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Introduction
Published in Chunguang Xu, Robotic Nondestructive Testing Technology, 2022
In a three-dimensional space, the position and attitude of a particular vector rotating around the specified axis are generally described by quaternions. For example, the rotation angle is expressed by α, and the direction cosine of the locating rotation axis is expressed by cos(βx), cos(βy) and cos(βz). Then, the elements in the above equation are: q0=cos(α/2)q1=sin(α/2)cos(βx)q2=sin(α/2)cos(βy)q3=sin(α/2)cos(βz)
Application Tracking and Navigation
Published in Bin Jia, Ming Xin, Grid-based Nonlinear Estimation and Its Applications, 2019
Additionally, gyro biases of the chief and the deputy spacecraft can be determined or corrected as well. The total dimension of the estimation system is 15 and thus it is a high-dimensional estimation problem. For the attitude estimation, there are generally two different categories of parameters to represent the relative attitude: constrained parameters such as the unit quaternion, and unconstrained parameters such as the Euler angles, the Rodrigues parameters, the modified Rodrigues parameters (MRP) (Crassidis et al. 2007, Crassidis and Markley 2003), and the generalized Rodrigues parameters (GRPs) (Crassidis and Markley 2003). The quaternion is widely used to represent the attitude because it is free of singularities and the quaternion kinematic equation is bilinear. However, the unit-norm constraint of the quaternion is often violated in the standard filtering process (Crassidis and Markley 2003). A common approach to overcome this problem is to use the quaternion for global nonsingular attitude representation and a set of unconstrained parameters for local attitude representation and filtering (Crassidis et al. 2007, Crassidis and Markley 2003).
Applications
Published in James J Y Hsu, Nanocomputing, 2017
Much of the attention to quaternion was initiated by Evans(1977). The quaternions are now widely used in the computer animation, robotics,global navigation,aerospace and satellite mechanics to track the trajectories of moving objects undergoing three-axis rotations. Supercritical Water has certain advantages as a nonpollutent agent to clean up (Mauro Boero, 2000). Water dynamics across the CNT has also been studied by several authors (seefor example Hummer 2001). Ice nanotube (Koga 2001) was found to have rather high melting point (up to room temperature).
Leader-follower and leaderless pose consensus of robot networks with variable time-delays and without velocity measurements
Published in International Journal of Control, 2022
Carlos I. Aldana, Luis Tabarez, Emmanuel Nuño, Jose Guadalupe Romero
This paper presents a distributed controller that solves the leader-follower and the leaderless pose consensus problems for networks composed of heterogeneous robots without velocity measurements. It is proved that, with a proportional control scheme plus damping injection through a virtual dynamic controller, the pose errors and the linear and angular velocities converge to zero. Moreover, it is demonstrated that the controller is robust to variable time-delays in the communication channels. The proposed approach employs, the singularity-free, unit-quaternions to represent the orientation of the robots end-effectors. Another contribution of our work is the application of the leaderless consensus solution to the control of bilateral teleoperators. Numerical simulations and experimental validation results with networks composed of industrial robots and haptic devices are presented to support the theoretical results of this paper. Future work will consider to extend these results to networks composed of mobile manipulators.
Comparative analysis of quaternion modulation system with OFDM systems
Published in International Journal of Electronics Letters, 2021
Anam Zahra, Qasim Umar Khan, Shahzad Amin Sheikh
A complex number is defined by, where are real numbers and is an imaginary number such that. Complex numbers are two-dimensional vectors space over the real numbers. In addition to, quaternions are constructed by adding two new imaginary units and with one real part. A quaternion is an extension of the complex number system (Catoni, Bordoni, Cannata, & Zampetti, 1997). In 1843, Irish mathematician William Rowan Hamilton was the first person who described quaternions and practically applied them in three-dimensional mechanics (Farouki, Al-Kandari, & Sakkalis, 2002). The mathematical notation of quaternions represents three-dimensional rotations of objects. A quaternion can be written as a sum of one real part and three imaginary parts.
Consensus and coordination on groups SO(3) and S 3 over constant and state-dependent communication graphs
Published in Automatika, 2021
Aladin Crnkić, Milojica Jaćimović, Vladimir Jaćimović, Nevena Mijajlović
Throughout the article we use the videos showing rotating bodies in order to visualize the evolution of gradient dynamical systems. These videos illustrate continuous rotations in the space, that is the motion on the group . The algorithms on are visualized by using map from onto . In this way, the trajectories on are mapped onto trajectories on . This corresponds to the representation of 3D rotations by unit quaternions, the technique that is frequently used as a working framework for rotations in Robotics and Computer Graphics. This approach has some advantages over the working with matrices directly. However, one drawback is that the map is not , as two antipodal points on (that is, unit quaternions q and ) correspond to the same rotation.