A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint
Abstract
:1. Introduction
2. Forward Kinematics
- Locate the origin of Frame at the intersection of the two axes of UJ ;
- Choose axis along the central axis of Link ;
- Choose axis along the common axis (Axis 1 of UJ ) of the two mounting holes (mounting holes 1 and 2) of Link for UJ ;
- Choose axis to complete a right-handed frame. At this time, this axis coincides with the Axis 2 of UJ when the corresponding rotation angle of UJ is equal to zero. When the angle is not equal to zero, the coincidence no longer exists.
- and denote the rotation matrix of the homogeneous transformation matrix and , respectively.
- and denote the position vector of the homogeneous transformation matrix and , respectively.
- and denote the expressions of the rotation matrix and , respectively.
- , , , and , , , denote the expressions of , , , and , , , , respectively.
3. Inverse Kinematics
3.1. General Spherical Joint
3.2. Closed-Form Solution for Single-GSJ Section
3.3. Closed-Form Solution for Multiple-GSJ Section
3.3.1. Locations of the GSJs
3.3.2. Determination of and
3.3.3. GSJ Angles for Multiple-GSJ Section
4. Simulation
4.1. Solutions for a Random Single Given Pose
4.2. Solutions for the Straight-Line Paths along the x-axis, y-axis, and z-axis of the Base Frame
4.3. Solution for a Circle Path
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Lou, Y.; Quan, P.; Lin, H.; Wei, D.; Di, S. A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint. Appl. Sci. 2021, 11, 1277. https://doi.org/10.3390/app11031277
Lou Y, Quan P, Lin H, Wei D, Di S. A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint. Applied Sciences. 2021; 11(3):1277. https://doi.org/10.3390/app11031277
Chicago/Turabian StyleLou, Ya’nan, Pengkun Quan, Haoyu Lin, Dongbo Wei, and Shichun Di. 2021. "A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint" Applied Sciences 11, no. 3: 1277. https://doi.org/10.3390/app11031277
APA StyleLou, Y., Quan, P., Lin, H., Wei, D., & Di, S. (2021). A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint. Applied Sciences, 11(3), 1277. https://doi.org/10.3390/app11031277