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 five fundamentally different and widely used movement encoding and generation frameworks: dynamic movement primitives (DMPs), time based Gaussian mixture regression (tbGMR), stable estimator of dynamical systems (SEDS), Probabilistic Movement Primitives (ProMP) and Optimal Control Primitives (OCP). 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 and OCPs are the most efficient 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, OCPs and task parameterized GMM (TP-GMM, movement generalisation framework based on tbGMR) lead to similar performance, which ProMPs only achieve when using many demonstrations for learning. All models outperform SEDS, which additionally proves to be difficult to fit. Furthermore we observe that TP-GMM and SEDS suffer from problems reaching the end-points of generalizations.These different quantitative results will help selecting the most appropriate models and designing trajectory representations in an improved task-dependent way in future robotic applications.

翻译：运动生成及其对未见情况的泛化能力在机器人学中扮演着重要角色。存在不同类型的运动生成方法，例如基于样条的方法、基于动力系统的方法以及基于高斯混合模型（GMM）的方法。本文利用一个大规模全新的人体操作运动数据集，对五种本质上不同且广泛使用的运动编码与生成框架进行了详细比较：动态运动基元（DMP）、基于时间的高斯混合回归（tbGMR）、动力系统稳定估计器（SEDS）、概率运动基元（ProMP）和最优控制基元（OCP）。我们从运动编码效率、重建精度和运动泛化能力三个方面对这些框架进行了比较。该新数据集包含由12名受试者执行的九种物体操作动作：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：在运动编码与重建方面，若使用足够数量的核函数，DMP和OCP在参数数量和重建精度上最为高效；在运动泛化至新起点和终点的情况下，DMP、OCP以及基于tbGMR的任务参数化GMM（TP-GMM）表现相近，而ProMP仅在利用大量演示学习时才能达到类似性能。所有模型均优于SEDS，且SEDS还表现出拟合困难的问题。此外，我们观察到TP-GMM和SEDS在泛化过程中难以到达终点。这些定量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选择最合适的模型并设计轨迹表示。