A better understanding of the nature of human relationships can aid the design of effective and appropriate social behaviour for robots. The investigation of human bonding via robotic modelling can also serve to test psychological theories in an embodied setting. In this work we present a robotic model of “attachment”—the primary bond between child and caregiver that shapes relationship behaviour throughout our lives. Following a dynamical systems approach, we model attachment as a behavioural coupling between motivational oscillators and show, by means of a dynamical analysis, that coupled robot dyads generate dynamical patterns that resemble caregiver-child interactions. By demonstrating coupling in an embodied model, we also show that measures of physical and emotional distance (a psychological variable), inferred from sensory data, can serve as effective control parameters for attachment behaviour. We find that this oscillator framework generates rich patterns of robot behaviours that can be associated with quantitative and qualitative observations of the “strange situation” procedure, an experimental paradigm that is widely studied in human relationship science, and of human avoidant and ambivalent attachment styles. The ability to estimate human attachment style and to generate appropriately-matched robot behaviours could be useful in social and companion robotics.