Configuration Space Approach to Analysis of Consensus and Formation

Stability analysis of multi-agent dynamical systems has been an active area of research recently. In this paper, a configuration space approach is used to investigate the stability of a multi-agent system with first-order dynamics and continuous or discontinuous aggregating function interconnected through a digraph. This approach is shown to be a more convenient tool in modeling and investigating stability of the system. Describing the common case of a connected swarm graph in the configuration space form, the general mathematical model is proposed and the stability and finite time convergence of such consensus problem is proved through a Lyuponov Function approach. Moreover a novel discontinuous aggregating function is proposed which shows attractive and repulsive behavior without getting infinite value. Asymptotic stability is guaranteed for the model. Simulation results show the validity of the approach.