In joint action, we succeed in “staying in-the-loop” thanks to sensorimotor synchronization (SMS), which allows us to develop internal models of both self-and other- actions, and to integrate these models in real-time. The present study aimed to evaluate whether and how SMS implemented on a humanoid robot can facilitate planned coordination and perception of shared agency in HRI. To this end, we developed a joint tapping task in which participants were asked to play a melody together with the humanoid iCub robot. Across different blocks, we manipulated the amount of temporal adaptation (reactive error correction) and anticipation (predictive processing) applied by the robot in relation to its human partner to resemble (or not) parameters of human behaviour. At the end of each block, participants rated the perceived shared agency with the robot. Results showed that better performance, i.e. lower mean asynchrony, and lower variability in asynchrony occurred when the robot acted based on human-like parameters of temporal adaptation and anticipation. In addition, shared agency ratings were affected by the human-likeness of the parameters applied to control iCub’s behaviour. Together, our results suggest that endowing robots with temporal adaptation and anticipation mechanisms allows humans to successfully stay in-the-loop in HRI, in two different ways. Firstly, the need to constantly update our internal model of iCub to reduce the prediction error about its performance results in higher synchronization and more strength in coupling when the robot is run based on human-like parameters. Secondarily, by increasing the perception of shared agency.