Distributed memoryless point convergence algorithm for mobile robots with limited visibility

We present a distributed algorithm for converging autonomous mobile robots with limited visibility toward a single point. Each robot is an omnidirectional mobile processor that repeatedly: 1) observes the relative positions of those robots that are visible; 2) computes its new position based on the observation using the given algorithm; 3) moves to that position. The robots' visibility is limited so that two robots can see each other if and only if they are within distance V of each other and there are no other robots between them. Our algorithm is memoryless in the sense that the next position of a robot is determined entirely from the positions of the robots that it can see at that moment. The correctness of the algorithm is proved formally under an abstract model of the robot system in which: 1) each robot is represented by a point that does not obstruct the view of other robots; 2) the robots' motion is instantaneous; 3) there are no sensor and control error; 4) the issue of collision is ignored. The results of computer simulation under a more realistic model give convincing indication that the algorithm, if implemented on physical robots, will be robust against sensor and control error.

[1]  Paul Keng-Chieh Wang.  Navigation strategies for multiple autonomous mobile robots moving in formation , 1991, J. Field Robotics.

[2]  Yoshikazu Arai,et al.  Realization of autonomous navigation in multirobot environment , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

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

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

[5]  Kazuhiro Kosuge,et al.  Handling of a single object by multiple autonomous mobile robots in coordination with body force sensor , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[6]  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.

[7]  D. Hearn,et al.  Geometrical Solutions for Some Minimax Location Problems , 1972 .

[8]  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.

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

[10]  Fumio Hara,et al.  Cooperative route-searching behavior of multi-robot system using hello-call communication , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

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

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

[13]  Hiroaki Yamaguchi,et al.  Adaptive formation control for distributed autonomous mobile robot groups , 1997, Proceedings of International Conference on Robotics and Automation.

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