Preview-based discrete-time dynamic formation control over directed networks via matrix-valued Laplacian

Abstract

This paper studies the dynamic formation control problem for cooperative agents with discrete-time dynamics over directed graphs. Unlike using absolute coordinate, relative coordinate, interagent distance, or interagent bearing to specify the target formation and coordinate agents to achieve the formation, we study a coordination problem where the desired formation varies with time and only its geometric shape is predefined. Matrix-valued Laplacian approach has been adopted to address this problem in the continuous-time setting. However, the discrete-time counterpart is more challenging due to the constraint in information exchange. On the other hand, observe that in many real operations, at a given time instant, the agents will be able to plan their target formation configurations for a period of time ahead. We propose preview-based P-like and PD-like controllers for the formation control. The controllers with proper parameter setting are proved to be effective to address the dynamic formation control problem. Numerical simulations are given to validate the effectiveness of the proposed controllers.