Contents I. Introduction
In the last two decades, distributed multi-agent coordination has been a very attractive research field in the robotics and control communities [1]–[3]. This topic has gained momentum as multi-agent systems offer many advantages ranging from robustness and reliability to reduced complexity of hardware design for the agents. A very common approach for developing coordination algorithm is to take inspiration from biology. For example, several multi-agent swarming protocols have been inspired by animal aggregations such as schools of fish, flocks of birds or swarms of bees, that are believed to use simple, local motion coordination rules at the individual level, [4]–[6]. As a matter of fact, swarming models have been a good solution to many engineering and computer science problems. One of the first related works is [7], where the authors describe and simulate a flock of birds that fly following a swarming model based on few simple rules and local interactions. In [8] it is possible to find a focus on ideas and concepts for the advancement of swarm robotics as an engineering field. The authors describe, from a general point of view, the limits, the advantages and the future developing of this discipline. In [9], the authors show a theoretical explanation for the behavior observed by Vicsek. In addition, convergence results are derived for several other similarly inspired models. For example, in [10] is considered an asynchronous distributed control for geometric pattern formation of multiple anonymous agents. A proof for the stability of the formation can be found in [11], [12], where the authors use a control Lyapunov function and formation constrains. Another Lyapunov function is used in [13] to show the convergence of the system to a steady state in a desired area, in which the agents move while preserving a minimal inter-distance. Many of the cited articles consider decentralized formation control laws. An example of this type of control is the one in [14], where is developed a decentralized controller to generate a desired two-dimensional geometric pattern for a swarm. One of the works that has brought to the swarming research community significant results, is the one by Gazi and Passino in [15], where a decentralized aggregation algorithm based on a continuous-time control law is given. Several papers have been successively developed along this direction, such as [16]–[18].
