Distributed Formation Control of Multiagent Systems With Specified Order

Abstract

In this article, we design the controller for multiagent systems such that the agents with nonlinear dynamics can form into arbitrarily given shapes, rotate around the formation centroid at the given angular velocity, track the reference trajectory, and dynamically adjust the formation for obstacle avoidance. In addition, the proposed design ensures that the agents can be positioned with a specified order in the formation. We propose an extended model for the system to facilitate the design. To deal with the order issue, we introduce the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">phase weighting parameter</i> and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">phase penalty flow exchange mechanism</i> such that the agent’s position can be adjusted to the desired order. With the aid of the proposed tools, we first design the formation controller for MAS with a planar unicycle model and then extend it to the three-dimensional space. The controller is designed based on information from the neighbors and is measured in the agents’ local reference frame. Moreover, unlike most of the existing works, the initial conditions are not restricted in our approach. Finally, system stability is proved via the Lyapunov theorem and several simulation examples are provided to validate our results.