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,linearandangularscaling.Invariantpropertiesof the proposed representation enable to recognize gestures in realistic scenarios with unexpected variations (e.g., changes inuser’sinitialpose,executiontimeoranobservationpoint), 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 recognizeshumanactionsandexecutesrobot’sproperbehaviors using same descriptors. By removing the dependency on absolute pose and scaling factors of the Cartesian trajectories the proposed descriptor achieves flexibility to generate differentmotioninstancesfromthesameinvariant representation.Inordertoillustratetheeffectivenessofourproposed descriptor in motion recognition and generation, it is tested onthreedatasetsandexperimentsonaNAOhumanoidrobot and a KUKA LWR IV+ manipulator and compared with other existing invariant representations.

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