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This paper presents a model that describes physical interactions during dyadic collaborative tasks. This model is based on a homotopy between two controllers and defines the behavior of each partner as the result of a time-varying balance between two roles: the leader role, which consists in acting according to a plan without considering the other partner's intentions; and the follower role, which conversely consists in acting only based on the intentions of the other partner. The continuous switch between these two attitudes is described by two variables whose time-profile can define a task signature. After a brief presentation of the model, two illustrative scenarios are detailed to give more insights on how the homotopy parameter can be used to describe different situations that can occur in collaborative tasks between two partners. We especially focus on how some recent results in the human-human interaction can be encompassed by our proposed model. Experiments are performed to assess the usability of the model as a control scheme to implement advanced collaborative behaviors on a robotic platform.