Synchronization is everywhere! This is the feeling one may get once alerted for it. Everyone is familiar with all kinds of biological rhythms ('biological clocks') that create some kind of conformity in time and in nature. This includes for instance neural activity and brain activity, but also the cardiac vascular system. Clearly, there are numerous other examples to be mentioned, sometimes much more controversial like the claimed synchronicity of the monthly period of nuns in a cloister, and so on. Synchronous motion was probably first reported by Huygens (1673), where he describes an experiment of two (marine) pendulum clocks hanging on a light weighted beam, and which exhibit (anti-)frequency synchronization after a short period of time. Synchronized sound in nearby organ tubes was reported by Rayleigh in 1877, who observed similar effects for two electrically or mechanically connected tuning forks. In the last century synchronization received a lot of attention in the Russian scientific community since it was observed in balanced and rotors and vibro-exciters. Perhaps an enlightening potential new application for coordinated motion is in the use of hundreds of piezo-actuators in order to obtain a desired motion of a large/heavy mechanical set-up like for instance an airplane or Mm-scanner, or the coordination of microactuators for manipulation at very small scales. In astronomy synchronization theory is used to explain the motion of celestial bodies, such as orbits and planetary resonances,  In biology, biochemistry and medicine many systems can be modelled as oscillatory or vibratory systems and those systems show a tendency towards synchronous behavior. Among evidences of synchronous behavior in the natural world, one can consider the chorusing of crickets, synchronous flash light in a group of fire-flies, and the metabolic synchronicity in yeast cell suspension. The subject of synchronization has received huge attention in the last decades, in particular by biologists and physicists. This attention probably centers around one of the fundamental issues in science, namely curiosity: how come we find synchronous motion in a large ensemble of identical systems? Also, new avenues of potential use of synchronicity are now being explored. Synchronization has much in common - and is in sense equivalent to-coordination and cooperation. In ancient times it was already understood that joint activity may enable to carry out tasks that are undoable for an individual. The authors' interest in the subject of synchronization is strongly influenced by a desire to understand what the basic ingredients are when coordinated motion is required in an engineering system. We therefore have concentrated in this book on synchronization or coordination of mechanical systems, like in robotic systems. This allows to delve, on the one hand, in the theoretic foundations of synchronous motion, but, on the other hand, made it possible to combine the theoretical findings with experimental verification in our research laboratorium. This book concentrates therefore on controlled synchronization of mechanical systems that are used in industry. In particular the book deals with robotic systems, which nowadays are common and important systems in production processes. However, the general ideas developed here can be extended to more general mechanical systems, such as mobile robots, ships, motors, microactuators, balanced and unbalanced rotors, vibro-exciters. The book is organized as follows: Chapter 1 gives a general introduction about synchronization, its definition and the different types of synchronization. Chapter 2 presents some basic material and results on which the book is based. In Section 2.1 some mathematical tools and stability concepts used throughout the book are presented. The dynamic models of rigid and flexible joint robots are introduced in Section 2.2, including their most important properties. The experimental set-up that will be used in later chapters is introduced in Section 2.3, where a brief description of the robots and their dynamic models is presented. Chapter 3 addresses the problem of external synchronization of rigid joint robots. The synchronization scheme formed by a feedback controller and model based observers is presented and a stability proof is developed. Simulation and experimental results on one degree of freedom systems are included to show the applicability and performance of the proposed controller. The main contribution of this chapter is a gain tuning procedure that ensures synchronization of the interconnected robot systems. The case of external synchronization for flexible joint robots is addressed in Chapter 4. The chapter starts by explaining the differences between rigid and flexible joint robots and the effects on the design of the synchronization scheme. The synchronization scheme for flexible joint robots and stability analysis is presented. The chapter includes a gain tuning procedure that guarantees synchronization of the interconnected robot systems. Simulation results on one degree of freedom systems are included to show the viability of the controller. The problem of internal (mutual) synchronization of rigid robots is treated in Chapter 5. This chapter presents a general synchronization scheme for the case of mutual synchronization of rigid robots. The chapter includes a general procedure to choose the interconnections between the robots to guarantee synchronization of the multi-composed robot system. Simulation and experimental results on one degree of freedom systems are included to show the properties of the controller. Chapter 6 presents a simulation and experimental study using two rigid robot manipulators and shows the applicability and performance of the synchronization schemes for rigid joint robots. Particular attention is given to practical problems that can be encountered at the moment of implementing the proposed synchronization schemes. The robots in the experimental setup have four degrees of freedom, such that the complexity in the implementation is higher than in the simulations and experiments included in Chapters 3 and 5. Further extensions of the synchronization schemes designed here are discussed in Chapter 7. Some conclusions related to synchronization in general and robot synchronization in particular are presented in Chapter 8.

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