We describe a decentralized formation problem for multiple robots, where an formation controller is proposed. The network of dynamic agents with external disturbances and uncertainties are discussed in formation problems. We first describe how to design social potential fields to obtain a formation with the shape of a polygon. Then, we provide a formal proof of the asymptotic stability of the system, based on the definition of a proper Lyapunov function and technique. The advantages of the proposed controller can be listed as robustness to input nonlinearity, external disturbances, and model uncertainties, while applicability on a group of any autonomous systems with -degrees of freedom. Finally, simulation results are demonstrated for a multiagent formation problem of a group of six robots, illustrating the effective attenuation of approximation error and external disturbances, even in the case of agent failure or leader tracking. 1. Introduction All around the world, nature presents examples of collective behavior in groups of insects, birds, and fishes. This behavior has produced sophisticated functions of the group that cannot be achieved by individual members [1, 2]. Therefore, the research on the coordination of robotic swarms has attracted considerable attention. Taking the advantages of distributed sensing and actuation, a robotic swarm can perform some cooperative tasks such as moving a large object that is usually not executable by a single robot [3–7]. Applications about the analysis and design of robotic swarms included autonomous unmanned aerial vehicles, congestion control of communication networks, and distributed sensor networks autonomous, and so forth [1, 2, 8–10]. In general, a robotic formation problem is defined as the organization of a swarm of agents into a particular shape in a 2D or 3D space [8]. This kind of control strategy can be applied into several different fields. For example, in the industrial field, this formation control strategy can be applied to a group of Automated Guided Vehicles (AGVs) moving in a warehouse for goods delivery. The main idea is to make a group of AGVs cooperatively deliver a certain amount of goods, moving in a formation. The creation of a formation with the desired shape is useful to precisely constrain the action zone of the AGVs, thus reducing the chance of collisions with other entities (e.g., human guided vehicles). In the literature, many different approaches to formation control can be found. The main existing approaches can be divided into two categories: centralized [11] and distributed
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