Planar Affine Formation Stabilization via Parameter Estimations.

Abstract

In this article, we study the problem of affine formation stabilization for multiagent systems in the plane. The challenges lie in the limited access to the information of the target formation in the sense that the prescribed values of the formation parameters, that is, the scaling size and rotation angle, are known only by one agent which we call the leader. Motivated by the fact that three agents (say, leaders) can determine the shape of a planar triangular formation using the stress matrix, we propose a class of estimators to guarantee that two agents in the leader set can gain access to the formation parameters. Then, an integrated control scheme is designed such that the target formation can be uniquely stabilized among all its affine transformations. The sufficient condition ensuring the stability of the closed-loop system is also given based on the cyclic-small-gain theorem. Simulations and experiments are carried out to show the effectiveness of the proposed control strategy.