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We investigate the following problem: design a distributed control law making n kinematic unicycles converge to a common circle of prespecified radius, whose centre is stationary but dependent on the initial conditions, and traverse the circle in a desired direction. Moreover, the vehicles are required to converge to a formation on the circle, expressed by desired separations and ordering of the unicycles. We present a solution for the case when the information flow graph is undirected. In part II of this paper we generalize the solution to the case of arbitrary information flow graphs, and to the case of dynamic unicycles.