Correspondence mapping induced state and action metrics for robotic imitation

This paper addresses the problem of body mapping in robotic imitation where the demonstrator and imitator may not share the same embodiment [degrees of freedom (DOFs), body morphology, constraints, affordances, and so on]. Body mappings are formalized using a unified (linear) approach via correspondence matrices, which allow one to capture partial, mirror symmetric, one-to-one, one-to-many, many-to-one, and many-to-many associations between various DOFs across dissimilar embodiments. We show how metrics for matching state and action aspects of behavior can be mathematically determined by such correspondence mappings, which may serve to guide a robotic imitator. The approach is illustrated and validated in a number of simulated 3-D robotic examples, using agents described by simple kinematic models and different types of correspondence mappings.