Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups

International audienceWhen performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a bi-invariant Riemannian metric, like compact Lie groups (e.g. rotations). However, bi-invariant Riemannian metrics do not exist for most non compact and non-commutative Lie groups. This is the case in particular for rigid-body transformations in any dimension greater than one, which form the most simple Lie group involved in biomedical image registration. In this paper, we propose to replace the Riemannian metric by an affine connection structure on the group. We show that the canonical Cartan connections of a connected Lie group provides group geodesics which are completely consistent with the composition and inversion. With such a non-metric structure, the mean cannot be defined by minimizing the variance as in Riemannian Manifolds. However, the characterization of the mean as an exponential barycenter gives us an implicit definition of the mean using a general barycentric equation. Thanks to the properties of the canonical Cartan connection, this mean is naturally bi-invariant. We show the local existence and uniqueness of the invariant mean when the dispersion of the data is small enough. We also propose an iterative fixed point algorithm and demonstrate that the convergence to the invariant mean is at least linear. In the case of rigid-body transformations, we give a simple criterion for the global existence and uniqueness of the bi-invariant mean, which happens to be the same as for rotations. We also give closed forms for the bi-invariant mean in a number of simple but instructive cases, including 2D rigid transformations. For general linear transformations, we show that the bi-invariant mean is a generalization of the (scalar) geometric mean, since the determinant of the bi-invariant mean is the geometric mean of the determinants of the data. Finally, we extend the theory to higher order moments, in particular with the covariance which can be used to define a local bi-invariant Mahalanobis distance

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

Failure Recovery in Robot-Human Object Handover

Object handover is a common physical interaction between humans. It is thus also of significant interest for human-robot interaction. In this paper, we are focused on robot-to-human object handover. The main challenge in this case is how to reduce the failure rate, i.e., to ensure that the object does not fall (object safety), while at the same time allowing the human to easily acquire the object (smoothness). To endow the robot with a failure recovery mechanism, we investigated how humans detect failure during the transfer phase of the handover. We conducted a human study that showed that a human giver primarily relies on vision rather than haptic sensing to detect the fall of the object. Motivated by this study, a robotic handover system is proposed that consists of a motion sensor attached to the robot's gripper, a force sensor at the base of the gripper, and a controller that is capable of regrasping the object if it starts falling. The proposed system is implemented on a Baxter robot and is shown to achieve a smooth and safe handover

Failure Recovery in Robot–Human Object Handover

Object handover is a common physical interaction between humans. It is thus also of significant interest for human-robot interaction. In this paper, we are focused on robot-to-human object handover. The main challenge in this case is how to reduce the failure rate, i.e., to ensure that the object does not fall (object safety), while at the same time allowing the human to easily acquire the object (smoothness). To endow the robot with a failure recovery mechanism, we investigated how humans detect failure during the transfer phase of the handover. We conducted a human study that showed that a human giver primarily relies on vision rather than haptic sensing to detect the fall of the object. Motivated by this study, a robotic handover system is proposed that consists of a motion sensor attached to the robot's gripper, a force sensor at the base of the gripper, and a controller that is capable of regrasping the object if it starts falling. The proposed system is implemented on a Baxter robot and is shown to achieve a smooth and safe handover

The Roles and Recognition of Haptic-Ostensive Actions in Collaborative Multimodal Human-Human Dialogues

The RoboHelper project has the goal of developing assistive robots for the elderly. One crucial component of such a robot is a multimodal dialogue architecture, since collaborative task-oriented human-human dialogue is inherently multimodal. In this paper, we focus on a specific type of interaction, Haptic-Ostensive (H-O) actions, that are pervasive in collaborative dialogue. H-O actions manipulate objects, but they also often perform a referring function. We collected 20 collaborative task-oriented human-human dialogues between a helper and an elderly person in a realistic setting. To collect the haptic signals, we developed an unobtrusive sensory glove with pressure sensors. Multiple annotations were then conducted to build the Find corpus. Supervised machine learning was applied to these annotations in order to develop reference resolution and dialogue act classification modules. Both corpus analysis, and these two modules show that H-O actions play a crucial role in interaction: models that include H-O actions, and other extra-linguistic information such as pointing gestures, perform better. For true human-robot interaction, all communicative intentions must of course be recognized in real time, not on the basis of annotated categories. To demonstrate that our corpus analysis is not an end in itself, but can inform actual human-robot interaction, the last part of our paper presents additional experiments on recognizing H-O actions from the haptic signals measured through the sensory glove. We show that even though pressure sensors are relatively imprecise and the data provided by the glove is noisy, the classification algorithms can successfully identify actions of interest within subjects