Stability of formation control using a consensus protocol under directed communications with two time delays and delay scheduling
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2014-03-13
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Abstract
We consider a linear algorithm to achieve formation control in a group of agents which are driven by second-order dynamics
and affected by two rationally independent delays. One of the delays is in the position and the other in the velocity information
channels. These delays are taken as constant and uniform throughout the system. The communication topology is assumed to
be directed and fixed. The formation is attained by adding a supplementary control term to the stabilising consensus protocol.
In preparation for the formation control logic, we first study the stability of the consensus, using the recent cluster treatment
of characteristic roots (CTCR) paradigm. This effort results in a unique depiction of the non-conservative stability boundaries
in the domain of the delays. However, CTCR requires the knowledge of the potential stability switching loci exhaustively
within this domain. The creation of these loci is done in a new surrogate coordinate system, called the ‘spectral delay space
(SDS)’. The relative stability is also investigated, which has to do with the speed of reaching consensus. This step leads
to a paradoxical control design concept, called the ‘delay scheduling’, which highlights the fact that the group behaviour
may be enhanced by increasing the delays. These steps lead to a control strategy to establish a desired group formation that
guarantees spacing among the agents. Example case studies are presented to validate the underlying analytical derivations.
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