Rendezvous Under Cyclic Pursuit With Heterogeneous Input and Communication Delays

The existing techniques solve the rendezvous problem and characterize the final convergence point in the absence or presence of homogeneous input/communication delays. In this brief, we analyze the rendezvous problem of double-integrator multi-agent system (MAS) in the presence of heterogeneous input and communication delays. We employ cyclic pursuit strategy to achieve rendezvous of the delayed MAS. It is established in the literature that accommodation of one negative position consensus gain will expand the reachable set beyond the convex hull of the initial position of the agents engaged in cyclic pursuit. Consonantly, we accommodate at most one negative position consensus gain in the system and derive sufficient conditions on the gains for a stable rendezvous. For double-integrator system, damping gains are upper bounded by the input delays while the lower bound of the negative position consensus gain does not depend on the input delays explicitly. The final rendezvous point varies with homogeneous/heterogeneous communication delays as well as with the heterogeneous input delays. The findings are illustrated by numerical simulations.