Orientation Motion Planning Using Cubic Spline Interpolation Based on Euler Parameters
Main Article Content
Abstract
Many engineering applications require smooth orientation planning, i.e., interpolating the orientation of a rigid body so that its motion is smooth through intermediate poses. This smooth motion ensures for instance the continuity of the control torques. There are several ways to represent the orientation of a rigid body, so there are also different ways to plan motion for orientation. Each way has its advantages and disadvantages. In general, the problem of motion planning for the orientation has been less studied due to its complexity compared to motion planning for the endpoint. This paper presents the motion planning for the orientation using Euler parameters when the initial and final directions, and a set of intermediate directions are known. First, the Euler parameters are interpolated using cubic splines, and then they are normalized. Numerical simulations are carried out to validate the effectiveness of the proposed method. The proposed algorithms presented here preserve the fundamental properties of the interpolated rotation. The algorithms presented in this paper provide interpolation tools for rotation that are accurate, easy to implement.
Keywords
Euler’s parameters, orientation motion planning, cubic splines, numerical simulation
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[2] Nguyen Quang Hoang, Foundations of Robotics - Mechanics and Control, Bachkhoa Publishing House, 2023. (In Vietnamese: Nguyễn Quang Hoàng: Cơ sở robotics - Cơ học và Điều khiển, Nhà xuất bản Bách khoa Hà Nội, 2023).
[3] Luigi Biagiotti, and Claudio Melchiorri, Trajectory Planning for Automatic Machines and Robots, Berlin, Germany: Springer Science & Business Media, 2008. https://doi.org/10.1007/978-3-540-85629-0
[4] Ricardo Campa, Karla Camarillo, and Lina Arias, Kinematic modeling and control of robot manipulators via unit quaternions in application to a spherical wrist, Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA, Dec. 13-15, 2006. https://doi.org/10.1109/CDC.2006.377155
[5] Nguyen Van Khang, Dynamics of Multi-body Systems, Ha Noi, Vietnam: Science and Technology Publishing House, 2017. (In Vietnamese: Nguyễn Văn Khang: Động lực học hệ nhiều vật, Nhà xuất bản Khoa học và Kỹ thuật, 2017).
[6] John J Craig, Introduction to Robotics: Mechanics and Control, UK: Pearson/Prentice Hall, 2005.
[7] Bruno Siciliano, Lorenzo Sciavicco, Luigi Villani, and Giuseppe Oriolo, Robotics: Modelling, Planning and Control, London, UK: Springer Science & Business Media, 2010. https://doi.org/10.1007/978-1-84628-642-1
[8] Spong M. W., Hutchinson S., and Vidyasagar M., Robot Modeling and Control, New York, USA: John Wiley & Sons, 2006.
[9] O. A. Bauchau, S. Han, Interpolation of rotation and motion, Multibody System Dynamics, vol. 31, pp. 339-370, Mar. 2014. https://doi.org/10.1007/s11044-013-9365-8
[10] G. Kang and F. C. Park, Cubic spline algorithms for orientation interpolation, International Journal Numerical Methods in Engineering, vol. 46, iss. 1, pp. 45-64, Jul. 1999.
[11] G. M. Nielson, ν-Quaternion splines for the smooth interpolation of orientations, in IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 2, pp. 224-229, Mar - Apr. 2004. https://doi.org/10.1109/TVCG.2004.1260774
[12] David Eberly: Quaternion Algebra and Calculus, Geometric Tools, Redmond WA 98052, Last Modified: Aug. 18, 2010.
[13] Matthias Neubauer and Andreas Müller, Smooth orientation path planning with quaternions using B-splines, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015.
[14] A. H. Barr, B. Currin, S. Gabriel, J. F. Hughes, Smooth interpolation of orientations with angular velocity constraints using quaternions, in SIGGRAPH ’92 proceedings of the 19th annual conference on computer graphics and interactive techniques, New York, pp. 313, Jul. 1992. https://doi.org/10.1145/133994.134086
[15] Andrea Tagliavini and Corrado Guarino Lo Bianco, A smooth orientation planner for trajectories in the cartesian space, in IEEE Robotics and Automation Letters, vol. 8, iss. 5, pp. 2606-2613, May 2023. https://doi.org/10.1109/LRA.2023.3256921