“Parallel Inverse Kinematics for Multithreaded Architectures” by Harish, Mahmudi, Callennec and Boulic

  • ©Pawan Harish, Mentr Mahmudi, Benoît Le Callennec, and Ronan Boulic




    Parallel Inverse Kinematics for Multithreaded Architectures





    In this article, we present a parallel prioritized Jacobian-based inverse kinematics algorithm for multithreaded architectures. We solve damped least squares inverse kinematics using a parallel line search by identifying and sampling critical input parameters. Parallel competing execution paths are spawned for each parameter in order to select the optimum that minimizes the error criteria. Our algorithm is highly scalable and can handle complex articulated bodies at interactive frame rates. We show results on complex skeletons consisting of more than 600 degrees of freedom while being controlled using multiple end effectors. We implement the algorithm both on multicore and GPU architectures and demonstrate how the GPU can further exploit fine-grain parallelism not directly available on a multicore processor. Our implementations are 10 to 150 times faster compared to a state-of-the-art serial implementation while providing higher accuracy. We also demonstrate the scalability of the algorithm over multiple scenarios and explore the GPU implementation in detail.


    1. O. A. Aguilar and J. C. Huegel. 2011. Inverse kinematics solution for robotic manipulators using a CUDA-based parallel genetic algorithm. In Advances in Artificial Intelligence, Ildar Batyrshin and Grigori Sidorov (Eds.). Lecture Notes in Computer Science, Vol. 7094. 490–503. 
    2. AMD. 2013. OpenCL Programming and Optimization. Retrieved from http://free.eol.cn/edu_net/edudown/AMDppt/OpenCLProgrammingandO ptimization-Part II.pdf.
    3. A. Aristidou and J. Lasenby. 2011. FABRIK: A fast, iterative solver for the inverse kinematics problem. Graphical Models 73, 5 (2011), 243–260. 
    4. P. Baerlocher. 2001. Inverse Kinematics Techniques of the Interactive Posture Control of Articulated Figures. Ph.D. Dissertation. École Polytechnique Fédérale de Lausanne (EPFL).
    5. J. Baillieul. 1985. Kinematic programming alternatives for redundant manipulators. In Proceedings of the 1985 IEEE International Conference on Robotics and Automation. Proceedings. Vol. 2. 722–728.
    6. S. R. Buss. 2009. Introduction to Inverse Kinematics with Jacobian Transpose Pseudoinverse and Damped Least Squares Methods. Technical Report. University of California.
    7. S. R. Buss and J.-S. Kim. 2004. Selectively damped least squares for inverse kinematics. Journal of Graphics Tools 10 (2004), 37–49.
    8. C. Cao, J. Dongarra, P. Du, M. Gates, P. Luszczek, and S. Tomov. 2014. clMAGMA: High performance dense linear algebra with OpenCL. In Proceedings of the International Workshop on OpenCL 2013 & 2014 (IWOCL’’14). 11–19. 
    9. M. de Lasa, I. Mordatch, and A. Hertzmann. 2010. Feature-based locomotion controllers. ACM Transactions on Graphics 29, 3 (2010), 1–10. 
    10. A. S. Deo and I. D. Walker. 1992. Robot subtask performance with singularity robustness using optimal damped least-squares. In Proceedings of the 1992 IEEE International Conference on Robotics and Automation. 434–441.
    11. K. L. Doty, C. Melchiorri, and C. Bonivento. 1993. A theory of generalized inverses applied to robotics. International Journal of Robotics Research 12, 1 (1993), 1–19. 
    12. S. Farzan and G. N. DeSouza. 2013. From D-H to inverse kinematics: A fast numerical solution for general robotic manipulators using parallel processing. In Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’13). 2507–2513.
    13. M. Girard and A. A. Maciejewski. 1985. Computational modeling for the computer animation of legged figures. In ACM SIGGRAPH 1985 papers (SIGGRAPH’85). ACM, 263–270. 
    14. G. Golub and W. Kahan. 1965. Calculating the singular values and pseudo-inverse of a matrix. Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis 2, 2 (1965), 205–224.
    15. K. Grochow, S. L. Martin, A. Hertzmann, and Z. Popović. 2004. Style-based inverse kinematics. In ACM SIGGRAPH 2004 Papers (SIGGRAPH’04). 522–531. 
    16. M. Harris, S. Sengupta, and J. D. Owens. 2007. Parallel prefix sum (scan) with CUDA. In GPU Gems 3, Hubert Nguyen (Ed.). Addison Wesley.
    17. D. Hildenbrand, H. Lange, F. Stock, and A. Koch. 2008. Efficient inverse kinematics algorithm based on conformal geometric algebra using reconfigurable hardware. In Proceedings of the International Conference on Computer Graphics Theory and Applications. 300–307.
    18. S. Lahabar and P. J. Narayanan. 2009. Singular value decomposition on GPU using CUDA. In IEEE International Symposium on Parallel Distributed Processing, 2009 (IPDPS’09). 1–10. 
    19. M. Lampton. 1997. Damping-undamping strategies for the Levenberg-Marquardt nonlinear least-squares method. Computer Physics 11, 1 (1997), 110–115. 
    20. B. Le Callennec. 2006. Interactive Techniques for Motion Deformation of Articulated Figures Using Prioritized Constraints. Ph.D. Dissertation. École Polytechnique Fédérale de Lausanne (EPFL).
    21. N. H. Lehment, D. Arsic, M. Kaiser, and G. Rigoll. 2010. Automated pose estimation in 3d point clouds applying annealing particle filters and inverse kinematics on a GPU. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW’10). 87–92.
    22. A. Liégeois. 1977. Automatic supervisory control of the configuration and behavior of multibody mechanisms. IEEE Transactions on Systems, Man and Cybernetics 7, 12 (1977), 868–871.
    23. H. Ltaief, J. Kurzak, and J. Dongarra. 2010. Parallel two-sided matrix reduction to band bidiagonal form on multicore architectures. IEEE Transactions on Parallel and Distributed Systems 21, 4 (2010), 417–423. 
    24. A. A. Maciejewski. 1990. Dealing with the ill-conditioned equations of motion for articulated figures. IEEE Computer Graphics and Applications 10, 3 (1990), 63–71. 
    25. W. Masinghe, G. Collier, A. Ordys, and T. Nanayakkara. 2012. A novel approach to determine the inverse kinematics of a human upper limb model with 9 degrees of freedom. In Proceedings of the 2012 IEEE EMBS Conference on Biomedical Engineering and Sciences (IECBES’12). 525–530.
    26. Y. Nakamura, H. Hanafusa, and T. Yoshikawa. 1987. Task-priority based redundancy control of robot manipulators. International Journal of Robotics Research 6, 2 (1987), 3–15. 
    27. C. R. Rao, J. L. Solka, and E. J. Wegman. 2005. Handbook of Statistics: Data Mining and Data Visualization. Elsevier. 
    28. M. Schroder, J. Maycock, H. Ritter, and M. Botsch. 2014. Real-time hand tracking using synergistic inverse kinematics. In Proceedings of the 2014 IEEE International Conference on Robotics and Automation (ICRA’14). 5447–5454.
    29. R. W. Sumner, M. Zwicker, C. Gotsman, and J. Popović. 2005. Mesh-based inverse kinematics. In ACM SIGGRAPH 2005 Papers (SIGGRAPH’05). ACM, 488–495. 
    30. A. N. Tikhonov. 1963. Solution of incorrectly formulated problems and the regularization method. Doklady Akademii Nauk SSSR 151 (1963), 501–504.
    31. M. K. Transtrum and J. P. Sethna. 2012. Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization. http://arxiv.org/abs/1201.5885 (01/ 2012).
    32. V. Volkov and J. Demmel. 2008. LU, QR and Cholesky Factorizations Using Vector Capabilities of GPUs. Technical Report. EECS Department, University of California, Berkeley.
    33. R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban. 2006. An interior algorithm for nonlinear optimization that combines line search and trust region steps. Mathematics Programming 107, 3 (2006), 391–408. 
    34. A. Watt and M. Watt. 1991. Advanced Animation and Rendering Techniques. ACM, New York, NY. 
    35. H. Zhang and R. P. Paul. 1991. A parallel inverse kinematics solution for robot manipulators based on multiprocessing and linear extrapolation. IEEE Transactions on Robotics and Automation 7, 5 (Oct. 1991), 660–669.

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