Cognitive neuroscience, traditionally focused on individual brains, is just beginning to investigate social cognition through realistic interpersonal interaction. However, quantitative investigation of the dynamical sensorimotor communication among interacting individuals in goal-directed ecological tasks is particularly challenging. Here, we recorded upper-body motion capture of 23 dyads, alternating their leader/follower role, in a tower-building task. Either a strategy of joining efforts or a strategy of independent action could in principle be used. We found that arm reach velocity profiles of participants tended to converge across trials. Automatic imitation of low-level motor control parameters demonstrates that the task is achieved through continuous action coordination as opposed to independent action planning. Moreover, the leader produced more consistent and predictable velocity profiles, suggesting an implicit strategy of signaling to the follower. This study serves as a validation of our joint goal-directed non-verbal task for future applications. In fact, the quantification of human-to-human continuous sensorimotor interaction, in a way that can be predicted and controlled, is probably one of the greatest challenges for the future of human-robot interaction.