Kernelized movement primitives

Abstract

Imitation learning has been studied widely as a convenient way to transfer human skills to robots. This learning approach is aimed at extracting relevant motion patterns from human demonstrations and subsequently applying these patterns to different situations. Despite many advancements have been achieved, the solutions for coping with unpredicted situations (e.g., obstacles and external perturbations) and high-dimensional inputs are still largely open. In this paper, we propose a novel kernelized movement primitive (KMP), which allows the robot to adapt the learned motor skills and fulfill a variety of additional constraints arising over the course of a task. Specifically, KMP is capable of learning trajectories associated with high-dimensional inputs due to the kernel treatment, which in turn renders a model with fewer open parameters in contrast to methods that rely on basis functions. Moreover, we extend our approach by exploiting local trajectory representations in different coordinate systems that describe the task at hand, endowing KMP with reliable extrapolation capabilities in broader domains. We apply KMP to the learning of time-driven trajectories as a special case, where a compact parametric representation describing a trajectory and its first-order derivative is utilized. In order to verify the effectiveness of our method, several examples of trajectory modulations and extrapolations associated with time inputs, as well as trajectory adaptations with high-dimensional inputs are provided.

Generalized Task-Parameterized Skill Learning

“…However, in many tasks (e.g., the robot bimanual task) the task frames are often relevant to each other, and thus the correlations between frames could be exploited, which might help to accelerate the learning process. In addition, since various movement primitives such as non-parametric [17] and parametric [18] formulations have been developed, a comprehensive comparison needs further exploitation.…”

Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives

“…Finally, it should be noted that the prediction capabilities of KMP are independent of the optimal control framework. Predicting full covariance matrices and uncertainty (as shown here), handling start-/via-/end-points [5], multi-dimensional inputs and orientations [22] are distinguishable features of KMP that we aim to leverage in other robotics applications.…”

“…In KMP, N and λ 2 do not affect the mean prediction as they do not parameterize the kernel function. Moreover, (2) is typically robust to their choice, providing freedom for tuning while yielding proper predictions (see [5] for details).…”

Towards Minimal Intervention Control with Competing Constraints

“…Note that this paper only considers competing constraints that are extracted from demonstrations, which might prevent its application to the cases where significantly different trajectories from demonstrated examples are required. One extension could be the combination of trajectory adaptation approaches (e.g., various movement primitives [19], [20], [21] and hybrid imitation learning [7]) and the presented work. Also, we set the weight matrix R in (6) empirically, which is undesired for complicated systems.…”