Abstract
Orientation noises in sensors always spontaneously occur in the distributed process of information transmission or measurement, e.g., aperture radar, ultrasonic and laser sensors. This kind of noises may result in the unalignment of any pair of agents communicated with each other. In this paper, the formation control problem is investigated, where the orientation noises are modeled by some random sequences. To realize the specified formation shape, the considered problem is transformed into a convergence problem with respect to the orientation noises. The main idea of the method in this paper is to construct several convex polytopes to analyze this convergence problem, and design some martingale sequences to deal with the effect of orientation noises. Then, a sufficient criterion is derived to ensure the specified formation shape in mean square and almost surely (a.s.), respectively. Finally, a numerical example is given to illustrate the derived result.
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