Invariant Representations of Rigid-body Motion Trajectories with Application to Motion Recognition and Robot Learning by Demonstration

Future robots are expected to operate in unpredictable and changing environments, not only in industry but also in domestic settings and in health care. These environments furthermore require a close interaction and collaboration with humans. To understand human motions and to successfully generate motions according to the changing state of the environment, an internal representation of the motion is required in the form of a motion model. Using the learning by demonstration approach, motion models can be constructed from the measured trajectory coordinates of demonstrated motions. However, these coordinates vary depending on the context in which the motion is recorded, such as the choice of reference frame, the chosen reference points on the tracked object, the location in space, and the motion profile with which the motion is executed. These contextual dependencies make it challenging for motion models to recognize and/or generate new motions in situations that are not demonstrated, so that extensive data sets are often required to compensate. The objective of this research is to represent demonstrated motions more generally in order to achieve fewer demonstrations for recognizing and generating motions in different situations. The focus is on motion trajectories of rigid bodies, such as manipulated objects by the human or the motion of the end effector of a robot manipulator. In the developed approach, demonstrated motions are first transformed to an innovative invariant representation that captures the essential, unchanging features of the given motion. As a consequence, these invariants no longer depend on the context in which the motion was recorded. This results in a clear separation between the essential motion information that is contained in the invariants and the contextual motion information. The first contribution of this thesis is a taxonomy of different existing and new invariant representations for rigid-body motion, listing their invariant properties. This allows application developers to select the invariant representation most suitable for their application. The second contribution is a validation of the invariant properties of the proposed trajectory descriptors in motion recognition experiments. The results show an improvement of the recognition rate when using invariant motion models, since a large reduction in search space is achieved during recognition. The third contribution is a novel optimization-based method for generalizing demonstrated motion trajectories to novel situations. Similarity with the original demonstration is guaranteed by minimizing deviation between the invariants of the generated trajectory and the invariants of the demonstrated trajectory. The context of the new situation can be imposed in the constraints of the optimization problem, including new target locations, robot platform constraints, or obstacle avoidance. The fourth and final contribution is a novel optimization-based method for calculating invariant representations. This method remedies typical calculation difficulties with respect to measurement noise sensitivity and singular points, where invariants are undefined. The new calculation method improves the recognition rate during motion recognition and eliminates trajectory errors before generalizing motions in learning by demonstration. These results encourage the use of invariant representations in motion recognition and learning by demonstration applications, since fewer demonstrations are required to construct generally valid motion models.status: publishe