Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Probabilistic Pose Estimation of Deformable Linear Objects

© 2018 IEEE. This paper presents a probabilistic framework for online tracking of nodes along deformable linear objects. The proposed framework does not require an a-priori model; instead, a Bayesian Committee Machine, starting as a tabula rasa, accumulates knowledge over time. The key benefits of this approach are a lack of reliance upon extensive pre-training data, which can be difficult to obtain in sufficiently large quantities, and the ability for robust estimation of nodes subject to occlusion. Another benefit is that the uncertainties obtained during inference from the underlying Gaussian Processes can be beneficial towards subsequent handling tasks. Comparisons of the non-time series framework were conducted against conventional regression models to measure the efficacy of the proposed framework

Environment-adaptive interaction primitives for human-robot motor skill learning

© 2016 IEEE. In complex environments where robots are expected to co-operate with human partners, it is vital for the robot to consider properties of their collaborative activity in addition to the behavior of its partner. In this paper, we propose to learn such complex interactive skills by observing the demonstrations of a human-robot team with additional external attributes. We propose Environment-adaptive Interaction Primitives (EalPs) as an extension of Interaction Primitives. In cooperation tasks between human and robot with different environmental conditions, EalPs not only improve the predicted motor skills of robot within a brief observed human motion, but also obtain the generalization ability to adapt to new environmental conditions by learning the relationships between each condition and the corresponding motor skills from training samples. Our method is validated in the collaborative task of covering objects by plastic bag with a humanoid Baxter robot. To achieve the task successfully, the robot needs to coordinate itself to its partner while also considering information about the object to be covered

A simple algorithm for finding all k-edge-connected components

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Environment-adaptive interaction primitives through visual context for human–robot motor skill learning

© 2018, The Author(s). In situations where robots need to closely co-operate with human partners, consideration of the task combined with partner observation maintains robustness when partner behavior is erratic or ambiguous. This paper documents our approach to capture human–robot interactive skills by combining their demonstrative data with additional environmental parameters automatically derived from observation of task context without the need for heuristic assignment, as an extension to overcome shortcomings of the interaction primitives framework. These parameters reduce the partner observation period required before suitable robot motion can commence, while also enabling success in cases where partner observation alone was inadequate for planning actions suited to the task. Validation in a collaborative object covering exercise with a humanoid robot demonstrate the robustness of our environment-adaptive interaction primitives, when augmented with parameters directly drawn from visual data of the task scene

Leaf segmentation and tracking using probabilistic parametric active contours

Active contours or snakes are widely used for segmentation and tracking. These techniques require the minimization of an energy function, which is generally a linear combination of a data fit term and a regularization term. This energy function can be adjusted to exploit the intrinsic object and image features. This can be done by changing the weighting parameters of the data fit and regularization term. There is, however, no rule to set these parameters optimally for a given application. This results in trial and error parameter estimation. In this paper, we propose a new active contour framework defined using probability theory. With this new technique there is no need for ad hoc parameter setting, since it uses probability distributions, which can be learned from a given training dataset

Phase behaviour of additive binary mixtures in the limit of infinite asymmetry

We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a very asymmetric mixture can only occur between a solvent-rich fluid and a permeated large particle solid or between two large particle solids with different packing fractions. Comparing with hard spheres mixtures we conclude that the phase behaviour of very asymmetric hard-particle mixtures can be determined from that of the large component interacting via an adhesive-like potential.Comment: Full rewriting of the paper (also new title). 4 pages, LaTeX, uses revtex, multicol, epsfig, and amstex style files, to appear in Phys. Rev. E (Rapid Comm.