Action, State and Effect Metrics for Robot 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 behaviour can be mathematically determined by such correspondence mappings, which may serve to guide a robotic imitator. The approach is illustrated in a number of examples, using agents described by simple kinematic models and different types of correspondence mappings. Also, focusing on aspects of displacement and orientation of manipulated objects, a selection of metrics are presented, towards a characterization of the space of effect metrics.