A mounting body of evidence in psychology and neuroscience points towards an embodied model of cognition, in which the mechanisms governing perception and action are strongly interconnected, and also play a central role in higher cognitive functions, traditionally modeled as amodal symbol systems. We argue that robots designed to interact fluidly with humans must adopt a similar approach, and shed traditional distinctions between cognition, perception, and action. In particular, embodiment is crucial to fluid joint action, in which the robot's performance must tightly integrate with that of a human counterpart, taking advantage of rapid sub-cognitive processes. We thus propose a model for embodied robotic cognition that is built upon three propositions: (a) modal, perceptual models of knowledge; (b) integration of perception and action; (c) top-down bias in perceptual processing. We then discuss implications and derivatives of our approach.