This article describes research in which embodied imitation and behavioral adaptation are investigated in collective robotics. We model social learning in artificial agents with real robots. The robots are able to observe and learn each others' movement patterns using their on-board sensors only, so that imitation is embodied. We show that the variations that arise from embodiment allow certain behaviors that are better adapted to the process of imitation to emerge and evolve during multiple cycles of imitation. As these behaviors are more robust to uncertainties in the real robots' sensors and actuators, they can be learned by other members of the collective with higher fidelity. Three different types of learned-behavior memory have been experimentally tested to investigate the effect of memory capacity on the evolution of movement patterns, and results show that as the movement patterns evolve through multiple cycles of imitation, selection, and variation, the robots are able to, in a sense, agree on the structure of the behaviors that are imitated.