相关论文: The Computation of All 4R Serial Spherical Wrists …
This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward…
The wrist plays a pivotal role in facilitating motion dexterity and hand functions. Wrist orthoses, from passive braces to active exoskeletons, provide an effective solution for the assistance and rehabilitation of motor abilities. However,…
This paper explores the development of a control and sensor strategy for an industrial wearable wrist exoskeleton by classifying and predicting workers' actions. The study evaluates the correlation between exerted force and effort…
The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the…
A spherical $t$-design is a finite subset $X$ of the unit sphere such that every polynomial of degree at most $t$ has the same average over $X$ as it does over the entire sphere. Determining the minimum possible size of spherical designs,…
The ropelength of a knot is the minimum length required to tie it. Computational upper bounds have previously been computed for every prime knot with up to 11 crossings. Here, we present ropelength measurements for the 2176 knots with 12…
In this paper, we construct infinitely many non-isotopic 3-knots in the 5-sphere, each of which has four critical points with respect to the standard height function of the 5-sphere. This contrasts with a theorem of Scharlemann which says…
In linear elasticity, a fourth order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties of a material. Due to Voigt, this tensor is conventionally represented by a $6\times 6$ symmetric…
The aim of this paper is to study supersoluble skew braces, a class of skew braces that encompasses all finite skew braces of square-free order. It turns out that finite supersoluble skew braces have Sylow towers, and that in an arbitrary…
In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension…
Supernumerary robotic arms (SRAs) can be used as the third arm to complement and augment the abilities of human users. The user carrying a SRA forms a connected kinodynamic chain, which can be viewed as a special class of floating-base…
Satellites (topological powers) of the famous figure-eight orbit are special periodic solutions of the planar three-body problem. In this paper we use a modified Newton's method based on the Continuous analog of Newton's method and high…
This work presents a three-dimensional geometric resolution method to calculate the complete inverse kinematics of a 7-degree-of-freedom articulated arm, including the hand itself. The method is classified as an analytical method with…
This paper presents a quadratic unconstrained binary optimization-based formulation framework for robot design optimization using kinematic structure-level evaluation metrics. In the proposed framework, classical computation is used to…
We classify all finite group actions on knots in the 3-sphere. By geometrization, all such actions are conjugate to actions by isometries, and so we may use orthogonal representation theory to describe three cyclic and seven dihedral…
In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both a circumcircle passing through the four vertices and an incircle having the four sides as tangents. Consider a bicentric quadrilateral with rational…
An operator T on Hilbert space is a 3-isometry if there exists operators B and D such that (T*)^n T^n = I+nB +n^2 D. An operator J is a Jordan operator if it the sum of a unitary U and nilpotent N of order two which commute. If T is a…
Besides mathematical interest, knots and knot theory have important applications in physics, chemistry, and biology. Stasiak and colleagues devised a constructive method for a knot "energy" using a Metropolis Monte Carlo algorithm to…
A slope $p/q$ is said to be characterizing for a knot $K$ if the homeomorphism type of the $p/q$-Dehn surgery along $K$ determines the knot up to isotopy. Extending previous work of Lackenby and McCoy on hyperbolic and torus knots…
Let $f$ be a positive definite (non-classic) integral quaternary quadratic form. We say $f$ is strongly $s$-regular if it satisfies a regularity property on the number of representations of squares of integers. In this article, we prove…