Decentralized generic rigidity evaluation in interconnected systems

In this paper, we consider the problem of evaluating the generic rigidity of an interconnected system in the plane, without a priori knowledge of the network´s topological properties. We propose the decentralization of the pebble game algorithm of Jacobs et. al., an O(n²) method that determines the generic rigidity of a planar network. Our decentralization is based on asynchronous inter-agent message-passing and a distributed memory architecture, coupled with consensus-based auctions for electing leaders in the system. We provide analysis of the asynchronous messaging structure and its interaction with leader election, and Monte Carlo simulations demonstrating complexity and correctness. Finally, a novel rigidity evaluation and control scenario in the accompanying media illustrates the applicability of our proposed algorithm.