Swarm robotics: a review from the swarm engineering perspective <s> Pattern formation <s> The development of higher organisms is controlled by a complex network of biochemical reactions that are under genetic control. The aim of the seminar is to demonstrate that it is possible to formulate models in a mathematical precise way that describe essential steps in spite of the appearing complexity of this process. Many of these models have found meanwhile direct support by molecular-genetic experiments. By computer simulations it will be shown that the models describe precisely the regulatory phenomena as they have been experimentally observed. <s> BIB001 </s> Swarm robotics: a review from the swarm engineering perspective <s> Pattern formation <s> Part 1 Basic concepts. Part 2 Investigation tools: experiment theoretical approaches. Part 3 Main types of convective-flow structures: two-dimensional rolls and three-dimensional cells patterns of quasi-two-dimensional rolls convection textures roll-pattern defects. Part 4 Convection-regime sequences, selection of the wavenumbers of convection rolls: wavenumbers in experiments with random initial disturbances searches for universal selection criteria stability of two-dimensional roll flows Lyapunov function and selection selection mechanisms. Part 5 Peculiarities of stratification and vertical structure of convection. <s> BIB002 </s> Swarm robotics: a review from the swarm engineering perspective <s> Pattern formation <s> This paper describes a control mechanism by which large numbers of inexpensive robots can be deployed as a distributed remote sensing instrument, and in which the desired large-scale properties of the sensing instrument emerge from the simple pair-wise interactions of its component robots. Such sensing instruments are called distributed robotic macrosensors. Robots in the macrosensor interact with their immediate neighbors using a virtual spring mesh abstraction, which is governed by a simple physics model. By carefully defining the nature of the spring mesh and the associated physics model, it is possible to create a number of desirable global behaviors without any global control or configuration. Properties of the resulting macrosensor include arbitrary scalability, the ability to function in complex environments, sophisticated target tracking ability, and natural fault tolerance. We describe the control mechanisms that yield these results, and the simulation results that demonstrate their efficacy. <s> BIB003 </s> Swarm robotics: a review from the swarm engineering perspective <s> Pattern formation <s> Stability analysis of decentralized control mechanisms for networked coordinating systems has generally focused on specific controller implementations, such as nearest-neighbor and other types of proximity graph control laws. This approach often misses the need for the addition of other control structures to improve global characteristics of the network. An example of such a situation is the use of a Gabriel graph, which is essentially a nearest-neighbor rule modified to ensure global connectivity of the network if the agents are pairwise connected through their sensor inputs. We present a method of ensuring provable stability of decentralized switching systems by employing a hysteresis rule that uses a zero-sum consensus algorithm. We demonstrate the application of this result to several special cases, including nearest-neighbor control laws, Gabriel graph rules, diffuse target tracking, and hierarchical heterogeneous systems. <s> BIB004 </s> Swarm robotics: a review from the swarm engineering perspective <s> Pattern formation <s> From an engineering point of view, the problem of coordinating a set of autonomous, mobile robots for the purpose of cooperatively performing a task has been studied extensively over the past decade. In contrast, in this paper we aim to understand the fundamental algorithmic limitations on what a set of autonomous mobile robots can or cannot achieve. We therefore study a hard task for a set of weak robots. The task is for the robots in the plane to form any arbitrary pattern that is given in advance. This task is fundamental in the sense that if the robots can form any pattern, they can agree on their respective roles in a subsequent, coordinated action. The robots are weak in several aspects. They are anonymous; they cannot explicitly communicate with each other, but only observe the positions of the others; they cannot remember the past; they operate in a very strong form of asynchronicity. We show that the tasks that such a system of robots can perform depend strongly on their common agreement about their environment, i.e. the readings of their environment sensors. If the robots have no common agreement about their environment, they cannot form an arbitrary pattern. If each robot has a compass needle that indicates North (the robot world is a flat surface, and compass needles are parallel), then any odd number of robots can form an arbitrary pattern, but an even number cannot (in the worst case). If each robot has two independent compass needles, say North and East, then any set of robots can form any pattern. <s> BIB005
Description Pattern formation aims at deploying robots in a regular and repetitive manner. Robots usually need to keep specific distances between each other in order to create a desired pattern. Source of inspiration Pattern formation can be found both in biology and in physics. Some biological examples are the spatial disposition of bacterial colonies and the chromatic patterns on some animal's fur BIB001 . Some physics examples are molecules distribution and crystal formation  , and Bénard cells BIB002 . Approaches The most common way to develop pattern formation behaviors in robot swarms is to use virtual physics-based design. Virtual physics-based design uses virtual forces to coordinate the movements of robots. (2004) developed a collective behavior for pattern formation that is one of the first applications of virtual physics-based design. In their work, they use the virtual forces to form a hexagonal lattice (see Fig. 5(a) ). In the same work, Spears et al. showed that, by creating two groups of robots with different attraction/repulsion thresholds, it is also possible to obtain a square lattice. More details can be found in a subsequent work  . BIB003 presented a behavior in which robots interact via virtual springs (see Fig. 5(b) ). These virtual springs are used by a robot to compute attraction/repulsion virtual forces. Differently from Spears et al.'s work, in this work, the robots can interact in different ways (full connectivity, first neighbors, N-nearest, . . . ). Each type of interaction has different characteristics and gives rise to slightly different patterns. Additional theoretical work is presented in a subsequent paper BIB004 . BIB005 focused on a theoretical analysis of pattern formation. The authors were able to formally prove that with a group of fully asynchronous robots it is possible to obtain only a subset of all possible patterns, whereas other patterns are achievable only with some kind of global knowledge such as a common orientation given by a compass.