not disconnect the graph of ternative of using a single sophisticated robot, we should note dirty grid points. This ensures that the robots will stop only that even the most complex and reliable robot may suffer an upon completing their mission. An important advantage of this unexpected malfunction which will prevent it from complet- approach, in addition to the simplicity of the agents, is fault- ing its task. When using a multi-agents system, on the other Wagner, Altshuler, Yanovski, and Bruckstein / Cooperative Cleaners: A Study in Ant Robotics 129 hand, even if a large number of the agents stop working for Computational resources: Although agents are assumed some reason the entire group will often be able to complete to employ only limited computational resources, a for- its task (albeit slower).