Periodic coordinated rotating motion control of second-Order multi-Agent systems under directed interaction topologies

Abstract

ABSTRACTThis paper investigates the problem of periodic motion control of second-order multi-agent systems in three dimensions under directed interaction topologies. Distributed algorithms for periodic rotating motion around a static and moving target were proposed by exploring the introduction of Cartestian coordinate coupling for each agent. In case of a static target, we show that when the nonsymmetric Laplacian matrix has certain properties, the damping gain is above a certain bound, and the Euler angle is equal to a critical value, all the agents will eventually rotate around the target periodically. In case of a moving target, the composite motion behaviours with translation and rotation will emerge, when this moving target's information can only be available to one or one subset of these agents and all agents have only local interactions. Tools like matrix theory, linear system theory and other mathematical skills were used for convergence analysis. Simulation results were provided to illustrate the effectiveness of the theoretical results.