Coordination on Double-Integrator Antagonistic Dynamics Robust to Velocity Constraint

This article studies the coordination problem for second-order multiagent systems with the presence of antagonistic information among participating agents, while suffering from the lack of the velocity information. To this end, a coordination algorithm, involving an external variable that enables us to circumvent the velocity information, is proposed, of which nonzero scaling parameters are used to characterize whether the underlying interactions are antagonistic or not. A distinctive feature of the devised coordination algorithm, apart from the interest of its own, is that there does not necessitate the signed graph and structurally balanced theories that are commonly adopted in the literature. We show that the proposed setup is amenable for coordination of the agents, with the help of some newly introduced transformation relaxing the dependence of the weighted states of agents or some reference signals that are global information, and are commonly used in most of the existing studies where consensus problems are recast into the stability counterparts of the corresponded error systems. We also show that weighted gains used to assure the underlying Laplacian "like" matrix acting a normal Laplacian matrix, scaling parameters, and communication topology are of great importance for the investigated coordination problem, giving rise to that there does not enjoy any trivial equivalence between the devised setup and these in the literature. Finally, two numerical examples, including a multirobot system, are carried out to support the developed method.