{'fraction_non_alphanumeric': 0.02046204620462046, 'fraction_numerical': 0.0013201320132013201, 'mean_word_length': 5.737777777777778, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dynamic Movement Primitives Plus: For enhanced reproduction quality and efficient trajectory modification using truncated kernels and Local Biases

Dynamic Movement Primitives (DMPs) are a generic approach for trajectory modeling in an attractor land-scape based on differential dynamical systems. DMPs guarantee stability and convergence properties of learned trajectories, and scale well to high dimensional data. In this paper, we propose DMP+, a modified formulation of DMPs which, while preserving the desirable properties of the original, 1) achieves lower mean square error (MSE) with equal number of kernels, and 2) allows learned trajectories to be efficiently modified by updating a subset of kernels. The ability to efficiently modify learned trajectories i) improves reusability of existing primitives, and ii) reduces user fatigue during imitation learning as errors during demonstration may be corrected later without requiring another complete demonstration. In addition, DMP+ may be used with existing DMP techniques for trajectory generalization and thus complements them. We compare the performance of our proposed approach against DMPs in learning trajectories of handwritten characters, and show that DMP+ achieves lower MSE in position deviation. We demonstrate in a second experiment that DMP+ can efficiently update a learned trajectory by updating only a subset of kernels. The update algorithm achieves modeling accuracy comparable to learning the adapted trajectory with the original DMPs.