Triangle Formation of Multi-Agent Systems with Leader-Following on Fuzzy Control

In recent years, there have been an increasing number of achievements dealing with the control of agent formations (Olfati-Saber, 2006; Tanner & Jadbabaie, 2007; Fax & Murray, 2004; Jadbabaie et al., 2003; Lin et al., 2004; Olfati-Saber & Murray, 2004). The formation control of multiple moving agents has emerged as a topic of widespread interest due to its broad range of applications in military missions, environmental surveying, and space missions. Multiple mobile autonomous agents coupled with each other through interactions can generate certain ordered behaviors, such as aggregation, cohesion, alignment, rotation and synchronization (Fax & Murray, 2004; Jadbabaie et al., 2003; Lin et al., 2004; Olfati-Saber & Murray, 2004). Among the typical approaches to formation control, distributed control strategies have aroused researchers’ outstanding attention because there is no centralized supervisor and only a little sense of communication information is needed. Recently, there has been a tendency to deal with the formation control as a consensus problem. In the multiagent systems, consensus means to reach an agreement by means of an interaction rule that specifies the information exchange between an agent and its neighbors (Fax & Murray, 2004; Jadbabaie et al., 2003; Lin et al., 2004; Olfati-Saber & Murray, 2004). Fax & Murry (Fax & Murray, 2004) analyzed the stability of the formation control with first-order consensus protocols based on the graph Laplacian. Jadbabaie et al. (Jadbabaie et al., 2003) demonstrated the results of the alignment problem which is concerned with reaching an agreement without computing any objective functions. Lin et al. (Lin et al., 2004) studied three formation strategies for groups of mobile autonomous agents with local communication topology. Moreover, by using a Lyapunov-based approach, Olfati-Saber & Murry (Olfati-Saber & Murray, 2004) solved the consensus problems in networks of agents with directed interconnection graphs and time delays. The key idea involved in nonlinear formation control is to preserve the inter-agent distances from decaying to zero during the motion for the purpose of collision avoidance. In the formation control, tracking control problems of multi-agent systems are studied increasingly, and many results have been obtained with nearest neighbor-based rule (Hong et al., 2006; Anderson et al., 2007; Chen & Tian, 2009). Hong et al. (Hong et al., 2006)