Self-Organizing Synchronization with Stochastic Coupling

Swarms of synchronously blinking fireflies are fascinating examples for self-organization in nature. The beauty of this spectacular phenomenon lies in its emergent behavior: only sim- ple rules in each entity and localized interactions lead to synchrony of the entire swarm. The mobile computing and telecommunications community has been interested to transfer mathematical models describing firefly synchronization to wireless systems where time syn- chronization is important for many functions. A one-to-one transfer is, however, infeasible due to the differences between biological and wireless communications. Many modifications and extensions were made to finally develop firefly-inspired algorithms that work well in wireless networks. It is an interesting finding that unreliable channels or intentionally incomplete communica- tion between entities can have beneficial effects on synchronization guarantees and preci- sion. Such stochastic coupling opens up an unprecedented degree of freedom for the design of network synchronization algorithms, which will be investigated in the proposed project. Our objective is to gain a deeper conceptual understanding and to exploit it in real networks. Results are expected to yield scientific contributions in synchronization theory and novel algorithms for use in practice. After assessing the theoretical gains of stochasticity in cou- pling, we develop different classes of decentralized adaptive algorithms for mobile networks in which each node continuously adjusts its individual coupling probability based only on its local system view. The synchronization precision and time are investigated experimentally using programmable hardware. Applications can be found for instance in large-scale sensor and robot networks in smart factories.

Nature reveals many phenomena of self-organization, like synchronizing fireflies and neurons in the brain, as well as coordinated movements in flocks of birds and schools of fish. What is fascinating about these systems is their emergent behavior: simple rules governing each entity and localized interactions lead to coordinated behavior of the entire system. There are numerous mathematical models on how the entities of self-organizing systems interact, i.e., how they exchange and adjust their states. It is an intriguing insight that unreliable or deliberately random interactions can yield advantageous effects regarding convergence and precision. This concept, called "stochastic coupling," grants an unprecedented degree of freedom for designing algorithms tailored to technological systems like robot swarms. This project contributed to a better understanding of stochastic coupling and its potential benefits. It showed how stochastic coupling and more general methods of randomization can significantly improve self-organized processes in many ways or enable them to work in the first place. With emphasis on self-organized synchronization (i.e., coordination in time), the following questions were tackled and treated: How do we synchronize wireless systems if interference disturbs the synchronization process? It was shown how randomization techniques can counteract interference in this context. To illustrate, we demonstrated that simple random switching between two or more transmit power levels can accelerate synchronization without raising the average power consumption. What causes non-synchronization, and how to avoid it? We identified reasons for networks not to synchronize, derived conditions for the occurrence of deadlocks, and demonstrated that the probability of synchronization improves if each entity uses a local rather than global coupling parameter. In addition to studying synchronization, we explored the fusion of synchronization and swarming into a cohesive model, where synchronization influences swarming and vice versa. Such systems, called "swarmalators" (O'Keeffe et al.), lead to visually appealing space-time patterns. One of our contributions was to make swarmalators more resource-efficient by using stochastic coupling to randomize interactions, thus reducing the overhead. Moreover, we demonstrated how to transfer the theories of synchronization and swarmalation to technology, specifically mobile robots with Wi-Fi connectivity, albeit requiring non-trivial modifications. We adapted and extended self-organized synchronization and swarmalators for wireless systems, implemented them in the Robot Operating System 2, and demonstrated their feasibility in multi-robot and drone systems. Doing so provided the first-ever proof of concept for swarmalators functioning within a technological system (see video: https://www.youtube.com/watch?v=atLhROLzsFo). Our extensions considered real-world constraints (like message-based communication, limited communication range, and physical collision avoidance) and disturbances (like non-identical clock rates, delays, and localization errors).