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Kinematic control of free rigid bodies using dual quaternions

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Abstract

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.

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Authors and Affiliations

  1. College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha, 410073, PRC

    Da-Peng Han & Qing Wei

  2. Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hongkong, PRC

    Ze-Xiang Li

Authors
  1. Da-Peng Han
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  2. Qing Wei
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  3. Ze-Xiang Li
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Correspondence to Da-Peng Han.

Additional information

Da-Peng Han received the B. Sc. degree in control science and engineering from National University of Defense Technology, Changsha, PRC, in 2002. Currently, he is a Ph.D. candidate at the College of Mechatronic Engineering and Automation in National University of Defense Technology. He has published about 10 refereed journal and conference papers. His research interests include robotics and nonlinear control.

Qing Wei received the B. Sc. degree in electrical engineering from Fudan University, Shanghai, PRC, in 1991, and the Ph.D. degree in control science and engineering, from National University of Defense Technology, Changsha, PRC, in 1996. Since 1997, he has been a faculty member at National University of Defense Technology. Currently, he is a professor at the College of Mechatronic Engineering and Automation in National University of Defense Technology, Changsha, PRC. He has published about 20 refereed journal and conference papers. His research interests include intelligent robot control, remote control, and force control.

Ze-Xiang Li received the B. Sc. degree in electrical engineering and economics (with honors) from Carnegie Mellon University, Pittsburgh, PA, USA, in 1983. He received the M. Sc. degree in mathematics and Ph.D. degree in electrical and computer science, both from the University of California, Berkeley, USA, in 1985 and 1989, respectively. He is a professor at the Electrical and Electronic Engineering Department, Hong Kong University of Science and Technology, PRC. He has published more than 100 refereed journal and conference papers. His research interests include robotics, nonlinear system theory, and manufacturing.

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Han, DP., Wei, Q. & Li, ZX. Kinematic control of free rigid bodies using dual quaternions. Int. J. Autom. Comput. 5, 319–324 (2008). https://doi.org/10.1007/s11633-008-0319-1

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  • DOI: https://doi.org/10.1007/s11633-008-0319-1

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