Double-Integrator Dynamics for Multiagent Systems With Antagonistic Reciprocity.

Abstract

This article is dedicated to the consensus problem for interacting agents of the double-integrator dynamics subject to antagonistic reciprocity, described by negative scalar parameters. To this end, we first show the existence of the weighted gains which play an essential role for solving the consensus problem. Then, we establish the relationship between the weighted gains and scalar parameters to guarantee that the underlying "Laplacian" matrix contains a simple zero eigenvalue and the remaining eigenvalues enjoy positive real parts. Based on the above analysis, we further proceed to solve the considered problem. A major difficulty is that the Laplacian matrices, associated with the position and velocity information, are entirely distinct from each other, leading to the failure of the conventional consensus method for the second-order dynamics. We derive some criteria involving the weighted gains, the scaling parameters, and the real/image parts of the Laplacian matrix of the interaction graph. Moreover, some special frameworks, which have been extensively studied in the literature, are also elaborated on. Compared with the Altafini's model, we do not need to redefine a new Laplacian matrix, and more important, the restriction on the digon sign-symmetry property is removed. It is worth mentioning that the proposed consensus algorithm cannot be deduced by the Altafini's model or its variants. Finally, a wheeled multirobot system is formulated to validate the efficiency of the theoretical results.