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The version of record is available online at: https://doi.org/10.1007/s10514-021-09976-7 ; 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. ; This work has been carried out within the project CLOTHILDE ("CLOTH manIpulation Learning from DEmonstrations") funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Advanced Grant agreement No 741930). Research at IRI is also supported by the Spanish State Research Agency through the Mar ́ıa de Maeztu Seal of Excellence to IRI MDM-2016-0656 ; Peer Reviewed ; Postprint (author's final draft)

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. ; Learning from Demonstration (LfD) is a paradigm that allows robots to learn complex manipulation tasks that can not be easily scripted, but can be demonstrated by a human teacher. One of the challenges of LfD is to enable robots to acquire skills that can be adapted to different scenarios. In this paper, we propose to achieve this by exploiting the variations in the demonstrations to retrieve an adaptive and robust policy, using Gaussian Process (GP) models. Adaptability is enhanced by incorporating task parameters into the model, which encode different specifications within the same task. With our formulation, these parameters can be either real, integer, or categorical. Furthermore, we propose a GP design that exploits the structure of replications, i.e., repeated demonstrations with identical conditions within data. Our method significantly reduces the computational cost of model fitting in complex tasks, where replications are essential to obtain a robust model. We illustrate our approach through several experiments on a handwritten letter demonstration dataset. ; This work has been partially funded by the European Union Horizon 2020 Programme under grant agreement no. 741930 (CLOTHILDE) and by the Spanish State Research Agency through the Mar ́ıa de Maeztu Seal of Excellence to IRI [MDM-2016-0656]. ; Peer Reviewed ; Postprint (author's final draft)