Global Reachability of Heterogeneous Multiagent Systems Under Collaborative Interaction Topology and Unknown Delays

Abstract

The multi-agent rendezvous problem for single- and double-integrator agents in the presence of unknown constant input and communication delays is investigated in this paper. Existing works address the rendezvous problem by incorporating negative gain(s) into the distributed consensus protocol and showing that negative gain(s) expands the reachable set beyond the initial configuration of the agents' convex hull. On the contrary, the present control protocol ensures global reachability of a network of agents with a directed communication topology having non-negative edge weights. This is accomplished with the help of a dynamic distributed control protocol, where the information exchange among agents occurs in the internal controller states. For homogeneous delays, the analytical expression of the rendezvous point confesses the non-dependency of the point with delays, which in turn signifies that rendezvous can be achieved with unknown and arbitrarily large but bounded delays. The very structure of the control protocol ensures rendezvous at any desired point, even if the input delays are heterogeneous and unknown. However, heterogeneity in communication delays has an effect on the rendezvous point, and hence, global reachability of agents can be established if these delays are exactly known. For heterogeneous multi-agent systems composed of single- and double-integrator agents, tuning of the design parameters gets simplified due to the single-integrator based internal controller structure for all agents. Numerical simulations are provided to validate the robustness of the protocol against delays.