Even since the pioneering work of Levine and Athans and Melzer and Kuo, control of vehicular formations has been a topic of active research. In spite of its apparent simplicity, this problem poses significant engineering challenges, and it has often inspired theoretical developments. In this article, we view vehicular formations as a particular instance of dynamical systems over networks and summarize fundamental performance limitations arising from the use of local feedback in formations subject to stochastic disturbances. In topology of regular lattices, it is impossible to have coherent large formations, which behave like rigid lattices, in one and two spatial dimensions; yet this is achievable in 3D. This is a consequence of the fact that, in 1D and 2D, local feedback laws with relative position measurements are ineffective in guarding against disturbances with slow temporal variations and large spatial wavelength.
Fundamental performance limitations Localized control Optimal control Relative information exchange Spatially invariant systems Toeplitz and circulant matrices Vehicular formations
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