Rendezvous of Heterogeneous Multiagent Systems With Nonuniform Time-Varying Information Delays: An Adaptive Approach

Abstract

This article considers the rendezvous problem of a group of heterogeneous second-order agents subject to information transmission delays. A major challenge to construct a fully distributed rendezvous protocol is to deal with these delays, which are assumed to be nonuniform and time-varying. Inspired by the fact that a large enough damping coefficient can improve the robustness of a second-order agent against external disturbance, we overcome the above challenge by studying the impact of the damping coefficient on the rendezvous problem. To theoretically analyze the impact, one type of static rendezvous protocol is first proposed and employed. It is interesting to find that agents can reach rendezvous under the static protocol if the damping coefficient is large enough, even though the duration of the time-delay is uncertain. This fact indicates that a large damping coefficient can make the static protocol be robust to the uncertainty of time-delay, which is consistent with the common sense. Then, we apply this impact to deal with the uncertainty introduced by the nonuniform time-varying information delays. To fully apply this impact, we adopt an adaptive approach to making the damping coefficient automatically adapt with the changes of the time-delay. Hence, two classes of fully distributed and adaptive rendezvous protocols are designed, which do not need the global information of the entire communication graph or the value of these time-delays at all. The difference between two classes of protocols is whether it can realize low-frequency learning or not. Finally, some numerical simulations are performed on multiple robots to illustrate the analytical results.