Kinematic Control of Free Rigid Bodies Using Dual Quaternions

• Published in: International journal of automation and computing Vol. 5; no. 3; pp. 319 - 324
• Main Authors: Han, Da-Peng, Wei, Qing, Li, Ze-Xiang
• Format: Journal Article
• Language: Chinese; English
• Published: Heidelberg Institute of Automation, Chinese Academy of Sciences 01.07.2008; Springer Nature B.V; College of Mechatronie Engineering and Automation, National University of Defense Technology, Changsha 410073, PRC%Departrnent of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hongkong, PRC
• Subjects: Automation; CAE) and Design; Computer Applications; Computer-Aided Engineering (CAD; Control; Control theory; Engineering; Feedback; Firearm laws & regulations; Kinematics; Laws; Liapunov functions; Logarithms; Mechatronics; Proportional control; Quaternions; Rigid structures; Rigid-body dynamics; Robotics; Studies; Tracking problem; 全向控制; 刚体; 双重四元数; 比例控制; 运动学控制; dual quaternion; Kinematic control; omnidirectional control; proportional control
• ISSN: 1476-8186; 2153-182X; 1751-8520; 2153-1838
• DOI: 10.1007/s11633-008-0319-1

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.