Movement generation, and especially generalisation to unseen situations, plays an important role in robotics. Different types of movement generation methods exist such as spline based methods, dynamical system based methods, and methods based on Gaussian mixture models (GMMs). Using a large, new dataset on human manipulations, in this paper we provide a highly detailed comparison of three most widely used movement encoding and generation frameworks: dynamic movement primitives (DMPs), time based Gaussian mixture regression (tbGMR) and stable estimator of dynamical systems (SEDS). We compare these frameworks with respect to their movement encoding efficiency, reconstruction accuracy, and movement generalisation capabilities. The new dataset consists of nine object manipulation actions performed by 12 humans: pick and place, put on top/take down, put inside/take out, hide/uncover, and push/pull with a total of 7,652 movement examples. Our analysis shows that for movement encoding and reconstruction DMPs are the most efficient framework with respect to the number of parameters and reconstruction accuracy if a sufficient number of kernels is used. In case of movement generalisation to new start- and end-point situations, DMPs and task parameterized GMM (TP-GMM, movement generalisation framework based on tbGMR) lead to similar performance and outperform SEDS. Furthermore we observe that TP-GMM and SEDS suffer from inaccurate convergence to the end-point as compared to DMPs. These different quantitative results will help designing trajectory representations in an improved task-dependent way in future robotic applications.

翻译：运动生成，特别是对未知情况的泛化，在机器人学中扮演着重要角色。目前存在不同类型的运动生成方法，如样条基方法、动力系统基方法以及基于高斯混合模型（GMMs）的方法。本文利用一个大规模、新颖的人类操作数据集，对三种最广泛使用的运动编码与生成框架进行了详尽比较：动态运动基元（DMPs）、基于时间的高斯混合回归（tbGMR）以及动力系统稳定估计器（SEDS）。我们从运动编码效率、重构精度以及运动泛化能力三个方面对这些框架进行了对比。该新数据集包含12名人类执行的9种物体操作动作：拾取与放置、放上/取下、放入/取出、隐藏/揭开以及推/拉，共计7,652个运动样本。我们的分析表明：在运动编码与重构方面，若使用足够数量的核函数，DMPs在参数数量与重构精度上是最有效的框架。在针对新起点和终点情况的运动泛化中，DMPs与任务参数化GMM（TP-GMM，基于tbGMR的运动泛化框架）表现相似，且均优于SEDS。此外，我们观察到与DMPs相比，TP-GMM和SEDS存在终点收敛不准确的问题。这些定量比较结果将有助于在未来的机器人应用中，以改进的任务依赖方式设计轨迹表示。