The goal of Learning from Demonstration is to automatically transfer the skill knowledge from human to robot. Current researches focus on the problem of modeling aperiodic/periodic robot motions and extracting dynamic task parameters from the recorded sensory information. However, it is still not adequate for describing complex behaviors in an unstructured environment, such as searching for an unknown fitting position or painting/polishing an irregular surface. The quasi-periodic and stochastic properties cause a high demand for generalization ability of the modeling techniques. This paper proposes a systematic framework for learning quasi-periodic robot motions, which contains three steps: decomposition, modeling, and synthesization. Firstly FFT transform is performed to identify all the frequencies in the quasi-periodic motion. Then the motion is decomposed into an offset component, a series of harmonic and corresponding envelop components based on the concept of equivalent transformation. The offset component is extracted by Empirical Mode Decomposition, harmonic is separated by notch filter, and envelope component is extracted by Hilbert Transform. These components are either periodic or aperiodic. The aperiodic motions can be modeled by conventional techniques such as Gaussian Mixture Model and recovered by Gaussian Mixture Regression. The periodic motions are modeled in closed-form expressions. Finally, they are synthesized together to regenerate the robot motion. This modeling process captures both the aperiodicity and periodicity of a quasi-periodic motion. Simulation and experiment show that the proposed methods are feasible, effective and can predict robot motions beyond demonstrations. With this generalization ability, it is able to reduce the programming difficulty and demonstration complexity.

中文翻译：

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通过演示学习准周期机器人运动

从演示中学习的目的是自动将技能知识从人转移到机器人。当前的研究集中在建模非周期性/周期性机器人运动以及从记录的感官信息中提取动态任务参数的问题。但是，它仍然不足以描述非结构化环境中的复杂行为，例如寻找未知的贴合位置或对不规则的表面进行涂漆/抛光。准周期和随机特性引起了对建模技术泛化能力的高要求。本文提出了一个学习准周期机器人运动的系统框架，该框架包含三个步骤：分解，建模和合成。首先，执行FFT变换以识别准周期运动中的所有频率。然后，根据等效变换的概念，将运动分解为偏移分量，一系列谐波和相应的包络分量。偏移分量通过经验模式分解提取，谐波通过陷波滤波器分离，包络分量通过希尔伯特变换提取。这些成分是周期性的或非周期性的。非周期性运动可以通过常规技术（例如高斯混合模型）建模，并通过高斯混合回归进行恢复。周期性运动以封闭形式表达。最后，将它们综合在一起以重新生成机器人运动。该建模过程同时捕获了准周期性运动的非周期性和周期性。仿真和实验表明，所提方法是可行的，有效并且可以预测演示以外的机器人动作。通过这种归纳能力，可以降低编程难度和演示复杂度。