Abstract
This article investigates the enclosing control without preset formation of second-order multi-agent systems for stationary targets. This article uses a directed graph to describe and the direction of information exchange between agents and targets. For continuous-time systems, an enclosing control algorithm is proposed, which does not need to preset the desired formation. The state transfer equation is used to transform the solution of the system into a matrix function of first-order linear constant-coefficient non-homogeneous differential equations. By analyzing the convergence of the solution, the value range of the gain parameter is obtained, and the requirements of topology are proposed. Then the discrete protocol is applied to the discrete-time system. Based on the Schur stability analysis of the system, the requirements of topology and parameter for the system to achieve enclosing control are given. Finally, the self-designed multi-agent platform is introduced, and simulation and experimental results are presented to validate the effectiveness of the protocol.
Highlights
With the development of intelligent robots, cooperative control algorithm has been applied to a great number of civilian and military fields [1]–[4]
According to different application fields, cooperative control can be classified into consensus control [5]–[7], containment control [8]–[10], formation control [11]–[13], consensus tracking [14]–[16], and so on
By analyzing the eigenvalues of the matrix related to the Laplace matrix, the gain range of the continuous-time protocol is obtained
Summary
With the development of intelligent robots, cooperative control algorithm has been applied to a great number of civilian and military fields [1]–[4]. Li and Dong studied the problem of formation-containment control, and the platform built in this article reduces the difficulty of control by decoupling the states of quadrotor [24] It provides a reference for the design of the enclosing control experimental platform. When using formation tracking control and surrounding control to solve the problem of enclosing control, it is generally to design vectors manually to describe the desire position between agents, that is, to set a convex hull manually. This process is cumbersome, and mainly used in the enclosing control of a single target. In is the n-th order identity matrix. diag{α1, · · · , αn} represents a diagonal matrix with diagonal elements α1, · · · , αn. 0n×m denotes a zero matrix with n rows and m columns. xrepresents the differential of x
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