  A variety of agent-based models has been proposed to account for the
emergence of coordinated collective behavior of animal groups from simple
interaction rules. A common, simplifying assumption of such collective movement
models, is the consideration of individual agents moving with a constant speed.
In this work we critically re-asses this assumption underlying a vast majority
of collective movement models. First, we show the omnipresent speed variability
observed in different species of live fish and artificial agents (RoboFish).
Based on theoretical considerations accounting for inertia and rotational
friction, we derive a functional dependence of the turning response of
individuals on their instantaneous speed (confirmed by experimental data). We
investigate how the interplay of variable speed and speed-dependent turning
affects self-organized collective behavior by implementing an agent-based model
which accounts for both effects. We show, that besides average speed, the
individual speed variability may have a dramatic impact on the emergent
collective dynamics, as two groups differing only in their speed variability,
and being otherwise identical in all other behavioral parameters, can be in two
fundamentally different stationary states. We find that the local coupling
between group polarization and individual speed is strongest at the
order-disorder transition. Furthermore, we demonstrate a decrease in
polarization with group size for groups of individuals with variable speed, and
a sudden decrease in mean individual speed at a critical group size (N=4 for
Voronoi interactions) linked to a topological transition from an all-to-all to
a distributed spatial interaction network. Overall, our work highlights the
importance to account for fundamental kinematic constraints in general, and
variable speed in particular, when modeling self-organized collective dynamics.
