Oscillatory Group-Bipartite Consensus in a Swarm of Robots With Multiple Oscillatory Leaders

Jun Liu, Shaorong Xie, Hengyu Li

Abstract: This article addresses the oscillatory group- bipartite consensus control problem for multiple robots modeled by the Euler–Lagrange equation with multiple oscillatory leaders. After introducing the definition of oscillatory group-bipartite consensus to the networked robot systems, an oscillatory group-bipartite consensus control protocol is provided by thoroughly exploiting the network topology. A new form of the Laplacian matrix involving the connection between agents is constructed that contains three parts, the weights between the agents from the oscillatory virtual leaders to the robot followers and the weights from the same subgroup and from different subgroups. The elements of each part have their own unique definition according to their characteristics. Moreover, a coordinate transformation is conducted based on such Laplacian matrix for stability analysis of controlled systems. Some criteria that ensure the swarm robots converge to oscillatory group-bipartite consensus are presented. Two simulations conducted under two typical group structure network topologies are given to validate the proposed control methodologies, respectively.