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Formation control is an important research topic within the research fields of multirobot systems. Three layers of control abstraction for formation control are formation shape, reference type, and robotic control. Reference types play an important role in formation control, but little research focuses on comparing the performance when using different reference types under the same formation shape and robotic control. In this paper, we propose three single reference types (i.e. the leader, predecessor, and neighbor reference types) and four hybrid reference types (i.e. the leader-predecessor, leader- neighbor, predecessor-neighbor, and leader-predecessor-neighbor reference types). We demonstrate by theorems and also by simulation results that these seven reference types can direct mobile robots to maintain formation. In addition, we apply these seven reference types to a double-platoon formation in order to investigate whether or not the reference types will affect deviation from formation. We compare the performance of these seven reference types and discuss how we can use these reference types in various environments.

Keywords: formation control, robot control, reference types, mobile robot, graph theory

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Received August 8, 2005; revised November 2, 2005; accepted December 14, 2005.
Communicated by Chin-Teng Lin.
^* This research was supported in part by the Ministry of Education under grant No. EX-91-E-FA06-4-4, the Ministry of Economic Affairs under grant No. 94-EC-17-A-02-S1-029, and the National Science Council under grant No. NSC-93-2213-E-194-039.