Related papers: Motion, Unit Dual Quaternion and Motion Optimizati…
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…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
Several common dual quaternion functions, such as the power function, the magnitude function, the $2$-norm function and the $k$th largest eigenvalue of a dual quaternion Hermitian matrix, are standard dual quaternion functions, i.e., the…
The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear…
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…
Recently, Zhuang, Roth, \& Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a…
Imitation learning techniques have been used as a way to transfer skills to robots. Among them, dynamic movement primitives (DMPs) have been widely exploited as an effective and an efficient technique to learn and reproduce complex discrete…
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex,…
The problem of planning for a robot that operates in environments containing a large number of objects, taking actions to move itself through the world as well as to change the state of the objects, is known as task and motion planning…
Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…
Quadrotors are among the most agile flying robots. However, planning time-optimal trajectories at the actuation limit through multiple waypoints remains an open problem. This is crucial for applications such as inspection, delivery, search…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
The realization of motion description is a challenging work for fixed-wing Unmanned Aerial Vehicle (UAV) acrobatic flight, due to the inherent coupling problem in ranslational-rotational motion. This paper aims to develop a novel maneuver…
This paper presents a trajectory optimization and control approach for the guidance of an orbital four-arm robot in extravehicular activities. The robot operates near the target spacecraft, enabling its arm's end-effectors to reach the…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…