In this paper, we investigate a control strategy of synthesized interaction-sounds. The framework of our research is based on the action/object paradigm that considers that sounds result from an action on an object. This paradigm presumes that there exists some sound invariants, i.e. perceptually relevant signal morphologies that carry information about the action or the object. Some of these auditory cues are considered for rubbing, scratching and rolling interactions. A generic sound synthesis model, allowing the production of these three types of interaction together with a control strategy of this model are detailed. The proposed control strategy allows the users to navigate continuously in an ”action space”, and to morph between interactions, e.g. from rubbing to rolling.