Kernelized movement primitives

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 the many advancements that have been achieved, solutions for coping with unpredicted situations (e.g., obstacles and external perturbations) and high-dimensional inputs are still largely absent. 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 owing 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

Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives

During the past few years, probabilistic approaches to imitation learning have earned a relevant place in the literature. One of their most prominent features, in addition to extracting a mean trajectory from task demonstrations, is that they provide a variance estimation. The intuitive meaning of this variance, however, changes across different techniques, indicating either variability or uncertainty. In this paper we leverage kernelized movement primitives (KMP) to provide a new perspective on imitation learning by predicting variability, correlations and uncertainty about robot actions. This rich set of information is used in combination with optimal controller fusion to learn actions from data, with two main advantages: i) robots become safe when uncertain about their actions and ii) they are able to leverage partial demonstrations, given as elementary sub-tasks, to optimally perform a higher level, more complex task. We showcase our approach in a painting task, where a human user and a KUKA robot collaborate to paint a wooden board. The task is divided into two sub-tasks and we show that using our approach the robot becomes compliant (hence safe) outside the training regions and executes the two sub-tasks with optimal gains.Comment: Published in the proceedings of IROS 201

Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives

During the past few years, probabilistic approaches to imitation learning have earned a relevant place in the literature. One of their most prominent features, in addition to extracting a mean trajectory from task demonstrations, is that they provide a variance estimation. The intuitive meaning of this variance, however, changes across different techniques, indicating either variability or uncertainty. In this paper we leverage kernelized movement primitives (KMP) to provide a new perspective on imitation learning by predicting variability, correlations and uncertainty about robot actions. This rich set of information is used in combination with optimal controller fusion to learn actions from data, with two main advantages: i) robots become safe when uncertain about their actions and ii) they are able to leverage partial demonstrations, given as elementary sub-tasks, to optimally perform a higher level, more complex task. We showcase our approach in a painting task, where a human user and a KUKA robot collaborate to paint a wooden board. The task is divided into two sub-tasks and we show that using our approach the robot becomes compliant (hence safe) outside the training regions and executes the two sub-tasks with optimal gains.Comment: Submitted to IROS1

A Non-parametric Skill Representation with Soft Null Space Projectors for Fast Generalization

Over the last two decades, the robotics community witnessed the emergence of various motion representations that have been used extensively, particularly in behavorial cloning, to compactly encode and generalize skills. Among these, probabilistic approaches have earned a relevant place, owing to their encoding of variations, correlations and adaptability to new task conditions. Modulating such primitives, however, is often cumbersome due to the need for parameter re-optimization which frequently entails computationally costly operations. In this paper we derive a non-parametric movement primitive formulation that contains a null space projector. We show that such formulation allows for fast and efficient motion generation with computational complexity O(n2) without involving matrix inversions, whose complexity is O(n3). This is achieved by using the null space to track secondary targets, with a precision determined by the training dataset. Using a 2D example associated with time input we show that our non-parametric solution compares favourably with a state-of-the-art parametric approach. For demonstrated skills with high-dimensional inputs we show that it permits on-the-fly adaptation as well

Non-parametric Imitation Learning of Robot Motor Skills

Unstructured environments impose several challenges when robots are required to perform different tasks and adapt to unseen situations. In this context, a relevant problem arises: how can robots learn to perform various tasks and adapt to different conditions? A potential solution is to endow robots with learning capabilities. In this line, imitation learning emerges as an intuitive way to teach robots different motor skills. This learning approach typically mimics human demonstrations by extracting invariant motion patterns and subsequently applies these patterns to new situations. In this paper, we propose a novel kernel treatment of imitation learning, which endows the robot with imitative and adaptive capabilities. In particular, due to the kernel treatment, the proposed approach is capable of learning human skills associated with high-dimensional inputs. Furthermore, we study a new concept of correlation-adaptive imitation learning, which allows for the adaptation of correlations exhibited in high-dimensional demonstrated skills. Several toy examples and a collaborative task with a real robot are provided to verify the effectiveness of our approach

Generalized Orientation Learning in Robot Task Space

In the context of imitation learning, several approaches have been developed so as to transfer human skills to robots, with demonstrations often represented in Cartesian or joint space. While learning Cartesian positions suffices for many applications, the end-effector orientation is required in many others. However, several crucial issues arising from learning orientations have not been adequately addressed yet. For instance, how can demonstrated orientations be adapted to pass through arbitrary desired points that comprise orientations and angular velocities? In this paper, we propose an approach that is capable of learning multiple orientation trajectories and adapting learned orientation skills to new situations (e.g., via-point and end-point), where both orientation and angular velocity are addressed. Specifically, we introduce a kernelized treatment to alleviate explicit basis functions when learning orientations. Several examples including comparison with the state-of-the-art dynamic movement primitives are provided to verify the effectiveness of our method

Leveraging Kernelized Synergies on Shared Subspace for Precision Grasping and Dexterous Manipulation

Manipulation in contrast to grasping is a trajectorial task that needs to use dexterous hands. Improving the dexterity of robot hands, increases the controller complexity and thus requires to use the concept of postural synergies. Inspired from postural synergies, this research proposes a new framework called kernelized synergies that focuses on the re-usability of same subspace for precision grasping and dexterous manipulation. In this work, the computed subspace of postural synergies is parameterized by kernelized movement primitives to preserve its grasping and manipulation characteristics and allows its reuse for new objects. The grasp stability of proposed framework is assessed with the force closure quality index, as a cost function. For performance evaluation, the proposed framework is initially tested on two different simulated robot hand models using the Syngrasp toolbox and experimentally, four complex grasping and manipulation tasks are performed and reported. Results confirm the hand agnostic approach of proposed framework and its generalization to distinct objects irrespective of their dimensions