In this work, an interactive control architecture based on velocity segments is developed to generate the human-like trajectories in the mirror game, a simple yet effective paradigm for studying interpersonal coordination, and the existence of velocity segments possessing a prescribed signature is theoretically guaranteed. Then an online control algorithm for the architecture is proposed to produce joint improvised motion with a human player or another virtual player while exhibiting some desired kinematic characteristics. Finally, the transition from solo motions to joint improvised motions is illuminated, and the proposed control architecture is validated by matching the experimental data.