Distributed Anonymous Mobile Robots: Formation of Geometric Patterns

Consider a system of multiple mobile robots in which each robot, at infinitely many unpredictable time instants, observes the positions of all the robots and moves to a new position determined by the given algorithm. The robots are anonymous in the sense that they all execute the same algorithm and they cannot be distinguished by their appearances. Initially they do not have a common x-y coordinate system. Such a system can be viewed as a distributed system of anonymous mobile processes in which the processes (i.e., robots) can “communicate” with each other only by means of their moves. In this paper we investigate a number of formation problems of geometric patterns in the plane by the robots. Specifically, we present algorithms for converging the robots to a single point and moving the robots to a single point in finite steps. We also characterize the class of geometric patterns that the robots can form in terms of their initial configuration. Some impossibility results are also presented.

[1]  Susan Hackwood,et al.  High-order Strictly Local Swarms , 1994 .

[2]  H. Kurokawa,et al.  Self-assembling machine , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[3]  Jing Wang,et al.  Cellular Robotic Systems: Self-organizing Robots And Kinetic Pattern Generation , 2002, IEEE International Workshop on Intelligent Robots.

[4]  Xavier A. Debest,et al.  Remark About Self-Stabilizing Systems , 1995, Commun. ACM.

[5]  Masafumi Yamashita,et al.  A Theory of Distributed Anonymous Mobile Robots Formation and Agreement Problems. , 1994 .

[6]  Masafumi Yamashita,et al.  Computing on Anonymous Networks: Part II-Decision and Membership Problems , 1996, IEEE Trans. Parallel Distributed Syst..

[7]  Ichiro Suzuki,et al.  Distributed motion coordination of multiple mobile robots , 1990, Proceedings. 5th IEEE International Symposium on Intelligent Control 1990.

[8]  Bruce Randall Donald,et al.  Information invariants in robotics. II. Sensors and computation , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[9]  Maja J. Matarić,et al.  Designing emergent behaviors: from local interactions to collective intelligence , 1993 .

[10]  Daniel E. Koditschek,et al.  Toward the automatic control of robot assembly tasks via potential functions: the case of 2-D sphere assemblies , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[11]  Yoshio Kawauchi,et al.  A principle of distributed decision making of Cellular Robotic System (CEBOT) , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[12]  Toshio Fukuda,et al.  Approach to the dynamically reconfigurable robotic system , 1988, J. Intell. Robotic Syst..

[13]  Kikuo Fujimura.  A model of reactive planning for multiple mobile agents , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[14]  Masafumi Yamashita,et al.  Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases , 1996, IEEE Trans. Parallel Distributed Syst..

[15]  Ichiro Suzuki,et al.  Distributed algorithms for formation of geometric patterns with many mobile robots , 1996, J. Field Robotics.

[16]  Lynne E. Parker.  Designing control laws for cooperative agent teams , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[17]  Bruce Randall Donald.  Information invariants in robotics. I. State, communication, and side-effects , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.