However, in our study a group of three robots with basic sensor units that are capable of detecting each other are desired to organize into a basic E formation starting from any arbitrary initial distribution.The modeling and stability analysis of the basic system considered in our study can also be extended and considered as a large interconnected system. Recently, analysis and stabilization of multiple time-delay interconnected systems is also receiving increasing attention from the scientific community [22�C26]. In practice, the interconnected systems include electric power systems, process control systems, different types of societal systems, and so on. Chen and Chiang [25] extended the T-S fuzzy control representation to the stability analysis for nonlinear interconnected systems with multiple time-delays using LMI theory and proposed a LMI-based stability criterion which can be solved numerically.

In [26], a fuzzy robust control design which combines H infinity control performance with T-S fuzzy control for the control of delayed nonlinear structural systems under external excitations is presented by them. The modeling error is further considered for resolution in this work. The emphasis of the work of Chen and Chiang is on the stability and stabilization of complex interconnected systems which are usually modeled as a unified formula. In contrast to many systems considered in the literature, in our study we are concerned with local interactive rule design so that an effective global behavior emerges from these rules.

By comparison, the time-delay and modeling error are not immensely significant in our study. Hence, they are not taken into account in the design and stability analysis of the TFA.The remainder of this paper is organized as follows: Section 2 gives the problem statement including the Batimastat state transition model and motion control equation of robotic sensors. The detailed design procedure of the interactive control algorithm, TFA, is presented in Section 3. In Section 4, we conduct the stability analysis of the TFA which can be executed by robotic sensors independently and asynchronously for E formation. Section 5 demonstrates E formation behavior and typical formation convergences of three neighboring robotic sensors through computer simulations. Finally, conclusions and future work are stated in Section 6.2.

?Problem StatementWe consider low cost homogeneous robots embodying simple and commonly available sensors. This means that the members cannot have strong capability, e.g., remote communication, and can only interact with neighbors or their environment. In fact, compared with single robotic sensors with complex structure and comprehensive function, there is less probability for a simple robotic sensor to be destroyed while performing tasks.