| dc.description.abstract | While self-organised complex systems in nature continually provide inspiration for the burgeoning field of swarm robotics, the intriguing phenomenon of bee shimmering, referring to the emergent patterns formed by bees on the nest surface as a defense mechanism in response to predator attacks, has yet to receive rigorous mathematical scrutiny. This research endeavours to fill this gap by presenting the first mathematical model for the bee shimmering phenomenon, aiming to leverage its inherent self-organisation and rapid communication for applications in swarm robotics, particularly in detection and search missions. The thesis initially sets out to develop the first mathematical model rigorously for bee shimmering, focusing on deriving conditions for the various types of wave propagation dynamics and wave strength emerging from interactions at the microscale. The development of detection and search algorithms for swarm robotics stems from the modelling of bee shimmering. A combination of computational and experimental modelling is grounded in statistical mechanics to investigate these algorithms, simulating up to 10,000 robotic agents and validating the results by employing the Kilobots. The dynamical systems model for bee shimmering not only simulates the different regimes of the phenomena with up to 1,000,000 bee agents, but also successfully supports the experimental studies showing that the constructed wave strength function can be adapted to peak between 50-150ms. The detection algorithm, rooted in complex network theory harnesses the rapid communication properties of the major shimmering waves to identify a desired agent within 5 seconds experimentally through the use of 13 Kilobot agents along with simulations consisting of up to 5000 robotic agents. A novel mathematical method is also presented using the properties of partition functions from statistical mechanics to solve mean-field equations for growing spatial networks. The search algorithm incorporates Boltzmann distributions, collision cylinders and branching processes from statistical mechanics, to locate a lost agent traversing as many agents as possible through Kilobot experiments and simulations. Moreover, the search algorithm shows versatility in replicating all bee shimmering wave types through simulation, consisting of up to 10,000 robotic agents. This work represents a pioneering advancement in mathematical biology and swarm robotics, establishing the first comprehensive analytical model of bee shimmering and its application. This advancement opens avenues for deploying autonomous swarms in complex tasks such as disaster response and environmental monitoring, where speed and coordination are critical. | en_US |
