3D Human Pose Tracking Priors using Geodesic Mixture Models

Abstract

Abstract:In many complex robotics systems, interaction takes place in all directions between human, robot, and environment. Performance of such a system depends on this interaction, and a proper evaluation of a system must build on a proper modeling of interaction, a relevant set of performance metrics, and a methodology to combine metrics into a single performance value. In this paper, existing models of human-robot interaction are adapted to fit complex scenarios with one or several humans and robots. The interaction and the evaluation process is formalized, and a general method to fuse performance values over time and for several performance metrics is presented. The resulting value, denoted interaction quality, adds a dimension to ordinary performance metrics by being explicit about the interplay between performance metrics, and thereby provides a formal framework to understand, model, and address complex aspects of evaluation of human-robot interaction.

Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control

“…Several approaches have been proposed to extend Gaussian distributions in Euclidean space to Riemannian manifolds [23]. Here, we focus on a simple approach that consists of estimating the mean of the Gaussian as a centroid on the manifold (also called Karcher/Fréchet mean), and representing the dispersion of the data as a covariance expressed in the tangent space at the mean [4], [24], providing a simple and easy-to-compute representation. Distortions arise when points are too far apart from the mean, but this distortion is negligible in nearly all robotics applications.…”

Programming by Demonstration for Shared Control With an Application in Teleoperation

“…The parameters of this Gaussian Mixture Model (GMM) can be estimated using Expectation Maximization (EM), an iterative process in which the data are given weights for each cluster (Expectation step), and the clusters are subsequently updated using a weighted MLE (Maximization step). We refer to [22] for a detailed description of EM for Riemannian GMMs. Statistical inference of GMM is done efficiently using GMR.…”

A Nonparametric Model for Multi-Manifold Clustering with Mixture of Gaussians and Graph Consistency

“…Straub et al [ 29 , 30 ] defined the Gaussian distribution on the sphere surface and introduced an auxiliary indicator vector zwith a DP prior. More than the sphere manifold, Simo et al [ 31 ] expanded the distribution to the manifold space with the logarithmic and exponential mapping. Although these models are quite powerful and have been widely studied in many applications, they have their drawbacks when the manifold structure is not prespecified [ 31 ].…”

“…More than the sphere manifold, Simo et al [ 31 ] expanded the distribution to the manifold space with the logarithmic and exponential mapping. Although these models are quite powerful and have been widely studied in many applications, they have their drawbacks when the manifold structure is not prespecified [ 31 ]. For example, the DP-space and temporal subspace clustering model is an expanding method of the linear manifold clustering method.…”

“…In the geodesic mixture model, the logarithmic and exponential mapping algorithms [ 32 , 33 ] used in this model depend mainly on the pre-defined geometric structure, which is always unavailable. For the sphere mixture model, the sphere manifold has not been extended to arbitrary manifolds [ 31 ].…”