Related papers: DQ Robotics: a Library for Robot Modeling and Cont…
Quaternions were appeared through Lagrangian formulation of mechanics in Symplectic vector space. Its general form was obtained from the Clifford algebra, and Frobenius' theorem, which says that "the only finite-dimensional real division…
Object transportation could be a challenging problem for a single robot due to the oversize and/or overweight issues. A multi-robot system can take the advantage of increased driving power and more flexible configuration to solve such a…
Graphical calculi are vital tools for representing and reasoning about quantum circuits and processes. Some are not only graphically intuitive but also logically complete. The best known of these is the ZX-calculus, which is an industry…
We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a…
Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal…
Soft robots, made from compliant materials, exhibit complex dynamics due to their flexibility and high degrees of freedom. Controlling soft robots presents significant challenges, particularly underactuation, where the number of inputs is…
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
This article investigates Kak neural networks, which can be instantaneously trained, for complex and quaternion inputs. The performance of the basic algorithm has been analyzed and shown how it provides a plausible model of human perception…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
Deep imitation learning is promising for solving dexterous manipulation tasks because it does not require an environment model and pre-programmed robot behavior. However, its application to dual-arm manipulation tasks remains challenging.…
Recent trends in robot arm control have seen a shift towards end-to-end solutions, using deep reinforcement learning to learn a controller directly from raw sensor data, rather than relying on a hand-crafted, modular pipeline. However, the…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
We consider quadrangles of perimeter $2$ in the plane with marked directed edge. To such quadrangle $Q$ a two-dimensional plane $\Pi\in\mathbb{R}^4$ with orthonormal base is corresponded. Orthogonal plane $\Pi^\bot$ defines a plane…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
A key challenge in intelligent robotics is creating robots that are capable of directly interacting with the world around them to achieve their goals. The last decade has seen substantial growth in research on the problem of robot…
This paper proposes a new control framework for manipulating soft objects. A Deep Reinforcement Learning (DRL) approach is used to make the shape of a deformable object reach a set of desired points by controlling a robotic arm which…
This paper presents a control strategy based on dual quaternions for the coordinated formation flying of small UAV groups. A virtual structure is employed to define the desired formation, enabling unified control of its position,…