Related papers: Using Products of Exponentials to Define (Draw) Or…
The Product of Exponentials (PoE) formulation is most commonly used in the field of robotics, but has recently been adapted for use in describing orbital motion. The PoE formula for orbital mechanics is an alternate method for defining and…
The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics…
While Product of Exponentials (POE) formula has been gaining increasing popularity in modeling the kinematics of a serial-link robot, the Denavit-Hartenberg (D-H) notation is still the most widely used due to its intuitive and concise…
Product of experts (PoE) are layered networks in which the value at each node is an AND (or product) of the values (possibly negated) at its inputs. These were introduced as a neural network architecture that can efficiently learn to…
An algorithm for numerically computing the exponential of a matrix is presented. We have derived a polynomial expansion of $e^x$ by computing it as an initial value problem using a symbolic programming language. This algorithm is shown to…
The Projection on Proper elements (PoPe) is a novel method of code control dedicated to 1) checking the correct implementation of models, 2) determining the convergence of numerical methods and 3) characterizing the residual errors of any…
Probability distributions are key components of many learning from demonstration (LfD) approaches. While the configuration of a manipulator is defined by its joint angles, poses are often best explained within several task spaces. In many…
This study defines an orbitwise expansive point (OE) as a point, such as $x$ in a metric space $(X,\rho)$, if there is a number $d>0$ such that the orbits of a few points inside an arbitrary open sphere will maintain a distance greater than…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
In this paper, we study the configuration space of orbits, a generalization of the configuration space of points but for algebraic varieties that are acted by an algebraic reductive group. The main objective of this work is to study the…
We present a simple and general method for construction of localized orbitals to describe electronic structure of extended periodic metals and insulators as well as confined systems. Spatial decay of these orbitals is found to exhibit…
Existing methods for constructing splines and Bezier curves on a Lie group G involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local…
The orientation of a polarization vector on the Poincare sphere is defined by its position angle (PA) and ellipticity angle (EA). The radio emission from pulsars, magnetars, and fast radio bursts can be elliptically polarized, and…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
Accurate robot kinematics is essential for precise tool placement in articulated robots, but non-geometric factors can introduce configuration-dependent model discrepancies. This paper presents a configuration-dependent kinematic…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
$ $Deriving a robot's equation of motion typically requires placing multiple coordinate frames, commonly using the Denavit-Hartenberg convention to express the kinematic and dynamic relationships between segments. This paper presents an…
The polarizable embedding (PE) model is a fragment-based quantum-classical approach aimed at accurate inclusion of environment effects in quantum-mechanical response property calculations. The aim of this tutorial is to give insight into…
Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…