  Collective motion by animal groups is affected by internal interactions,
external constraints and the influx of information. A quantitative
understanding of how these different factors give rise to different modes of
collective motion is, at present, lacking.} Here, we study how ants that
cooperatively transport a large food item react to an obstacle blocking their
path. Combining experiments with a statistical physics model of mechanically
coupled active agents, we show that the constraint induces a deterministic
collective oscillatory mode that facilitates obstacle circumvention. We provide
direct experimental evidence, backed by theory, that this motion is an emergent
group effect that does not require any behavioral changes at the individual
level. We trace these relaxation oscillations to the interplay between two
forces; informed ants pull the load towards the nest while uninformed ants
contribute to the motion's persistence along the tangential direction. The
model's predictions that oscillations appear above a critical system size, that
the group can spontaneously transition into its ordered phase, and that the
system can exhibit complete rotations are all verified experimentally. We
expect that similar oscillatory modes emerge in collective motion scenarios
where the structure of the environment imposes conflicts between individually
held information and the group's tendency for cohesiveness.
