Communication-Delay-Dependent Rendezvous With Possible Negative Controller Gain in Cyclic Pursuit

In this article, we address the multiagent rendezvous problem for a group of single-integrator agents in the presence of a constant arbitrarily large bounded homogeneous communication delay. The agents are required to meet at a tunable desired point, which is unknown to all agents. To achieve this objective, we choose the cyclic pursuit strategy, which requires the minimum number of communication links. It is shown that the rendezvous can be achieved with at most one zero or negative gain in the presence of delay. A negative controller gain implies an antagonistic interaction of the agent with its neighbor, whereby it moves away from the neighbor. We find the bound on the negative gain such that rendezvous among all agents is possible. The margin on the negative gain decreases due to the presence of delay. An analytical expression has been obtained for the reachable rendezvous points in terms of an initial configuration of the agents, controller gains, and the delay. For fixed controller gains and increasing delay, the rendezvous point lies along the line joining the weighted centroid and the centroid of the initial configuration with the asymptotic nature toward the centroid when all gains are positive, while away from it when one gain is negative. For finite controller gains, the reachable set remains unchanged even in the presence of any finite delay. Numerical examples illustrate the presented results.