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Self-organisation refers to the ability of systems made of a large number of independent agents inter-acting through local rules to generate large-scale spatio-temporal coherent structures. The emergent properties of interacting agents span systems and scales, from cells forming biological tissues, fish schools moving in synchrony, animal migrations across continents, to robot swarms.

By bringing together analysts, mathematical biologists and robotics researchers, this workshop provided a broad overview of the various self-organisation mechanisms that prevail at the various scales and the mathematical models by which they can be described. The aim was to make progress towards determining the key mechanisms that enable self-organisation at each scale and across the scales and towards the derivation of suitable ‘universal’ mathematical models able to describe them.

The microscopic control available in swarm robotic systems adds novel challenges in the modelling of interactions and their optimal design. For the mathematicians, this new application will broaden the repertoire of systems and research questions with which to confront their methodologies and practice.