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In this paper we propose a new bidirectional invariant motion descriptor of a rigid body. The proposed invariant representation is not affected by rotations, translations, time, linear and angular scaling. Invariant properties of the proposed representation enable to recognize gestures in realistic scenarios with unexpected variations (e.g., changes in user’s initial pose, execution time or an observation point), while Cartesian trajectories are sensitive to these changes. The proposed invariant representation also allows reconstruction of the original motion trajectory, which is useful for human-robot interaction applications where a robot recognizes human actions and executes robot’s proper behaviors using same descriptors. By removing the dependency on absolute pose and scaling factors of the Cartesian trajectories the proposed descriptor achieves flexibility to generate different motion instances from the same invariant representation. In order to illustrate the effectiveness of our proposed descriptor in motion recognition and generation, it is tested on three datasets and experiments on a NAO humanoid robot and a KUKA LWR IV+ \ud manipulator and compared with other existing invariant representations

Bidirectional invariant representation of rigid body motions and its application to gesture recognition and reproduction