Distributed Algorithm for Edge Agreement Over Nonlinear Constraints

In this paper, we introduce a comprehensive framework called edge agreement, where agents collaboratively strive to reach an agreement on non-linear edge constraints de-fined for each of their neighbors on every edge. This provides a novel perspective on the traditional ‘global consensus' problem, extending the goal beyond reaching the same value to achieving agreement over the whole multi-agent team. We present a dis-tributed algorithm for achieving edge agreement, along with a convergence guarantee based on certain assumptions. Addition-ally, we illustrate how this framework encompasses a variety of cooperation problems, including global consensus, recent results on edge agreement with linear constraints, distributed solutions to linear algebraic equations, and formation control (distance and displacement-based) as special cases. Finally, to validate and demonstrate the significance of this framework, we provide numerical simulations for all the mentioned applications.