Constrained agreement protocols for tree graph topologies

This article presents a novel way of manipulating the initial conditions in the consensus equation such that a constrained agreement problem is solved across a distributed network of agents, particularly for a network represented by a tree graph. The presented method is applied to the problem of coordinating multiple pendula attached to mobile bases. The pendula should move in such a way that their motion is synchronised, which calls for a constrained optimal control problem for each pendulum as well as the constrained agreement problem across the network. Simulation results are presented that support the viability of the proposed approach as well as a hardware demonstration.