Effect of time delays on agents' interaction dynamics

While speaking about social interaction, psychology claims as crucial the temporal correlations between interactants’ behaviours: to give to their partners a feeling of natural interaction, interactants, be human, robotic or virtual, must be able to react on appropriate time. Recent approaches consider autonomous agents as dynamical systems and the interaction as a coupling between these systems. These approaches solve the issue of time handling and enable to modelise synchronisation and turn-taking as phenomenon emerging with the coupling. But when complex computations are added to their architecture, such as processing of video and audio signals, delays appear within the interaction loop and disrupt this coupling. We modelise here a dyad of agents where processing delays are controlled. These agents, driven by oscillators, synchronise and take turns when there is no delay. We describe the methodology enabling to evaluate the synchrony and turn-taking emergence. We test oscillators coupling properties when there is no delay: coupling occurs if coupling strenght is inferior to the parameter controlling oscillators natural period and if the ratio between oscillators periods is inferior to 1/2. We quantify the maximal delays between agents which do not disrupt the interaction: the maximal delay tolerated by agents is proportional to the natural period of the coupled system and to the strenght of the coupling. These results are put in perspective with the different time constraints of human-human and human-agent interactions.