In response to the cognitivistic paradigm and its problems, the embodied cognition viewpoint was proposed. In robotics, this resulted in a radical move away from higher-level cognitive functions toward direct, almost "brain-less" interaction with the environment (e.g., behavior-based robotics). While some remarkable behaviors were demonstrated, the complexity of tasks the agents could master remained limited. A natural extension of this approach lies in letting the agents extract regularities in sensorimotor space and exploit them for more effective action guidance. We will use a collection of case studies featuring a quadruped robot to concretely explore this space of minimally cognitive phenomena and contrast the concepts of body schema, forward internal models, and sensorimotor contingencies. The results will be interpreted from a "grounded cognition" and a non-representationalist or enactive perspective. Finally, the utility of robots as cognitive science tools and their compatibility with different cognitive science paradigms will be discussed.