Kinematic control of free rigid bodies using dual quaternions |
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Authors: | Da-Peng Han Qing Wei Ze-Xiang Li |
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Affiliation: | [1]College of Mechatronic Engineering and Automation~ National University of Defense Technology, Changsha 410073, PRC [2]Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hongkong, PRC |
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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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Keywords: | Kinematic control dual quaternion omnidirectional control proportional control |
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