Related papers: DQ Robotics: a Library for Robot Modeling and Cont…
Most object manipulation strategies for robots are based on the assumption that the object is rigid (i.e., with fixed geometry) and the goal's details have been fully specified (e.g., the exact target pose). However, there are many tasks…
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
Deformable object manipulation (DOM) is an emerging research problem in robotics. The ability to manipulate deformable objects endows robots with higher autonomy and promises new applications in the industrial, services, and healthcare…
Deep reinforcement learning is an emerging machine learning approach which can teach a computer to learn from their actions and rewards similar to the way humans learn from experience. It offers many advantages in automating decision…
Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra.…
High degree-of-freedom dual-arm robots are becoming increasingly common due to their morphology enabling them to operate effectively in human environments. However, motion planning in real-time within unknown, changing environments remains…
Motion planning in high-dimensional space is a challenging task. In order to perform dexterous manipulation in an unstructured environment, a robot with many degrees of freedom is usually necessary, which also complicates its motion…
We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on $\mathrm{SE}(3)$. The controller is formulated in the dual quaternion framework and operates at the…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
In many industries, the scale and complexity of systems can present significant barriers to the development of accurate digital twin models. This paper introduces a novel methodology and a modular computational tool utilizing machine…
In this paper, we introduce and explore augmented quaternions and augmented unit quaternions, and present an augmented unit quaternion optimization model. An augmented quaternion consist of a quaternion and a translation vector. The…
An ideal is a classical object of study in the field of algebraic number theory. In maximal quadratic orders of number fields, ideals usually represented by the $\mathbb Z$-basis. This form of representation is used in most of the…
Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regions. While duality is well established experimentally, our…
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…
Bias problems in the estimation of $Q$-values are a well-known obstacle that slows down convergence of $Q$-learning and actor-critic methods. One of the reasons of the success of modern RL algorithms is partially a direct or indirect…
We present fast and accurate ways to normalize two and three dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the…
More than 150 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the paths of moving objects undergoing three-axis rotations. It is shown here that they…
Quaternion-valued differential equations (QDEs) is a new kind of differential equations which have many applications in physics and life sciences. The largest difference between QDEs and ODEs is the algebraic structure. On the…