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Motion optimization using Gaussian process dynamical models

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Abstract

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.

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References

  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. Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  3. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  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. 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. Lawrence, N.D.: Gaussian process latent variable models for visualization of high dimensional data. Adv. Neural Inf. Process. Syst. 16, 329–336 (2004)

    MathSciNet  Google Scholar 

  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. 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. 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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  12. Featherstone, R.: Robot Dynamics Algorithms. Kluwer, Boston (1987)

    Google Scholar 

  13. Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  17. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)

    Google Scholar 

  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. Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30(7), 846–894 (2011)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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Correspondence to Hyuk Kang.

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Kang, H., Park, F.C. Motion optimization using Gaussian process dynamical models. Multibody Syst Dyn 34, 307–325 (2015). https://doi.org/10.1007/s11044-014-9441-8

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