Biomimetic robots are promising tools in animal behavioural studies. If they are socially integrated in a group of animals, they can produce calibrated social stimuli to test the animal responses. However, the design of such social robots is challenging as it involves both a luring capability including appropriate robot behaviours, and the acceptation of the robots by the animals as social companions. Here, we investigate the integration of a biomimetic robot driven by biomimetic behavioural models into a group of zebrafish (Danio rerio). The robot behaviours are based on a stochastic model linking zebrafish visual perception to individual behaviour and calibrated experimentally to correspond to the behaviour of zebrafish. We show that our robot can be integrated into a group of zebrafish, mimic their behaviour and exhibit similar collective dynamics compared to fish-only groups. This study shows that an autonomous biomimetic robot was enhanced by a biomimetic behavioural model so that it can socially integrate into groups of fish.