Kinematic metric functions, which allow us to make metric measurements such as “distance”, “length” and “angle”, are often needed in robotics. However, some commonly used metric functions are not well-defined because of their dependence upon choice of reference frame. This paper presents formal and practical conditions for kinematic metric functions to be well-defined. In order to properly anal...

For more than a century, rigid-body displacements have been viewed as affine transformations described as homogeneous transformation matrices wherein the linear part is a rotation matrix. In group-theoretic terms, this classical description makes rigid-body motions a semi-direct product. The distinction between a rigid-body displacement of Euclidean space and a change in pose from one reference...

Keywords: 3D model based coding, rigid head tracking, 3D motion estimation, feature tracking The presented work proposes substantial improvements to established methods for the two-dimensional tracking of an image and the rigid adaptation of a three-dimensional face model to a 2D projection. These are combined to produce a robust system for the rigid 3D tracking of a human head which is promisi...

In this paper 1 we describe in precise the structure of all rigid modal rooted frames of depth 2. The interest to rigid frames came from the paper [5] where it has been showed that any given quasi-characterizing inference rule is self-admissible if and only if the frame of the algebra generated that rule is not rigid. The study of admissibility of inference rules was, in particular, motivated b...

Rigid geometric structures on manifolds, introduced by Gromov, are characterized by the fact that their infinitesimal automorphisms are determined by their jets of a fixed order. Important examples of such structures are those given by an H-reduction of the first order frame bundle of a manifold, where the Lie algebra of H is of finite type; in fact, for structures given by reductions to closed...

ABSTRACT There are various useful metrics for finding the distance between two points in Euclidean space. Metrics for finding the distance between two rigid body locations in Euclidean space depend on both the coordinate frame and units used. A metric independent of these choices is desirable. This paper presents a metric for a finite set of rigid body displacements. The methodology uses the pr...

An isosceles triangular frame with rotationally resistive joints under a tip load is studied. The large in-plane deformation elastica equations are formulated. Stability analysis shows the frame can buckle symmetrically or asymmetrically. Post-buckling behavior showing limit load and hysteresis are obtained by shooting and homotopy numerical algorithms. The behavior of a frame with rigid joints...