On the discrepancy between the task and communication graphs in multi-agent control systems

Motivated by applications in which agents need to perform collaborative tasks under limited communication, in this work we consider the asymptotic satisfaction of relative-position based spatial tasks by a leader-follower network. As opposed to existing approaches, the spatial tasks may involve non-communicating agents and/or a subset of the multi-agent team. In order to ensure the satisfaction of the constraints using local information, as a first contribution, we express the incidence matrix of the task graph in terms of the corresponding matrix of the communication graph. In addition, for undirected spanning tree communication graphs, we show that the relation of the incidence matrices of these graphs is unique. Building upon this relation, as a second contribution we propose a two-hop communication based distributed feedback control law that ensures asymptotic satisfaction of the constraints with a predetermined robustness. The proposed control law employs the line graph of the communication graph and does not require knowledge of a complete row of the constraint matrix.