The main result of this paper is a new model based on homotopy switching between intrinsically distinct controllers, to encompass most behaviors encountered in dyadic haptic collaborative tasks through an intermediate object. The basic idea is to switch continuously between two distinct extreme behaviors (leader and follower) for each individual, which creates an implicit bilateral coupling within the dyad. The physical collaborative interaction is then described only with two distinct homotopy time-functions that vary independently. These functions can likely describe the signature of a collaborative task. A virtual reality haptic set-up is used to assess the proposed theory.