Related papers: DQ Robotics: a Library for Robot Modeling and Cont…
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…
We introduce motions as real six-dimensional vectors. A motion means a rotation and a translation. We define a motion operator which maps unit dual quaternions to motions, and a UDQ operator which maps motions to unit dual quaternions. By…
Deep learning is a research hot topic in the field of machine learning. Real-value neural networks (Real NNs), especially deep real networks (DRNs), have been widely used in many research fields. In recent years, the deep complex networks…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Denavit and Hartenberg-based methods, such as Cardan, Fick, and Euler angles, describe the position and orientation of an end-effector in three-dimensional (3D) space. However, these methods have a significant drawback as they impose a…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted…
Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from very few training samples. This phenomenon of data-efficiency…
This paper presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton-Euler formulation and uses twists and wrenches, which are…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
Many problems in robotics are fundamentally problems of geometry, which lead to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie…
In this paper, the implementation of two Reinforcement learnings namely, Q Learning and Deep Q Network(DQN) on a Self Balancing Robot Gazebo model has been discussed. The goal of the experiments is to make the robot model learn the best…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
MAVs have great potential to assist humans in complex tasks, with applications ranging from logistics to emergency response. Their agility makes them ideal for operations in complex and dynamic environments. However, achieving precise…
This paper performs the modeling of a Cubli, a cube with three reaction wheels mounted on orthogonal faces that becomes a reaction wheel based 3D inverted pendulum when positioned in one of its vertices. The approach novelty is that…
Nowadays, we have seen that dual quaternion algorithms are used in 3D coordinate transformation problems due to their advantages. 3D coordinate transformation problem is one of the important problems in geodesy. This transformation problem…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…