Embodied timing turns a robotic tug-of-war into cooperative transport
Living systems move loads with agents that pull against one another. Kinesin and dynein pull one vesicle, ants haul a dead insect, and antagonist muscles move a joint. Whether the timing of the forces can, by itself, determine which side moves the load is not well understood. Here, combining experiments, theory, and simulations of a tug-of-war between two matched teams of spring-coupled robots, we show that the relative timing of the pull forces breaks the symmetry and decides the contest. Teams pulling in unison or in strict alternation tie. Between these, the lagging team wins, most strongly near a quarter cycle, because the springs unload while the leading team coasts and the lagging team still pulls. In the model and in robot simulations, braking rather than coasting between pulls, once strong enough, shifts the advantage to the leading team. Winning and losing leave distinct signatures in each robot's motor current. Using these local signals, we formulate an embodied decentralized phase-adaptation rule that enables transient leadership to switch between teams, allowing the collective to transport high-friction cargo and to navigate around obstacles towards a prescribed target without explicit communication.