  It is highly believed that the individuals' mobility plays an important role
in phase transition in animal collective motion. Here, we propose a model to
study the effects of individuals' mobility in a distributed animal collective
decision-making process, during which each individual faces two options with
equal quality. We implement the quorum response rule, a type of social
interaction rule which is taxonomically recognized in animal collective
decision-making, as the sole interaction rule. After the introduction of
individuals' mobility, we find that the group can reach a consensus decision at
one of the options at some critical points even the interaction is local. This
result is an obvious contrast to the stationary individuals, the population of
which is always equally distributed between the two options with fluctuations.
In order to explore the information dynamics, we introduce an important
information-theoretic measure, mutual information, to study the critical
behaviors. Furthermore, we study the case when individuals interact globally,
and also find some qualitative similar critical behaviors.
