This paper proposes to enrich robot motion data with trajectory curvature information. To do so, we use an approximate implementation of a topological feature named writhe, which measures the curling of a closed curve around itself, and its analog feature for two closed curves, namely the linking number. Despite these features have been established for closed curves, their definition allows for a discrete calculation that is well-defined for non-closed curves and can thus provide information about how much a robot trajectory is curling around a line in space. Such lines can be predefined by a user, observed by vision or, in our case, inferred as virtual lines in space around which the robot motion is curling. We use these topological features to augment the data of a trajectory encapsulated as a Movement Primitive (MP). We propose a method to determine how many virtual segments best characterize a trajectory and then find such segments. This results in a generative model that permits modulating curvature to generate new samples, while still staying within the dataset distribution and being able to adapt to contextual variables.

本文提出用轨迹曲率信息来丰富机器人运动数据。为此，我们使用名为writhe的拓扑特征的近似实现，该特征测量围绕自身的闭合曲线的卷曲，以及两条闭合曲线的模拟特征，即链接数. 尽管已经为闭合曲线建立了这些特征，但它们的定义允许对非闭合曲线进行明确定义的离散计算，因此可以提供有关机器人轨迹围绕空间线卷曲多少的信息。这些线可以由用户预定义，通过视觉观察，或者在我们的例子中，推断为机器人运动围绕的空间中的虚拟线。我们使用这些拓扑特征来增强封装为运动基元 (MP) 的轨迹数据。我们提出了一种方法来确定有多少虚拟段最能表征轨迹，然后找到这些段。这导致生成模型允许调节曲率以生成新样本，同时仍保持在数据集分布范围内并能够适应上下文变量。