Extended Consensus Algorithms

An extension of the linear consensus protocol for agents moving in the plane is considered. For single integrator agents the use of a vector perpendicular to the standard consensus feedback leads to a large family of trajectories. If the new perpendicular term is applied only sustained oscillations are facilitated. For special congurations the form of the system trajectories is given in form of eigenvalues and {vectors of the system matrix. A proof is given that this additional term does not eect stability. On the other hand it is motivated that robustness against discrete implementation and switching topologies can be decreased. The control strategy is also applied to agents with double integrator dynamics. Stability can be archived with suciently high velocity feedback and the eect of this feedback on the system performance is further discussed. Using the results for single integrators a self{triggered consensus control strategy is proposed based on the assumption of bounded input magnitude of the other agents. Additional communication of the actual input leads to asymptotic convergence. By applying similar reasoning it is shown how local controllers at the agents can avoid circular regions in state{space while moving towards consensus.

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