Related papers: Fused Angles and the Deficiencies of Euler Angles
This work tries to contribute to the design of legged robots with capabilities boosted through thruster-assisted locomotion. Our long-term goal is the development of robots capable of negotiating unstructured environments, including land…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
Motivated by the challenging formation stabilization problem for mobile robotic teams when no distance or relative displacement measurements are available and each robot can only measure some of those angles formed by rays towards its…
Quadcopter trajectory tracking control has been extensively investigated and implemented in the past. Available controls mostly use the Euler angle standards to describe the quadcopters rotational kinematics and dynamics. As a result, the…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
This paper presents a unified metric-based framework for triangle geometric inequalities using barycentric coordinates. By interpreting classical inequalities as squared distances between points(a process termed metricization)we derive and…
A significant challenge in object detection is accurate identification of an object's position in image space, whereas one algorithm with one set of parameters is usually not enough, and the fusion of multiple algorithms and/or parameters…
The Euler characteristic transform (ECT) is a simple to define yet powerful representation of shape. The idea is to encode an embedded shape using sub-level sets of a a function defined based on a given direction, and then returning the…
Accurate quantification of complex human movements, such as gait, is essential for clinical diagnosis and rehabilitation but is often limited by traditional linear models rooted in Euclidean geometry. These frameworks frequently fail to…
We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different…
The Euler Characteristic Transform (ECT) is a robust method for shape classification. It takes an embedded shape and, for each direction, computes a piecewise constant function representing the Euler Characteristic of the shape's sublevel…
In this work, we introduce a new geometry based on the difference angle, an angle defined as the difference of slopes of two lines, together with an axiomatic system for angles. This framework provides a constructive approach to the…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
The bifurcation problem of a circular Euler-Bernoulli rod subject to a uniform radial force distribution is investigated under three distinct loading conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.) dead load.…
This paper details an accessible geometric derivation of the forward and inverse kinematics of a parallel robotic linkage known as the Canfield joint, which can be used for pointing applications. The original purpose of the Canfield joint…
Point cloud segmentation (PCS) is to classify each point in point clouds. The task enables robots to parse their 3D surroundings and run autonomously. According to different point cloud representations, existing PCS models can be roughly…
Legged robots can have a unique role in manipulating objects in dynamic, human-centric, or otherwise inaccessible environments. Although most legged robotics research to date typically focuses on traversing these challenging environments,…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…