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dual quaternions and dual quaternion Vectors

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Communications on Applied Mathematics and Computation 2022年第4期4卷 1494-1508页

作者： Liqun Qi Chen Ling Hong Yan Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018ZhejiangChina Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina Department of Electrical Engineering and Centre for Intelligent Multidimensional Data Analysis City University of Hong KongKowloonHong KongChina

We introduce a total order and an absolute value function for dual *** absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of real *** define the magnitude of a dual quaternion,as a dual *** upon these,we extend 1-norm,co-norm,and 2-norm to dual quaternion vectors.

关键词： dual number Absolute value function dual quaternion Magnitude Norm

Integrated modeling of spacecraft relative motion dynamics using dual quaternion

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Journal of Systems Engineering and Electronics 2018年第2期29卷 367-377页

作者： PENG Xuan SHI Xiaoping GONG Yupeng Control and Simulation Center Harbin Institute of Technology Research Center of Satellite Technology Harbin Institute of Technology

To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom(6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative(PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.

关键词： relative motion dual quaternion position and attitude coupling integrated modeling

Comparison of strapdown inertial navigation algorithm based on rotation vector and dual quaternion

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Chinese Journal of Aeronautics 2013年第2期26卷 442-448页

作者： Wang Zhenhuan Chen Xijun Zeng Qingshuang Space Control and Inertial Technology Research Center Harbin Institute of Technology

For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.

关键词： dual quaternion Inertial navigation system Navigation algorithm quaternion Rotation vector

A study on dual quaternion based cooperative relative navigation of multiple UAVs with monocular vision-inertial integration

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Chinese Journal of Aeronautics 2024年第11期37卷 335-354页

作者： Byungjin LEE Sangkyung SUNG Academy of Applied Science and Technology Konkuk UniversitySeoul 05029South Korea Department of Mechanical and Aerospace Engineering Konkuk UniversitySeoul 05029South Korea

This paper addresses a cooperative relative navigation problem for multiple aerial agents,relying on visual tracking information between *** research aims to investigate a sensor fusion architecture and algorithm that leverages partially available absolute navigation knowledge while exploiting collaborative visual interaction between vehicles in mission flight areas,where satellite navigation-denied regions are irregularly *** achieve this,the paper introduces a new approach to defining the relative poses of cameras and develops a corresponding process to secure the relative pose *** contrasts with previous research,which simply linearized the relative pose information of aircraft cameras into navigation states defined in an absolute coordinate ***,the target pose in relative navigation is defined,and the pose of the camera and feature points are directly derived using dual quaternion representation,which compactly represents both translation and ***,a mathematical model for the relative pose of the camera is derived through the dual quaternion framework,enabling an explicit pose formulation of relative *** study investigates navigation performance in typical mission flight scenarios using an in-house high-fidelity simulator and quantitatively highlights the contributions of the proposed scheme by comparing the navigation error ***,the proposed method demonstrates to have navigation accuracy in decimeter level even in GNSS-denied environments and an improved 3D Root Mean Square(RMS)error by30%smaller than the conventional absolute navigation framework.

关键词： Cooperative navigation Relative pose dual quaternion Camera High-fidelity simulator

dual quaternion CURVE INTERPOLATION ALGORITHM FOR FORMATION SATELLITES

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Transactions of Nanjing University of Aeronautics and Astronautics 2012年第1期29卷 90-95页

作者：李静王惠南刘海颖南京航空航天大学自动化学院南京航空航天大学航天学院南京航空航天大学高新技术研究院

The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.

关键词： formation satellites dual quaternion interpolation algorithm relative position and attitude

Closed Form Solution for Relative Orientation Using dual quaternion

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Closed Form Solution for Relative Orientation Using Dual Qua...

Research on the Measurement in RVD Based on dual quaternion

2009年度海峡两岸工程力学研讨会

作者： Yi-Te Chiang Yang-Hsing Lin 姜義德 Dept.of Electrical Engineering Lee-Ming Institute of Technology Dept of Electrical Engineering National Taiwan University 职黎明技术学院电机系

In this thesis,we use dual quaternion to solve relative orientation in closed-form,which replaces the traditional way of coplanarity condition and least square *** best benefit of dualquaternion is that it is able to handle rotation and translation simultaneously and apply continuous product of dual quaternion operating with a kind of special vector,named dual vector to express a serious of rotation and *** use two cameras to observe the target lines,and find the lines respect to RIGHT coordinate *** solve the relative orientation in closed form by finding *** of the benefit of dual quaternion-easily to handle and express a serious of transformation,we make above solution more practically and reality using dual-quaternion.

关键词： quaternion dual quaternion relative orientation.

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Research on the Measurement in RVD Based on Dual Quaternion

Multi-spacecraft position-attitude coupling model based on dual quaternion

2011 Chinese Control and Decision Conference（CCDC）

作者： Guangren Duan Ze Zhang,Yong Sun are with Faculty of Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin,China.

the measurement of the final approaching part in Rendezvous and Dock are all based on computer vision,the basic ideas are:In the close part utilizing the camera to catch the motion parameters and the traditional method is a process of solving the rotation matrix and the translation *** this method the imaging is the most important *** shortcomings of this method are the decomposition of the integrity for the rigid *** this paper,the dual quaternion is *** overcomes the shortcomings of the former method,the rotation and translation relationship between the two coordinates is considered on the same ***,the simulation shows the method.

关键词： Rendezvous and Docking Vision Measurement dual quaternion Rotation Matrix Translation Vector

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Multi-spacecraft position-attitude coupling model based on d...

Kinematic Control of Free Rigid Bodies Using dual quaternions

第37届中国控制会议

作者： Chengchen Deng Zhen Shi Xinzhu Sun XiANDe Wu Wenbin Bai Shiyi Li Qingrui Zhou Yong Hao College of Automation Harbin Engineering University College of Aerospace and Civil Engineering Harbin Engineering University Qian Xuesen Laboratory of Space Technology

With the development of space science and technology, the requirements of spacecraft are increasing, and it is significant to research the multi-spacecraft system model. Based on the dual quaternion theory, this paper deduces the coupling kinematics equation of multi-spacecraft, and points out the coupling effect of relative position and attitude. After that, the simulation analysis of 6 kinds of multi-spacecraft is carried out based on the established multi-spacecraft position and orbit integration model, in which the six cases are 5, 15, 25, 35, 45 and 55 satellites respectively. Finally, the correctness and practicability of the model are verified by comparing between Matlab and STK simulation results.

关键词： Attitude-position coupling model dual quaternion Multi-spacecraft

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International Journal of Automation and computing 2008年第3期5卷 319-324页

作者： Da-Peng Han Qing Wei Ze-Xiang Li College of Mechatronic Engineering and Automation~ National University of Defense Technology Changsha 410073 PRC Department of Electrical and Electronic Engineering Hong Kong University of Science and Technology Hongkong PRC

This paper proposes a new type of control laws for free rigid bodies. The start point is the dual quaternion and its characteristics. The logarithm of a dual quaternion is defined, based on which kinematic control laws can be developed. Global exponential convergence is achieved using logarithmic feedback via a generalized proportional control law, and an appropriate Lyapunov function is constructed to prove the stability. Both the regulation and tracking problems are tackled. Omnidirectional control is discussed as a case study. As the control laws can handle the interconnection between the rotation and translation of a rigid body, they are shown to be more applicable than the conventional method.

关键词： Kinematic control dual quaternion omnidirectional control proportional control