Decentralized minimal‐time planar formation control of multi‐agent system

Abstract

SummaryIn this paper, the problems of decentralized minimal‐time planar formation control are investigated for both static and dynamic cases. For the static one, the discrete‐time dynamics of multi‐agent system in which each agent exchanges information according to a complex weighted network is studied. On the basis of a minimal polynomial, a decentralized minimal‐time static formation method is proposed to compute the final formation positions of the agents in the minimal number of steps without global coordinates. The proposed method allows an arbitrarily chosen agent in the network to compute its final formation position. For the dynamic one in a leader–follower framework, the path information of the agents satisfies linear regression equations that are determined by interaction topology and input signals. In order to obtain the coefficients of such linear regression equations, a Kronecker‐theorem‐based algorithm is presented. Similar to the results for the static case, any agent is allowed to use the minimum number of successive history state values to compute the future dynamic formation track. The minimal number of steps can be computed by checking the rank condition of the Hankel matrix constructed in terms of the path information. Meanwhile, the simulation examples are given to demonstrate the validity of the proposed minimal‐time planar formation control methods. The results in the paper combine the matrix polynomial analysis into the framework of formation control design and show how to predict the motion of the agents in a decentralized manner. Copyright © 2017 John Wiley & Sons, Ltd.