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Open AccessArticle

Existence Conditions and General Solutions of Closed-form Inverse Kinematics for Revolute Serial Robots

1
School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
2
School of Computer Science & Technology, Beijing Institute of Technology, Beijing 100081, China
3
School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(20), 4365; https://doi.org/10.3390/app9204365
Received: 14 August 2019 / Revised: 18 September 2019 / Accepted: 10 October 2019 / Published: 16 October 2019
(This article belongs to the Special Issue Soft Robotics: New Design, Control, and Application)
This study proposes a method for judging the existence of closed-form inverse kinematics solutions based on the Denavit–Hartenberg (DH) model. In this method, serial robots with closed-form solutions are described using three types of sub-problems from the viewpoint of solving algebraic equations. If a serial robot can be described using these three types of sub-problems, i.e., if the inverse kinematics problems can be solved by several basic problems, then there is a closed-form solution. Based on the above method, we design a set of universal closed-form inverse kinematics solving algorithms. Since there is a definite formula solution for the three types of sub-problems, the joint angles can be rapidly determined. In addition, because the DH parameters can directly reflect the linkage of the robot, the judgment of the sub-problems is also quick and accurate. More importantly, the algorithm can be applied to serial robots with low degrees of freedom. This enables the algorithm to not only quickly and accurately solve inverse kinematics problems but also to exhibit high universality. This proposed theory improves the existence conditions for closed-form reverse solutions and further promotes the development of motion control techniques for serial robots. View Full-Text
Keywords: inverse kinematics; Denavit–Hartenberg method; closed-form solution; existence condition; universal inverse kinematics algorithm inverse kinematics; Denavit–Hartenberg method; closed-form solution; existence condition; universal inverse kinematics algorithm
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Shanda, W.; Xiao, L.; Qingsheng, L.; Baoling, H. Existence Conditions and General Solutions of Closed-form Inverse Kinematics for Revolute Serial Robots. Appl. Sci. 2019, 9, 4365.

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