Synchronization properties of self-sustained mechanical oscillators

We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained systems may become standard in the design of frequency-control devices at microscopic scales. Our analysis is thus focused on their synchronization properties under the action of external forces, and on the joint dynamics of two to many coupled oscillators. Existence and stability of synchronized motion are assessed in terms of the mechanical properties of individual oscillators --namely, their natural frequencies and damping coefficients-- and synchronization frequencies are determined. Similarities and differences with synchronization phenomena in other coupled oscillating systems are emphasized.Comment: To appear in Phys. Rev.

Emergent coordination between humans and robots

Emergent coordination or movement synchronization is an often observed phenomenon in human behavior. Humans synchronize their gait when walking next to each other, they synchronize their postural sway when standing closely, and they also synchronize their movement behavior in many other situations of daily life. Why humans are doing this is an important question of ongoing research in many disciplines: apparently movement synchronization plays a role in children’s development and learning; it is related to our social and emotional behavior in interaction with others; it is an underlying principle in the organization of communication by means of language and gesture; and finally, models explaining movement synchronization between two individuals can also be extended to group behavior. Overall, one can say that movement synchronization is an important principle of human interaction behavior. Besides interacting with other humans, in recent years humans do more and more interact with technology. This was first expressed in the interaction with machines in industrial settings, was taken further to human-computer interaction and is now facing a new challenge: the interaction with active and autonomous machines, the interaction with robots. If the vision of today’s robot developers comes true, in the near future robots will be fully integrated not only in our workplace, but also in our private lives. They are supposed to support humans in activities of daily living and even care for them. These circumstances however require the development of interactional principles which the robot can apply to the direct interaction with humans. In this dissertation the problem of robots entering the human society will be outlined and the need for the exploration of human interaction principles that are transferable to human-robot interaction will be emphasized. Furthermore, an overview on human movement synchronization as a very important phenomenon in human interaction will be given, ranging from neural correlates to social behavior. The argument of this dissertation is that human movement synchronization is a simple but striking human interaction principle that can be applied in human-robot interaction to support human activity of daily living, demonstrated on the example of pick-and-place tasks. This argument is based on five publications. In the first publication, human movement synchronization is explored in goal-directed tasks which bare similar requirements as pick-and-place tasks in activities of daily living. In order to explore if a merely repetitive action of the robot is sufficient to encourage human movement synchronization, the second publication reports a human-robot interaction study in which a human interacts with a non-adaptive robot. Here however, movement synchronization between human and robot does not emerge, which underlines the need for adaptive mechanisms. Therefore, in the third publication, human adaptive behavior in goal-directed movement synchronization is explored. In order to make the findings from the previous studies applicable to human-robot interaction, in the fourth publication the development of an interaction model based on dynamical systems theory is outlined which is ready for implementation on a robotic platform. Following this, a brief overview on a first human-robot interaction study based on the developed interaction model is provided. The last publication describes an extension of the previous approach which also includes the human tendency to make use of events to adapt their movements to. Here, also a first human-robot interaction study is reported which confirms the applicability of the model. The dissertation concludes with a discussion on the presented findings in the light of human-robot interaction and psychological aspects of joint action research as well as the problem of mutual adaptation.Spontan auftretende Koordination oder Bewegungssynchronisierung ist ein häufig zu beobachtendes Phänomen im Verhalten von Menschen. Menschen synchronisieren ihre Schritte beim nebeneinander hergehen, sie synchronisieren die Schwingbewegung zum Ausgleich der Körperbalance wenn sie nahe beieinander stehen und sie synchronisieren ihr Bewegungsverhalten generell in vielen weiteren Handlungen des täglichen Lebens. Die Frage nach dem warum ist eine Frage mit der sich die Forschung in der Psychologie, Neuro- und Bewegungswissenschaft aber auch in der Sozialwissenschaft nach wie vor beschäftigt: offenbar spielt die Bewegungssynchronisierung eine Rolle in der kindlichen Entwicklung und beim Erlernen von Fähigkeiten und Verhaltensmustern; sie steht in direktem Bezug zu unserem sozialen Verhalten und unserer emotionalen Wahrnehmung in der Interaktion mit Anderen; sie ist ein grundlegendes Prinzip in der Organisation von Kommunikation durch Sprache oder Gesten; außerdem können Modelle, die Bewegungssynchronisierung zwischen zwei Individuen erklären, auch auf das Verhalten innerhalb von Gruppen ausgedehnt werden. Insgesamt kann man also sagen, dass Bewegungssynchronisierung ein wichtiges Prinzip im menschlichen Interaktionsverhalten darstellt. Neben der Interaktion mit anderen Menschen interagieren wir in den letzten Jahren auch zunehmend mit der uns umgebenden Technik. Hier fand zunächst die Interaktion mit Maschinen im industriellen Umfeld Beachtung, später die Mensch-Computer-Interaktion. Seit kurzem sind wir jedoch mit einer neuen Herausforderung konfrontiert: der Interaktion mit aktiven und autonomen Maschinen, Maschinen die sich bewegen und aktiv mit Menschen interagieren, mit Robotern. Sollte die Vision der heutigen Roboterentwickler Wirklichkeit werde, so werden Roboter in der nahen Zukunft nicht nur voll in unser Arbeitsumfeld integriert sein, sondern auch in unser privates Leben. Roboter sollen den Menschen in ihren täglichen Aktivitäten unterstützen und sich sogar um sie kümmern. Diese Umstände erfordern die Entwicklung von neuen Interaktionsprinzipien, welche Roboter in der direkten Koordination mit dem Menschen anwenden können. In dieser Dissertation wird zunächst das Problem umrissen, welches sich daraus ergibt, dass Roboter zunehmend Einzug in die menschliche Gesellschaft finden. Außerdem wird die Notwendigkeit der Untersuchung menschlicher Interaktionsprinzipien, die auf die Mensch-Roboter-Interaktion transferierbar sind, hervorgehoben. Die Argumentation der Dissertation ist, dass die menschliche Bewegungssynchronisierung ein einfaches aber bemerkenswertes menschliches Interaktionsprinzip ist, welches in der Mensch-Roboter-Interaktion angewendet werden kann um menschliche Aktivitäten des täglichen Lebens, z.B. Aufnahme-und-Ablege-Aufgaben (pick-and-place tasks), zu unterstützen. Diese Argumentation wird auf fünf Publikationen gestützt. In der ersten Publikation wird die menschliche Bewegungssynchronisierung in einer zielgerichteten Aufgabe untersucht, welche die gleichen Anforderungen erfüllt wie die Aufnahme- und Ablageaufgaben des täglichen Lebens. Um zu untersuchen ob eine rein repetitive Bewegung des Roboters ausreichend ist um den Menschen zur Etablierung von Bewegungssynchronisierung zu ermutigen, wird in der zweiten Publikation eine Mensch-Roboter-Interaktionsstudie vorgestellt in welcher ein Mensch mit einem nicht-adaptiven Roboter interagiert. In dieser Studie wird jedoch keine Bewegungssynchronisierung zwischen Mensch und Roboter etabliert, was die Notwendigkeit von adaptiven Mechanismen unterstreicht. Daher wird in der dritten Publikation menschliches Adaptationsverhalten in der Bewegungssynchronisierung in zielgerichteten Aufgaben untersucht. Um die so gefundenen Mechanismen für die Mensch-Roboter Interaktion nutzbar zu machen, wird in der vierten Publikation die Entwicklung eines Interaktionsmodells basierend auf Dynamischer Systemtheorie behandelt. Dieses Modell kann direkt in eine Roboterplattform implementiert werden. Anschließend wird kurz auf eine erste Studie zur Mensch- Roboter Interaktion basierend auf dem entwickelten Modell eingegangen. Die letzte Publikation beschreibt eine Weiterentwicklung des bisherigen Vorgehens welche der Tendenz im menschlichen Verhalten Rechnung trägt, die Bewegungen an Ereignissen auszurichten. Hier wird außerdem eine erste Mensch-Roboter- Interaktionsstudie vorgestellt, die die Anwendbarkeit des Modells bestätigt. Die Dissertation wird mit einer Diskussion der präsentierten Ergebnisse im Kontext der Mensch-Roboter-Interaktion und psychologischer Aspekte der Interaktionsforschung sowie der Problematik von beiderseitiger Adaptivität abgeschlossen

Dynamic synchronization of sympathetic oscillators

Synchronous activity of single postganglionic sympathetic neurones (PGNs) underlies rhythmical or semi-rhythmical burst discharges recorded from peripheral sympathetic nerves. It is still controversial whether this rhythmicity is generated by an autonomous sympathetic oscillator. Previous studies have demonstrated that activity of single PGNs innervating the caudal ventral artery (CVA) of the rat's tail has a dominant rhythm (T-rhythm). The frequency of T- rhythm is different from the cardiac frequency and can be different from those of ventilatory and respiratory rhythms, suggesting that T-rhythm is generated by an oscillator independent of periodic drives originating from the arterial baroreceptors, the ventilation afferents and the respiratory network. Using the rat's tail circulation as a model, the purpose of the present study is: 1) to determine whether activity from different single PGNs is generated by multiple oscillators. 2) to establish whether synchronization of single PGNs is an obligatory feature and if not, how it is regulated. 3) to determine whether periodically driven single PGN oscillators exhibit dynamics as predicted by the theory of nonlinear coupled oscillators. 4) to explain the discharge behaviour of whole nerve activity based on the findings at single PGN level. The experiments were conducted in anaesthetized Sprague-Dawley rats. Population PGN activity was recorded from the ventral collector nerve (VCN) of the tail. Single PGN activity was recorded focally from the surface of the CVA. The interaction between two single PGNs was studied by recording two units simultaneously. The discharge behaviours of PGNs in response to a periodic input were studied using the central respiratory drive (CRD) and lung-inflation cycle (LlC)-related activity as the driving forces. The findings from the present study suggest that: 1) Activity of CVA PGNs is generated by multiple oscillators independent of CRD, LIC-related activity and cardiac activity. 2) The multiple PGN oscillators are capable of dynamic synchronization. 3) When subjected to frequency changes of LICs, single PGNs exhibit dynamics, such as 1:1 entrainment, relative coordination, high order rational frequency-lock, asynchrony, characterising nonlinear coupled oscillators. 4) Population PGN activity should be considered as output activity from a pool of dynamically interactive multiple oscillators rather than that from a single oscillator

Decentralized Event-Triggered Consensus of Linear Multi-agent Systems under Directed Graphs

An event-triggered control technique for consensus of multi-agent systems with general linear dynamics is presented. This paper extends previous work to consider agents that are connected using directed graphs. Additionally, the approach shown here provides asymptotic consensus with guaranteed positive inter-event time intervals. This event-triggered control method is also used in the case where communication delays are present. For the communication delay case we also show that the agents achieve consensus asymptotically and that, for every agent, the time intervals between consecutive transmissions is lower-bounded by a positive constant.Comment: 9 pages, 5 figures, A preliminary version of this manuscript has been submitted to the 2015 American Control Conferenc

Synchronization of heterogeneous harmonic oscillators for generalized uniformly jointly connected networks

The synchronization problem for heterogeneous harmonic oscillators is investigated. In practice, the communication network among oscillators might suffer from equipment failures or malicious attacks. The connection may switch extremely frequently without dwell time, and can thus be described by generalized uniformly jointly connected networks. We show that the presented typical control law is strongly robust against various unreliable communications. Combined with the virtual output approach and generalized Krasovskii-LaSalle theorem, the stability is proved with the help of its cascaded structure. Numerical examples are presented to show the correctness of the control law

Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation.

This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation. In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The main contribution is threefold. First of all, a convergence analysis of the iterative behavior of two novel classes of order-preserving nonlinear maps is carried out, thus establishing sufficient conditions which guarantee convergence toward a fixed point of the map: nonnegative row-stochastic matrices turns out to be a special case. Secondly, these results are applied to MASs, both in discrete and continuous-time: local properties of the agents' dynamics have been identified so that the global interconnected system falls into one of the above mentioned classes, thus guaranteeing its global stability. Lastly, a sufficient condition on the connectivity of the communication network is provided to restrict the set of equilibrium points of the system to the consensus points, thus ensuring the agents to achieve consensus. These results do not rely on standard tools (e.g., Lyapunov theory) and thus they constitute a novel approach to the analysis and control of multi-agent dynamical systems. In the second part the focus is on the design of dynamic estimation algorithms in large networks which enable to solve specific problems. The first problem consists in breaking synchronization in networks of diffusively coupled harmonic oscillators. The design of a local state feedback that achieves desynchronization in connected networks with arbitrary undirected interactions is provided. The proposed control law is obtained via a novel protocol for the distributed estimation of the Fiedler vector of the Laplacian matrix. The second problem consists in the estimation of the number of active agents in networks wherein agents are allowed to join or leave. The adopted strategy consists in the distributed and dynamic estimation of the maximum among numbers locally generated by the active agents and the subsequent inference of the number of the agents that took part in the experiment. Two protocols are proposed and characterized to solve the consensus problem on the time-varying max value. The third problem consists in the average state estimation of a large network of agents where only a few agents' states are accessible to a centralized observer. The proposed strategy projects the dynamics of the original system into a lower dimensional state space, which is useful when dealing with large-scale systems. Necessary and sufficient conditions for the existence of a linear and a sliding mode observers are derived, along with a characterization of their design and convergence properties