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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.

A topological extension of movement primitives for curvature modulation and sampling of robot motion