Multibody System Dynamics

, Volume 34, Issue 4, pp 307–325 | Cite as

Motion optimization using Gaussian process dynamical models

  • Hyuk KangEmail author
  • F. C. Park


We propose an efficient method for generating suboptimal motions for multibody systems using Gaussian process dynamical models. Given a dynamical model for a multibody system, and a trial motion, a lower-dimensional Gaussian process dynamical model is fitted to the trial motion. New motions are then generated by performing a dynamic optimization in the lower-dimensional space. We introduce the notion of variance tubes as an intuitive and efficient means of restricting the optimization search space. The performance of our algorithm is evaluated through detailed case studies of raising motions for an arm and jumping motions for a humanoid.


Robot dynamics Motion optimization Machine learning Gaussian process dynamical model 


  1. 1.
    Lim, B., Ra, S., Park, F.C.: Movement primitives, principal component analysis, and the efficient generation of natural motions. In: IEEE International Conference on Robotics and Automation, pp. 4641–4646 (2005) Google Scholar
  2. 2.
    Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000) CrossRefGoogle Scholar
  3. 3.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000) CrossRefGoogle Scholar
  4. 4.
    Roweis, S., Saul, L., Hinton, G.E.: Global coordination of local linear models. In: Advances in Neural Information Processing Systems, vol. 14, pp. 889–896 (2001) Google Scholar
  5. 5.
    Teh, W.Y., Roweis, S.: Automatic alignment of local representations. In: Advances in Neural Information Processing Systems, vol. 15, pp. 841–848. MIT Press, Cambridge (2003) Google Scholar
  6. 6.
    Lawrence, N.D.: Gaussian process latent variable models for visualization of high dimensional data. Adv. Neural Inf. Process. Syst. 16, 329–336 (2004) MathSciNetGoogle Scholar
  7. 7.
    Grochow, K., Martin, S.L., Hertzmann, A., Popović, Z.: Style-based inverse kinematics. In: ACM Transactions on Graphics (TOG), vol. 23, pp. 522–531. ACM, New York (2004) Google Scholar
  8. 8.
    Yamane, K., Ariki, Y., Hodgins, J.: Animating non-humanoid characters with human motion data. In: ACM SIGGRAPH Symposium on Computer Animation, pp. 169–178. ACM, New York (2010) Google Scholar
  9. 9.
    Kang, H., Park, F.C.: Humanoid motion optimization via nonlinear dimension reduction. In: IEEE International Conference on Robotics and Automation, pp. 1444–1449 (2012) Google Scholar
  10. 10.
    Wang, J.M., Fleet, D.J., Hertzmann, A.: Gaussian process dynamical models for human motion. IEEE Trans. Pattern Anal. Mach. Intell. 30(2), 283–298 (2008) CrossRefGoogle Scholar
  11. 11.
    Park, F.C., Bobrow, J.E., Ploen, S.R.: A Lie group formulation of robot dynamics. Int. J. Robot. Res. 14(6), 609–618 (1995) CrossRefGoogle Scholar
  12. 12.
    Featherstone, R.: Robot Dynamics Algorithms. Kluwer, Boston (1987) Google Scholar
  13. 13.
    Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994) Google Scholar
  14. 14.
    Babić, J., Lim, B., Omrćen, D., Lenarćić, J., Park, F.C.: A biarticulated robotic leg for jumping movements: theory and experiments. J. Mech. Robot. 1(1), 011013 (2009) CrossRefGoogle Scholar
  15. 15.
    Bobrow, J.E., Martin, B., Sohl, G., Wang, E.C., Kim, J., Park, F.C.: Optimal robot motions for physical criteria. J. Robot. Syst. 18(12), 785–795 (2001) CrossRefGoogle Scholar
  16. 16.
    Lee, S.H., Kim, J.G., Kim, M.S., Park, F.C., Bobrow, J.E.: Newton-type algorithms for dynamic-based robot motion optimization. IEEE Trans. Robot. 21(4), 657–667 (2005) CrossRefGoogle Scholar
  17. 17.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006) Google Scholar
  18. 18.
    Webb, D.J., Berg, J.V.D.: Kinodynamic RRT*: asymptotically optimal motion planning for robots with linear dynamics. In: IEEE International Conference on Robotics and Automation, pp. 5054–5061 (2013) Google Scholar
  19. 19.
    Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30(7), 846–894 (2011) CrossRefGoogle Scholar
  20. 20.
    Park, J., Han, J., Park, F.C.: Convex optimization algorithms for active balancing of humanoid robots. IEEE Trans. Robot. 23(4), 817–822 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringSeoul National UniversitySeoulKorea

Personalised recommendations