We contend that our relationship with robots is too often seen within a universalistic and individualistic mind-frame. We propose a specific perspective in social robotics that we call anthrobotics. Anthrobotics starts with the choice to consider the human-machine intertwining as a dynamic union of more or less institutionalised collectives rather than separated discrete realities (individual humans, on one side, and discrete individualised machines on the other). We draw on our research in types of social interaction and esprit de corps to imagine more plural and harmonious forms of shared natural-artificial cognitive systems. We propose to look at four types of organised groups: conformative, autonomist, creative, and universalistic, that may provide guiding principles for the design of more diverse anthrobots.