The flexible coordination of individuals’ movements ensures rapid and coherent
changes in direction of travel of fish schools for instance as a reaction to a
predator detected in the neighbourhood. However the ’microscopic level’
interaction rules involved in the coordination of fish movements and the
adapted collective response of a school still remain to a large extent
unknown. Knowing such interaction rules could offer new sources of inspiration
to design distributed control algorithms for swarms of drones. Here we present
a systematic methodology to measure and analyze social interactions
controlling the collective motion of animal groups. Contrary to classical
forces between physical objects, social interactions between individuals
explicitly depend on their relative headings and are affected by their
anisotropic and asymmetric perception of their environment. Hence they
strongly break the Newtonian’s law of action-reaction. When applied to fish
groups, this approach leads to the quantitative measurement of the spontaneous
behaviour of a fish, of its avoidance interaction with the tank walls, and of
its attraction and alignment interaction with another fish. We use the results
of this analysis to build an explicit and faithful model that convincingly
reproduces quantitative and qualitative features of the actual fish dynamics.
We also show that the type of models derived from such analysis reproduces the
main collective states observed in actual fish schools, when one varies the
intensity of the alignment and attraction interactions between fish.