153 research outputs found
Learning task-space synergies using Riemannian geometry
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
Programming by Demonstration on Riemannian Manifolds
This thesis presents a Riemannian approach to Programming by Demonstration (PbD).
It generalizes an existing PbD method from Euclidean manifolds to Riemannian manifolds.
In this abstract, we review the objectives, methods and contributions of the presented
approach.
OBJECTIVES
PbD aims at providing a user-friendly method for skill transfer between human and
robot. It enables a user to teach a robot new tasks using few demonstrations. In order
to surpass simple record-and-replay, methods for PbD need to \u2018understand\u2019 what to
imitate; they need to extract the functional goals of a task from the demonstration data.
This is typically achieved through the application of statisticalmethods.
The variety of data encountered in robotics is large. Typical manipulation tasks involve
position, orientation, stiffness, force and torque data. These data are not solely
Euclidean. Instead, they originate from a variety of manifolds, curved spaces that are
only locally Euclidean. Elementary operations, such as summation, are not defined on
manifolds. Consequently, standard statistical methods are not well suited to analyze
demonstration data that originate fromnon-Euclidean manifolds. In order to effectively
extract what-to-imitate, methods for PbD should take into account the underlying geometry
of the demonstration manifold; they should be geometry-aware.
Successful task execution does not solely depend on the control of individual task
variables. By controlling variables individually, a task might fail when one is perturbed
and the others do not respond. Task execution also relies on couplings among task variables.
These couplings describe functional relations which are often called synergies. In
order to understand what-to-imitate, PbDmethods should be able to extract and encode
synergies; they should be synergetic.
In unstructured environments, it is unlikely that tasks are found in the same scenario
twice. The circumstances under which a task is executed\u2014the task context\u2014are more
likely to differ each time it is executed. Task context does not only vary during task execution,
it also varies while learning and recognizing tasks. To be effective, a robot should
be able to learn, recognize and synthesize skills in a variety of familiar and unfamiliar
contexts; this can be achieved when its skill representation is context-adaptive.
THE RIEMANNIAN APPROACH
In this thesis, we present a skill representation that is geometry-aware, synergetic and
context-adaptive. The presented method is probabilistic; it assumes that demonstrations
are samples from an unknown probability distribution. This distribution is approximated
using a Riemannian GaussianMixtureModel (GMM).
Instead of using the \u2018standard\u2019 Euclidean Gaussian, we rely on the Riemannian Gaussian\u2014
a distribution akin the Gaussian, but defined on a Riemannian manifold. A Riev
mannian manifold is a manifold\u2014a curved space which is locally Euclidean\u2014that provides
a notion of distance. This notion is essential for statistical methods as such methods
rely on a distance measure. Examples of Riemannian manifolds in robotics are: the
Euclidean spacewhich is used for spatial data, forces or torques; the spherical manifolds,
which can be used for orientation data defined as unit quaternions; and Symmetric Positive
Definite (SPD) manifolds, which can be used to represent stiffness and manipulability.
The Riemannian Gaussian is intrinsically geometry-aware. Its definition is based on
the geometry of the manifold, and therefore takes into account the manifold curvature.
In robotics, the manifold structure is often known beforehand. In the case of PbD, it follows
from the structure of the demonstration data. Like the Gaussian distribution, the
Riemannian Gaussian is defined by a mean and covariance. The covariance describes
the variance and correlation among the state variables. These can be interpreted as local
functional couplings among state variables: synergies. This makes the Riemannian
Gaussian synergetic. Furthermore, information encoded in multiple Riemannian Gaussians
can be fused using the Riemannian product of Gaussians. This feature allows us to
construct a probabilistic context-adaptive task representation.
CONTRIBUTIONS
In particular, this thesis presents a generalization of existing methods of PbD, namely
GMM-GMR and TP-GMM. This generalization involves the definition ofMaximum Likelihood
Estimate (MLE), Gaussian conditioning and Gaussian product for the Riemannian
Gaussian, and the definition of ExpectationMaximization (EM) and GaussianMixture
Regression (GMR) for the Riemannian GMM. In this generalization, we contributed
by proposing to use parallel transport for Gaussian conditioning. Furthermore, we presented
a unified approach to solve the aforementioned operations using aGauss-Newton
algorithm. We demonstrated how synergies, encoded in a Riemannian Gaussian, can be
transformed into synergetic control policies using standard methods for LinearQuadratic
Regulator (LQR). This is achieved by formulating the LQR problem in a (Euclidean) tangent
space of the Riemannian manifold. Finally, we demonstrated how the contextadaptive
Task-Parameterized Gaussian Mixture Model (TP-GMM) can be used for context
inference\u2014the ability to extract context from demonstration data of known tasks.
Our approach is the first attempt of context inference in the light of TP-GMM. Although
effective, we showed that it requires further improvements in terms of speed and reliability.
The efficacy of the Riemannian approach is demonstrated in a variety of scenarios.
In shared control, the Riemannian Gaussian is used to represent control intentions of a
human operator and an assistive system. Doing so, the properties of the Gaussian can
be employed to mix their control intentions. This yields shared-control systems that
continuously re-evaluate and assign control authority based on input confidence. The
context-adaptive TP-GMMis demonstrated in a Pick & Place task with changing pick and
place locations, a box-taping task with changing box sizes, and a trajectory tracking task
typically found in industr
Riemannian geometry as a unifying theory for robot motion learning and control
Riemannian geometry is a mathematical field which has been the cornerstone of
revolutionary scientific discoveries such as the theory of general relativity.
Despite early uses in robot design and recent applications for exploiting data
with specific geometries, it mostly remains overlooked in robotics. With this
blue sky paper, we argue that Riemannian geometry provides the most suitable
tools to analyze and generate well-coordinated, energy-efficient motions of
robots with many degrees of freedom. Via preliminary solutions and novel
research directions, we discuss how Riemannian geometry may be leveraged to
design and combine physically-meaningful synergies for robotics, and how this
theory also opens the door to coupling motion synergies with perceptual inputs.Comment: Published as a blue sky paper at ISRR'22. 8 pages, 2 figures. Video
at https://youtu.be/XblzcKRRIT
Early Predictability of Grasping Movements by Neurofunctional Representations: A Feasibility Study
Human grasping is a relatively fast process and control signals for upper limb prosthetics cannot be generated and processed in a sufficiently timely manner. The aim of this study was to examine whether discriminating between different grasping movements at a cortical level can provide information prior to the actual grasping process, allowing for more intuitive prosthetic control. EEG datasets were captured from 13 healthy subjects who repeatedly performed 16 activities of daily living. Common classifiers were trained on features extracted from the waking-state frequency and total-frequency time domains. Different training scenarios were used to investigate whether classifiers can already be pre-trained by base networks for fine-tuning with data of a target person. A support vector machine algorithm with spatial covariance matrices as EEG signal descriptors based on Riemannian geometry showed the highest balanced accuracy (0.91 ± 0.05 SD) in discriminating five grasping categories according to the Cutkosky taxonomy in an interval from 1.0 s before to 0.5 s after the initial movement. Fine-tuning did not improve any classifier. No significant accuracy differences between the two frequency domains were apparent (p > 0.07). Neurofunctional representations enabled highly accurate discrimination of five different grasping movements. Our results indicate that, for upper limb prosthetics, it is possible to use them in a sufficiently timely manner and to predict the respective grasping task as a discrete category to kinematically prepare the prosthetic hand
Non-parametric regression for robot learning on manifolds
Many of the tools available for robot learning were designed for Euclidean
data. However, many applications in robotics involve manifold-valued data. A
common example is orientation; this can be represented as a 3-by-3 rotation
matrix or a quaternion, the spaces of which are non-Euclidean manifolds. In
robot learning, manifold-valued data are often handled by relating the manifold
to a suitable Euclidean space, either by embedding the manifold or by
projecting the data onto one or several tangent spaces. These approaches can
result in poor predictive accuracy, and convoluted algorithms. In this paper,
we propose an "intrinsic" approach to regression that works directly within the
manifold. It involves taking a suitable probability distribution on the
manifold, letting its parameter be a function of a predictor variable, such as
time, then estimating that function non-parametrically via a "local likelihood"
method that incorporates a kernel. We name the method kernelised likelihood
estimation. The approach is conceptually simple, and generally applicable to
different manifolds. We implement it with three different types of
manifold-valued data that commonly appear in robotics applications. The results
of these experiments show better predictive accuracy than projection-based
algorithms.Comment: 17 pages, 15 figure
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