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Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant manipulators

Published online by Cambridge University Press:  29 April 2015

Wenfu Xu*
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China Shenzhen Engineering Laboratory of Digital Stage Performance Robot, Shenzhen, P. R. China
Lei Yan
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China Shenzhen Engineering Laboratory of Digital Stage Performance Robot, Shenzhen, P. R. China
Zonggao Mu
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China Aerospace Dongfanghong Development Ltd, Shenzhen, P. R. China
Zhiying Wang
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, P. R. China
*Corresponding author. E-mail:


An S-R-S (Spherical-Revolute-Spherical) redundant manipulator is similar to a human arm and is often used to perform dexterous tasks. To solve the inverse kinematics analytically, the arm-angle was usually used to parameterise the self-motion. However, the previous studies have had shortcomings; some methods cannot avoid algorithm singularity and some are unsuitable for configuration control because they use a temporary reference plane. In this paper, we propose a method of analytical inverse kinematics resolution based on dual arm-angle parameterisation. By making use of two orthogonal vectors to define two absolute reference planes, we obtain two arm angles that satisfy a specific condition. The algorithm singularity problem is avoided because there is always at least one arm angle to represent the redundancy. The dual arm angle method overcomes the shortcomings of traditional methods and retains the advantages of the arm angle. Another contribution of this paper is the derivation of the absolute reference attitude matrix, which is the key to the resolution of analytical inverse kinematics but has not been previously addressed. The simulation results for typical cases that include the algorithm singularity condition verified our method.

Copyright © Cambridge University Press 2015 

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