Robots can smile, and human mothers can react to that. This study tuned up the timing of this dance:
“Infants Time Their Smiles to Make Their Moms Smile,” Paul Ruvolo, Daniel Messinger, Javier Movellan, PLoS ONE 10(9), 2015, e0136492. The authors, at Olin College of Engineering, the University of Miami, and the University of California San Diego, explain:

“The results of our analysis show that by the time infants reach 4 months of age both mothers and infants time their smiles in a purposeful, goal-oriented manner. In our study, mothers consistently attempted to maximize the time spent in mutual smiling, while infants tried to maximize mother-only smile time. To validate this finding, we ported the smile timing strategy used by infants to a sophisticated child-like robot that automatically perceived and produced smiles while interacting with adults. As predicted, this strategy proved successful at maximizing adult-only smile time. The results indicate that by 4 months of age infants interact with their mothers in a goal-oriented manner, utilizing a sophisticated understanding of timing in social interactions.”
