Gaussian Mixture Model for 3-DoF orientations

Abstract-In the context of robotic control, synergies can form elementary units of behavior. By specifying taskdependent coordination behaviors at a low control level, one can achieve task-specific disturbance rejection. In this work we present an approach to learn the parameters of such lowlevel controllers by demonstration. We identify a synergy by extracting covariance information from demonstration data. The extracted synergy is used to derive a time-invariant state feedback controller through optimal control. To cope with the non-Euclidean nature of robot poses, we utilize Riemannian geometry, where both estimation of the covariance and the associated controller take into account the geometry of the pose manifold. We demonstrate the efficacy of the approach experimentally in a bimanual manipulation task.

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“…[18]- [20]). In [5], we showed how operations commonly used in probabilistic imitation learning can be generalized to Riemannian manifolds.…”

Section: Preliminariesmentioning

confidence: 99%

Learning task-space synergies using Riemannian geometry

Zeestraten

Havoutis

Calinon

et al. 2017

2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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“…Similar issue also arises in the contracting dynamics model [15]. Another solution of learning orientation was proposed in [16], where GMM was employed to model the distribution of quaternion displacements so as to avoid the quaternion constraint. However, this approach only focuses on orientation reproduction without addressing the adaptation issue.…”

Section: Introductionmentioning

confidence: 96%

“…However, this approach only focuses on orientation reproduction without addressing the adaptation issue. In contrast to [16] that learns the quaternion displacement, the Riemannian topology of the S 3 manifold was exploited in [17] to probabilistically encode and reproduce distributions of quaternions. Moreover, [17] provides an extension to task-parameterized movements, which allows for adapting orientation tasks to different initial and final orientations.…”

Section: Introductionmentioning

confidence: 99%

“…If we consider the problem of adapting quaternions and angular velocities to pass through arbitrary desired points (e.g., via-point and end-point), no previous work in the scope of imitation learning (e.g., [1], [12], [13], [14], [15], [16], [17]) provides an all-encompassing solution. In addition, as suggested in [7], [18], probability distributions of multiple demonstrations could facilitate learning of important motion features and the design of optimal controllers [19], [20], [21].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Orientation Learning in Robot Task Space

Huang

Abu‐Dakka

Silvério

et al. 2019

2019 International Conference on Robotics and Automation (ICRA)

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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.

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“…Representing an orientation as a vector in Euclidean space may lead to inaccurate and unstable motions, due to its directional nature and vulnerability to singularities. Several works have proposed tailor-made learning approaches that consider the non-Euclidean geometry of the SO(3) space to generate rotational motion [18] [19] [20]. These approaches, however, require an explicit coupling between position and orientation, that might cause discontinuities in the resulting motion.…”

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confidence: 99%

Learning Augmented Joint-Space Task-Oriented Dynamical Systems: A Linear Parameter Varying and Synergetic Control Approach

Shavit

Figueroa

Salehian

et al. 2018

IEEE Robot. Autom. Lett.

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In this paper, we propose an asymptotically stable joint-space dynamical system (DS) that captures desired behaviors in joint-space while converging towards a task-space attractor in both position and orientation. To encode joint-space behaviors while meeting the stability criteria, we propose a DS constructed as a Linear Parameter Varying (LPV) system combining different behavior synergies and provide a method for learning these synergy matrices from demonstrations. Specifically, we use dimensionality reduction to find a low-dimensional embedding space for modulating joint synergies, and then estimate the parameters of the corresponding synergies by solving a convex semi-definite optimization problem that minimizes the joint velocity prediction error from the demonstrations. Our proposed approach is empirically validated on a variety of motions that reach a target in position and orientation, while following a desired joint-space behavior.

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Gaussian Mixture Model for 3-DoF orientations

Cited by 33 publications

References 21 publications

Learning task-space synergies using Riemannian geometry

Learning task-space synergies using Riemannian geometry

Generalized Orientation Learning in Robot Task Space

Learning Augmented Joint-Space Task-Oriented Dynamical Systems: A Linear Parameter Varying and Synergetic Control Approach

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