Abstract
In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point (so-called Gimbal Lock). However, quaternion interpolation has the advantage of natural (specifically smooth) orientation interpolation without Gimbal Lock. This work presents the application of quaternion interpolation, specifically Spherical Linear IntERPolation (SLERP), to the orientation control of the 6-axis articulated robot (RS2) using LabVIEW® and RecurDyn®. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement (profile) of joint angles (torques), the two methods are dynamically simulated on RS2 by using both LabVIEW® and RecurDyn®. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW® motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional (linear) Euler interpolation.
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References
FU K S, GONZALEZ R C, LEE C S G. Robotics: Control, sensing, vision and intelligence [M]. New York: McGraw-Hill, 1987:22.
HOAG D. Apollo guidance and Navigation: Considerations of apollo imu gimbal lock [M]. Canbridge: MIT Instrumentation Laboratory, 1963: 1–64.
JONES E M, FJELD P. Gimbal Angles, Gimbal Lock, and a Fourth Gimbal for Christmas [EB/OL]. http://www.hq.nasa.gov/office/pao/History/alsj/gimbals.html, 2002.
PURWAR A, JIN Z, GE Q J. Computer aided synthesis of piecewise rational motions for spherical 2R and 3R robot arms [C]// Annual Mechanisms and Robotics Conference, Las Vegas, 2006: 1209–1222.
AHLERS S G, McCARTHY J M. The clifford algebra of double quaternions and the optimization of Ts robot design, applications of clifford algebras in computer science and engineering [M], Birkhauser Inc, 2000.
CHUNG W J, KIM K J, KIM S H. Steering control algorithm of an inter-block locomotion robot using a quaternion with spherical cubic interpolation [J]. Systemics Cybernetics and Informatics 2005: 374–379.
DAM E B, KOCH M, LILLHOLM M. Quaternions, interpolation and animation. DIKU-TR9815 [R]. Copenhagen: department of Computer Science, University of Copenhagen, 1998.
AHN J S, CHUNG W J. On design prototype and gain optimization for heavy duty handling articulated manipulator (hdham) with 6 DOF [C]// The 14th World Multi-Conference on Systemics, Cybernetics and Informatics: WMSCI 2010, Orlando, 2010: 174–179.
SPONG M, VIDYASAGAR M. Robot dynamics and control [M]. Hoboken: John Wiley and Sons, 1989: 20–70.
AHN J S, CHUNG W J. A Study on 6-axis articulated robot using a quaternion interpolation [C]// KSMTE of Spring Conference 2010, Seoul, 2010: 294–300.
SHOEMAKE K. Animating rotation with quaternion curves [C]// Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques, San Francisco, 1985: 245–254.
MEBIUS J E. Derivation of the Euler-rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations [J]. arXiv General Mathematics, 2007: 0701659vl.
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Foundation item: Project supported by the Second Stage of Brain Korea 21 Projects
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Ahn, Js., Chung, Wj. & Jung, Cd. Realization of orientation interpolation of 6-axis articulated robot using quaternion. J. Cent. South Univ. 19, 3407–3414 (2012). https://doi.org/10.1007/s11771-012-1422-6
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DOI: https://doi.org/10.1007/s11771-012-1422-6