Cooperative Shape–Translation Estimation and Control for Time-Varying Linear Formation

This article investigates the time-varying formation control problem of multiagent systems. A novel leader–follower formation architecture is proposed, termed “linear formation control.” In this architecture, both the shape of the formation and its translational motions are represented by a linear transformation matrix determined by the positions of the leaders. This setup allows the leaders' movements to generate time-varying desired formations. To facilitate followers' tracking of desired formations, an integrated control structure is proposed, comprising two estimators and a compatible controller. The first estimator is responsible for obtaining the time-varying linear formation shape parameters by measuring the leaders' relative displacements, the kernel of which essentially involves solving a system of time-varying linear equations in a distributed manner. The second estimator focuses on inferring the time-varying translation parameters using leaders' positions. Subsequently, utilizing the outputs of these estimators, a tracking controller is proposed to track the desired time-varying formation precisely. Finally, the effectiveness of the proposed estimation and control schemes is demonstrated through simulations.