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String Instability in Classes of Linear Time Invariant Formation Control With Limited Communication Range

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2 Author(s)
Middleton, R.H. ; Hamilton Inst., N.U.I. Maynooth, Maynooth, Ireland ; Braslavsky, J.H.

This paper gives sufficient conditions for string instability in an array of linear time-invariant autonomous vehicles with communication constraints. The vehicles are controlled autonomously and are subject to a rigid or semi-rigid formation policy. The individual controllers are assumed to have a limited range of forward and backward communication with other vehicles. Sufficient conditions are given that imply a lower bound on the peak of the frequency response magnitude of the transfer function mapping a disturbance to the leading vehicle to a vehicle in the chain. This lower bound quantifies the effect of spacing separation policy, intervehicle communication policy, and vehicle settling response performance. These results extend earlier works to give a unified treatment of heterogeneous, non-nearest neighbor communication and semi-rigid one-dimensional formation control.

Published in:

Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 7 )