Advertisement

Towards Unified Framework for Trajectory Optimization Using General Differential Kinematics and Dynamics

  • Eiichi YoshidaEmail author
  • Ko Ayusawa
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 10)

Abstract

This paper presents a new framework for trajectory optimization using comprehensive differential kinematics and dynamics theory, and also its applications and perspectives. For a robotic system with large degrees of freedom including humanoid robots, numerical gradient computation is not practical in terms of precision and time. Trajectory optimization is more and more demanded in different fields not only for usual motion planning but also motion imitation, dynamic parameter identification and human motion understanding. The proposed theory is based on the comprehensive motion transformation matrix (CMTM) that allows describing variational relationship in differential kinematics and dynamics including velocity and acceleration based on a simple chain product. This enables analytical gradient computation of various physical quantities such as joint force or torque with respect to trajectory parameters, which is beneficial to various optimization problems. We overview the possible evolution brought by this technique and demonstrate its advantages through examples of efficient optimization of dynamic motions for a redundant robot and a humanoid under severe constraints. Also, we discuss the possibility of its integration in optimal control method.

Notes

Acknowledgements

This research has been partly supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (A) Number 17H00768.

References

  1. 1.
    Ayusawa, K., Morisawa, M., Yoshida, E.: Motion retargeting for humanoid robots based on identification to preserve and reproduce human motion features. In: Proceedings of the 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2774–2779 (2015)Google Scholar
  2. 2.
    Ayusawa, K., Nakamura, Y.: Fast inverse kinematics algorithm for large dof system with decomposed gradient computation based on recursive formulation of equilibrium. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3447–3452 (2012)Google Scholar
  3. 3.
    Ayusawa, K., Rioux, A., Yoshida, E., Venture, G., Gautier, M.: Generating persistently exciting trajectory based on condition number optimization. In: Proceedings of the 2017 IEEE International Conference Robotics and Automation, pp. 6518–6524 (2017)Google Scholar
  4. 4.
    Ayusawa, K., Venture, G., Nakamura, Y.: Identification of humanoid robots dynamics using floating-base motion dynamics. In: Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2854–2859 (2008)Google Scholar
  5. 5.
    Ayusawa, K., Yoshida, E.: Comprehensive theory of differential kinematics and dynamics for motion optimization. In: Robotics: Science and Systems XIII (2017)Google Scholar
  6. 6.
    Ayusawa, K., Yoshida, E.: Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework. Int. J. Rob. Res. (2018). (Under review)Google Scholar
  7. 7.
    Bouyarmane, K., Kheddar, A.: On the dynamics modeling of free-floating-base articulated mechanisms and applications to humanoid whole-body dynamics and control. In: Proceedings of the 2012 IEEE-RAS International Conference on Humanoid Robots, pp. 36–42 (2012)Google Scholar
  8. 8.
    Caron, S., Kheddar, A.: Multi-contact walking pattern generation based on model preview control of 3D com accelerations. In: Proceedings of the 2016 IEEE-RAS International Conference on Humanoid Robots, pp. 550–557 (2016)Google Scholar
  9. 9.
    Dai, H., Valenzuela, A., Tedrake, R.: Whole-body motion planning with centroidal dynamics and full kinematics. In: Proceedings of the 2014 IEEE-RAS International Conference on Humanoid Robots, pp. 295–302 (2014)Google Scholar
  10. 10.
    Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley-Interscience, New York (1897)Google Scholar
  11. 11.
    Imamura, Y., Ayusawa, K., Yoshida, E.: Risk estimation for intervertebral disc pressure through musculoskeletal joint reaction force simulation. In: Proceedings of the 39th IEEE Annual International Conference Engineering in Medicine and Biology Society (2017). To appearGoogle Scholar
  12. 12.
    Jovic, J., Escande, A., Ayusawa, K., Yoshida, E., Kheddar, A., Venture, G.: Humanoid and human inertia parameter identification using hierarchical optimization. IEEE Trans. Robot. 32(3), 726–735 (2016).  https://doi.org/10.1109/TRO.2016.2558190CrossRefGoogle Scholar
  13. 13.
    Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K., Hirukawa, H.: Biped walking pattern generation by using preview control of zero-moment point. In: Proceedings of the 2003 IEEE International Conference on Robotics and Automation, pp. 1620–1626 (2003)Google Scholar
  14. 14.
    Kaneko, K., Kanehiro, F., Morisawa, M., Akachi, K., Miyamori, G., Hayashi, A., Kanehira, N.: Humanoid robot HRP-4 - humanoid robotics platform with lightweight and slim body. In: Proceedings of the 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4400–4407 (2011)Google Scholar
  15. 15.
    Khatib, O.: A unified approach for motion and force control of robot manipulators: the operational space formulation. Int. J. Robot. Res. 3(1), 43–53 (1987)Google Scholar
  16. 16.
    Lengagne, S., Vaillant, J., Yoshida, E., Kheddar, A.: Generation of whole-body optimal dynamic multi-contact motions. Int. J. Robot. Res. 32(9–10), 1104–1119 (2013).  https://doi.org/10.1177/0278364913478990CrossRefGoogle Scholar
  17. 17.
    Liu, M., Micaelli, A., Evrard, P., Escande, A., Andriot, C.: Interactive virtual humans: a two-level prioritized control framework with wrench bounds. IEEE Trans. Robot. 28(6), 1309–1322 (2012)CrossRefGoogle Scholar
  18. 18.
    Miossec, S., Yokoi, K., Kheddar, A.: Development of a software for motion optimization of robots - application to the kick motion of the hrp-2 robot. In: Proceedings of the 2006 IEEE International Conference on Robotics and Biomimetics, pp. 299–304 (2006)Google Scholar
  19. 19.
    Mombaur, K.: Using optimization to create self-stable human-like running. Robotica 27, 321–330 (2009)CrossRefGoogle Scholar
  20. 20.
    Murai, A., Kurosaki, K., Yamane, K., Nakamura, Y.: Computationally fast estimation of muscle tension for realtime bio-feedback. In: Proceedings of the 31st Annual International Conference of the IEEE EMBS, pp. 6546–6549 (2009)Google Scholar
  21. 21.
    Nakamura, Y., Yamane, K., Fujita, Y., Suzuki, I.: Somatosensory computation for man-machine interface from motion-capture data and musculoskeletal human model. IEEE Trans. Robot. 21(1), 58–66 (2005)CrossRefGoogle Scholar
  22. 22.
    Nakaoka, S.: Choreonoid: extensible virtual robot environment built on an integrated gui framework. In: Proceedings of the 2012 IEEE/SICE International Symposium on System Integration, pp. 79–85 (2012)Google Scholar
  23. 23.
    Nakaoka, S., Komura, T.: Interaction mesh based motion adaptation for biped humanoid robots. In: Proceedings of the 2012 IEEE-RAS International Conference on Humanoid Robots, pp. 625–631 (2012)Google Scholar
  24. 24.
    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
  25. 25.
    Ramirez-Alpizar, I.G., Harada, K., Yoshida, E.: Motion planning for dual-arm assembly of ring-shaped elastic objects. In: Proceedings of the 2014 IEEE-RAS International Conference on Humanoid Robots, pp. 594–600 (2014)Google Scholar
  26. 26.
    Ratliff, N., Zucker, M., Bagnell, J.A., Srinivasa, S.: CHOMP: gradient optimization techniques for efficient motion planning. In: Proceedings 2009 IEEE International Conference on Roboics and Automation, pp. 489–494 (2009)Google Scholar
  27. 27.
    Schulman, J., Ho, J., Lee, A., Awwal, I., Bradlow, H., Abbeel, P.: Finding locally optimal, collision-free trajectories with sequential convex optimization. In: Proceedings of the Robotics: Science and Systems IX (2013)Google Scholar
  28. 28.
    Sohl, G.A., Bobrow, J.E.: A recursive multibody dynamics and sensitivity algorithm for branched kinematic chains. J. Dyn. Syst. Meas. Control 123(3), 391–399 (2001)CrossRefGoogle Scholar
  29. 29.
    Suleiman, W., Yoshida, E., Kanehiro, F., Laumond, J.P., Monin, A.: On human motion imitation by humanoid robot. In: Proceedings of the 2008 IEEE International Conference Robotics and Automation, pp. 2697–2704 (2008)Google Scholar
  30. 30.
    Suleiman, W., Yoshida, E., Laumond, J.P., Monin, A.: On humanoid motion optimization. In: Proceedings of 7th IEEE-RAS International Conference on Humanoid Robots, pp. 180–187 (2007)Google Scholar
  31. 31.
    Tassa, Y., Erez, T., Todorov, E.: Synthesis and stabilization of complex behaviors through online trajectory optimization. In: Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4906–4913 (2012)Google Scholar
  32. 32.
    Vaillant, J., Kheddar, A., Audren, H., Keith, F., Brossette, S., Escande, A., Bouyarman, K., Kaneko, K., Morisawa, M., Gergondet, P., Yoshida, E., Kajita, S., Kanehiro, F.: Multi-contact vertical ladder climbing with an hrp-2 humanoid. Auton. Robot. 40(3), 561580 (2016).  https://doi.org/10.1007/s10514-016-9546-4CrossRefGoogle Scholar
  33. 33.
    Vukobratović, M., Borovac, B.: Zero-moment point - thirty-five years of its life. Int. J. Humanoid Robot. 1(1), 157–174 (2004)CrossRefGoogle Scholar
  34. 34.
    Wieber, P.B.: Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. In: Proceedings of the 2006 IEEE-RAS International Conference on Humanoid Robots, pp. 137–142 (2006)Google Scholar
  35. 35.
    Yamane, K., Anderson, S.O., Hodgins, J.K.: Controlling humanoid robots with human motion data: Experimental validation. In: Proceedings 2010 IEEE-RAS International Conference on Humanoid Robots, pp. 504–510 (2010)Google Scholar
  36. 36.
    Yoshida, E., Belousov, I., Esteves, C., Laumond, J.P.: Humanoid motion planning for dynamic tasks. In: Proceedings of 5th IEEE-RAS International Conference on Humanoid Robots, pp. 1–6 (2005)Google Scholar
  37. 37.
    Yoshida, E., Esteves, C., Belousov, I., Laumond, J.P., Sakaguchi, T., Yokoi, K.: Planning 3D collision-free dynamic robotic motion through iterative reshaping. IEEE Trans. Robot. 24(5), 1186–1198 (2008).  https://doi.org/10.1109/TRO.2008.2002312CrossRefGoogle Scholar
  38. 38.
    Yoshida, E., Kanoun, O., Esteves, C., Laumond, J.P., Yokoi, K.: Task-driven support polygon reshaping for humanoids. In: Proceedings of 6th IEEE-RAS International Conference on Humanoid Robots, pp. 827–832 (2006)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.CNRS-AIST JRL (Joint Robotics Laboratory)TsukubaJapan

Personalised recommendations