This paper studies the dynamic frictional interactions of the underactuated vibro-driven capsule systems with the viscoelastic property. Frictional dynamics of the capsule systems is an active research domain, while the online implementation and control of the friction models are still intractable tasks. This paper investigates the frictional characteristics of the capsule systems in the dynamic regime, including particularly the non-reversible drooping and hysteresis. Firstly, the frictional interaction dynamics is modelled and characterized using a combined physics-based and analytical-based approach. Subsequently, the qualitative changes in the capsule dynamics and friction-induced vibrational responses that triggered by multiple control parameters are discussed. It is found that the capsule dynamics is mainly periodic, and the motion velocity of the capsule systems can be controlled by appropriate tuning of the control parameters around the identified control points. Simulation results have a good agreement with the experimentally observed frictional characteristics. The effectiveness of the proposed method is verified in terms of satisfaction of the energy requirements and quenching of the friction-induced vibrations. It is also found that the frictional interaction dynamics of the capsule systems can be predicted for a wide range of vibrational behaviours. Finally, the importance of a concrete understanding and accurate description of the dynamic friction at the sliding substrate is highlighted.