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Animals are able to imitate each others' behavior, despite their difference in biomechanics. In contrast, imitating other similar robots is a much more challenging task in robotics. This problem is called cross domain imitation learning (CDIL). In this paper, we consider CDIL on a class of similar robots. We tackle this problem by introducing an imitation learning algorithm based on invariant representation. We propose to learn invariant state and action representations, which align the behavior of multiple robots so that CDIL becomes possible. Compared with previous invariant representation learning methods for similar purposes, our method does not require human-labeled pairwise data for training. Instead, we use cycle-consistency and domain confusion to align the representation and increase its robustness. We test the algorithm on multiple robots in the simulator and show that unseen new robot instances can be …