Formation control of networked multi-agent systems

Abstract

In this paper, a systematic framework is developed for the consensus problem, in particular, for formation control of networked dynamic agents. In view of the complexity of the framework with switching coupling topology and nonlinearity, a new decentralized formation strategy based on artificial potential functions (APF) is proposed. Due to the existence of local minima in the APF, the formation controller is designed to introduce some special functions to settle that limitation. A new concept of relative-position-based formation stability is defined, and a Lyapunov approach is used along with an extended LMI algorithm to analyze the condition for formation stability. Finally, an example with simulation is given to demonstrate the effectiveness of the designed formation controller.

Stability Analysis and Implementation of a Decentralized Formation Control Strategy for Unmanned Vehicles

“…In [24], a formation Lyapunov stability function is defined as a weighted sum of the control Lyapunov function for each vehicle to support the formation stability analysis. In [25], the idea of relative-position-based formation stability was proposed and the Lyapunov method was also used to design the decentralized controllers, along with an extended linear matrix inequality (LMI) to analyze the conditions required for formation stability. Moreover, paper [26] proposed a Lyapunovbased approach to give a sufficient condition to make all the agents converge to a common value, and a common Lyapunov function was explicitly constructed in the case of switching jointly connected topologies.…”

“…and applying the above inequalities to (25) produces the final result for showing the stability of the overall formation. Thus…”

Formation stability analysis of unmanned multi-vehicles under interconnection topologies

“…In the paper (Ögren, Egerstedt, & Hu, 2002), a formation Lyapunov stability function was defined as a weighted sum of the control Lyapunov function for each vehicle to support the formation stability analysis. The idea of relative-position-based formation stability was proposed by Xue et al (2010),and the Lyapunov method was also used to design the decentralised controllers, along with an extended LMI to analyse the conditions required for formation stability. Moreover, Hong, Gao, Cheng, and Hu (2007) proposed a Lyapunov-based approach to give a sufficient condition to make all the agents converge to a common value, and a common Lyapunov function was explicitly constructed in the case of switching jointly connected topologies.…”

“…Each vehicle has its own relative position in the body and tracks the desired trajectory which is translated from the desired motion of the rigid body (Askari, Mortazavi, & Talebi, 2013;Li & Liu, 2008). The standard artificial potential field (APF) approach is based on applying the negative gradient of an artificial potential function as control inputs to drive the overall formation to convergence (Do, 2007;Krick, Broucke, & Francis, 2009;Xue, Yao, Chen, & Yu, 2010). Further, a unified optimal control approach consisting of formation control, trajectory tracking, and obstacle avoidance was presented by J.…”

Robust H ∞ consensus control of uncertain multi-agent systems with time delays

“…During the past decade, the decentralized cooperative control of multi-agent systems has been widely studied, such as flocking or swarming behaviors [1,2], formation control [3], and path planning [4], in which the consensus problem is commonly accepted as one of the most important and fundamental issues. For a multiagent system, consensus means that the states of all agents are driven to a common value by implementing distributed protocols, based on the communication networks.…”