Related papers: Using Lie derivatives with dual quaternions for pa…
A Lie algebroid over a manifold is a vector bundle over that manifold whose properties are very similar to those of a tangent bundle. Its dual bundle has properties very similar to those of a cotangent bundle: in the graded algebra of…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the…
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two…
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…
I consider differential of mapping $f$ of continuous division ring as linear mapping the most close to mapping $f$. Different expressions which correspond to known deffinition of derivative are supplementary. I explore the Gateaux…
Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler…
This work introduces an analytical approach for detecting and estimating external forces acting on deformable linear objects (DLOs) using only their observed shapes. In many robot-wire interaction tasks, contact occurs not at the…
The recursive Newton-Euler Algorithm (RNEA) is a popular technique for computing the dynamics of robots. RNEA can be framed as a differentiable computational graph, enabling the dynamics parameters of the robot to be learned from data via…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
Screw theory provides geometrical insight into the mechanics of rigid bodies. Screw axis is defined as the line coinciding with the joint axis. Line transformations in the form of a screw operator are used to determine the joint axes of a…
One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of…
Deep learning for predicting or generating 3D human pose sequences is an active research area. Previous work regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain,…
This work explores the potential of using differentiable simulation for learning quadruped locomotion. Differentiable simulation promises fast convergence and stable training by computing low-variance first-order gradients using robot…
Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of…
The general 4D rotation matrix is specialised to the general 3D rotation matrix by equating its leftmost top element (a00) to 1. Its associate matrix of products of the left-hand and right-hand quaternion components is specialised…
The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…