Momentum control with hierarchical inverse dynamics on a torque-controlled humanoid

Abstract

Hierarchical inverse dynamics based on cascades of quadratic programs have been proposed for the control of legged robots. They have important benefits but to the best of our knowledge have never been implemented on a torque controlled humanoid where model inaccuracies, sensor noise and real-time computation requirements can be problematic. Using a reformulation of existing algorithms, we propose a simplification of the problem that allows to achieve real-time control. Momentum-based control is integrated in the task hierarchy and a LQR design approach is used to compute the desired associated closed-loop behavior and improve performance. Extensive experiments on various balancing and tracking tasks show very robust performance in the face of unknown disturbances, even when the humanoid is standing on one foot. Our results demonstrate that hierarchical inverse dynamics together with momentum control can be efficiently used for feedback control under real robot conditions.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Notes

  1. 1.

    Part of the material presented in this paper has been presented at the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

  2. 2.

    We originally proposed the simplification in a technical note (Herzog et al. 2013).

  3. 3.

    The part of \(\mathbf{M_l}\) multiplying the base acceleration is always full rank.

  4. 4.

    The movie is also available on www.youtube.com/watch?v=jMj3Uv2Q8Xg.

References

  1. Ayusawa, K., Venture, G., & Nakamura, Y. (2014). Identifiability and identification of inertial parameters using the underactuated base-link dynamics for legged multibody systems. The International Journal of Robotics Research, 33, 446–468.

    Article  Google Scholar 

  2. Bloesch, M., Hutter, M., Hoepflinger, M. H., Remy, C. D., Gehring, C., & Siegwart, R. (2012). State estimation for legged robots consistent fusion of leg kinematics and IMU. Sydney: Robotics: science and systems (R:SS).

  3. Boaventura, T., Focchi, M., Frigerio, M., Buchli, J., Semini, C., Medrano-Cerda, G.A., & Caldwell, D. (2012). On the role of load motion compensation in high-performance force control. In IEEE/RSJ international conference on intelligent robots and systems.

  4. Boaventura, T., Semini, C., Buchli, J., Frigerio, M., Focchi, M., & Caldwell, D. (2012). Dynamic torque control of a hydraulic quadruped robot. In IEEE international conference on robotics and automation.

  5. Cheng, G., Sang-Ho, H., Ude, A., Morimoto, J., Hale, J.G., Hart, J., Nakanishi, J., Bentivegna, D., Hodgins, J., Atkeson, C., Mistry, M., Schaal, S., & Kawato, M. (2008). CB: Exploring neuroscience with a humanoid research platform. In IEEE international conference on robotics and automation.

  6. de Lasa, M., Mordatch, I., & Hertzmann, A. (2010). Feature-based locomotion controllers. ACM Transactions on Graphics, 29(3).

  7. Escande, A., Mansard, N., & Wieber, P. B. (2014). Hierarchical quadratic programming: Fast online humanoid-robot motion generation. The International Journal of Robotics Research, 33(7), 1006–1028.

    Article  Google Scholar 

  8. Faraji, S., Pouya, S., Atkeson, C., & Ijspeert, A. (2014). Versatile and robust 3d walking with a simulated humanoid robot (atlas): a model predictive control approach. In IEEE international conference on robotics and automation.

  9. Feng, S., Xinjilefu, X., Huang, W., & Atkeson, C. (2014). 3D walking based on online optimization. In IEEE international conference on robotics and automation.

  10. Goldfarb, D., & Idnani, A. (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming, 27(1), 1–33.

    Article  MathSciNet  MATH  Google Scholar 

  11. Herzog, A., Righetti, L., Grimminger, F., Pastor, P., & Schaal, S. (2013). Momentum-based balance control for torque-controlled humanoids. http://arxiv.org/abs/1305.2042v1.

  12. Herzog, A., Righetti, L., Grimminger, F., Pastor, P., & Schaal, S. (2014). Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics. In IEEE/RSJ international conference on intelligent robots and systems.

  13. Hutter, M., Hoepflinger, M.A., Gehring, C., Bloesch, M., Remy, C.D., & Siegwart, R. (2012). Hybrid operational space control for compliant legged systems. Sydney: Robotics: science and systems (R:SS).

  14. Hyon, S. H., Hale, J. G., & Cheng, G. (2007). Full-body compliant human-humanoid interaction: Balancing in the presence of unknown external forces. IEEE Transactions on Robotics, 23(5), 884–898.

    Article  Google Scholar 

  15. Jarquin, G., Escande, A., Arechavaleta, G., Moulard, T., Yoshida, E., & Parra-Vega, V. (2013). Real-time smooth task transitions for hierarchical inverse kinematics. In IEEE-RAS international conference on humanoid robots.

  16. Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K., & Hirukawa, H. (2003) Resolved momentum control: Humanoid motion planning based on the linear and angular momentum. In IEEE/RSJ international conference on intelligent robots and systems.

  17. Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., & Schaal, S. (2011). Learning, planning, and control for quadruped locomotion over challenging terrain. The International Journal of Robotics Research, 30(2), 236–258.

    Article  Google Scholar 

  18. Kanoun, O., Lamiraux, F., & Wieber, P. B. (2011). Kinematic control of redundant manipulators: Generalizing the task-priority framework to inequality task. IEEE Transactions on Robotics, 27(4), 785–792.

    Article  Google Scholar 

  19. Kuindersma, S., Permenter, F., & Tedrake, R. (2014). An efficiently solvable quadratic program for stabilizing dynamic locomotion. In IEEE international conference on robotics and automation.

  20. Lee, S.H., & Goswami, A. (2010). Ground reaction force control at each foot: A momentum-based humanoid balance controller for non-level and non-stationary ground. In IEEE/RSJ international conference on intelligent robots and systems (pp. 3157–3162).

  21. Lee, S. H., & Goswami, A. (2012). A momentum-based balance controller for humanoid robots on non-level and non-stationary ground. Autonomous Robots, 33, 399–414.

    Article  Google Scholar 

  22. Mansard, N. (2012). A dedicated solver for fast operational-space inverse dynamics. In IEEE international conference on robotics and automation.

  23. Mason, S., Righetti, L., & Schaal, S. (2014). Full dynamics lqr control of a humanoid robot: An experimental study on balancing and squatting. In IEEE-RAS international conference on humanoid robots.

  24. Mistry, M., Schaal, S., & Yamane, K. (2009). Inertial parameter estimation of floating base humanoid systems using partial force sensing. In IEEE-RAS international conference on humanoid robots.

  25. Moro, F., Gienger, M., Goswami, A., Tsagarakis, N., & Caldwell, D. (2013). An attractor-based whole-body motion control (wbmc) system for humanoid robots. In IEEE-RAS international conference on humanoid robots.

  26. Nakamura, Y., Hanafusa, H., & Yoshikawa, T. (1987). Task-priority based redundancy control of robot manipulators. The International Journal of Robotics Research, 6, 3–15.

    Article  Google Scholar 

  27. Orin, D.E., & Goswami, A. (2008). Centroidal momentum matrix of a humanoid robot: Structure and properties. In IEEE/RSJ international conference on intelligent robots and systems.

  28. Ott, C., Roa, M.A., & Hirzinger, G. (2011) Posture and balance control for biped robots based on contact force optimization. In IEEE-RAS international conference on humanoid robots.

  29. Pratt, J., Koolen, T., De Boer, T., Rebula, J., Cotton, S., Carff, J., et al. (2012). Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid. The International Journal of Robotics Research, 31(10), 1117–1133.

    Article  Google Scholar 

  30. Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., & Schaal, S. (2013). Optimal distribution of contact forces with inverse-dynamics control. The International Journal of Robotics Research, 32(3), 280–298.

    Article  Google Scholar 

  31. Righetti, L., Buchli, J., Mistry, M., & Schaal, S. (2011) Control of legged robots with optimal distribution of contact forces. In: 11th IEEE-RAS international conference on humanoid robots (pp. 318–324).

  32. Rotella, N., Bloesch, M., Righetti, L., & Schaal, S. (2014). State estimation for a humanoid robot. In IEEE/RSJ international conference on intelligent robots and systems.

  33. Saab, L., Ramos, O., Mansard, N., Soueres, P., & Fourquet, J. Y. (2013). Dynamic whole-body motion generation under rigid contacts and other unilateral constraints. IEEE Transactions on Robotics, 29, 346–362.

    Article  Google Scholar 

  34. Salini, J., Padois, V., & Bidaud, P. (2011) Synthesis of complex humanoid whole-body behavior: A focus on sequencing and tasks transitions. In IEEE international conference on robotics and automation.

  35. Sentis, L., & Khatib, O. (2005). Synthesis of whole-body behaviors through hierarchical control of behavioral primitives. International Journal of Humanoid Robotics, 2, 505–518.

    Article  Google Scholar 

  36. Stephens, B.J., & Atkeson, C.G. (2010). Dynamic balance force control for compliant humanoid robots. In IEEE/RSJ international conference on intelligent robots and systems.

  37. Urata, J., Nshiwaki, K., Nakanishi, Y., Okada, K., Kagami, S., & Inaba, M. (2012). Online walking pattern generation for push recovery and minimum delay to commanded change of direction and speed. In IEEE/RSJ international conference on intelligent robots and systems.

  38. Vaillant, J., Kheddar, A., Audren, H., Keith, F., Brossette, S., Kaneko, K., Morisawa, M., Yoshida, E., & Kanehiro, F. (2014) Vertical ladder climbing by the HRP-2 humanoid robot. In Humanoids 2014 14th IEEE-RAS international conference on humanoid robots (pp. 671–676).

  39. Wensing, P., & Orin, D. (2013). Generation of dynamic humanoid behaviors through task-space control with conic optimization. In IEEE international conference on robotics and automation.

  40. Wieber, P. (2006). Fast motions in biomechanics and robotics (pp. 411–425)., Holonomy and nonholonomy in the dynamics of articulated motion Berlin: Springer.

    Google Scholar 

Download references

Acknowledgments

We would like to thank Ambarish Goswami and Seungkook Yun for hosting us at the Honda Research Institute for one week and for their precious help in understanding the original momentum-based controller. We would also like to thank Ambarish Goswami and Sung-Hee Lee for giving us an early access to their publication. We are also grateful to Daniel Kappler for helping us with the videos. Last, but not least, we would like to thank the anonymous reviewers for their very valuable comments that helped improve the final version of the paper. This research was supported in part by National Science Foundation Grants IIS-1205249, IIS-1017134, CNS-0960061, EECS-0926052, the DARPA program on Autonomous Robotic Manipulation, the Office of Naval Research, the Okawa Foundation, and the Max-Planck-Society. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding organizations.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Alexander Herzog.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 16300 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Herzog, A., Rotella, N., Mason, S. et al. Momentum control with hierarchical inverse dynamics on a torque-controlled humanoid. Auton Robot 40, 473–491 (2016). https://doi.org/10.1007/s10514-015-9476-6

Download citation

Keywords

  • Whole-body control
  • Multi-contact interaction
  • Hierarchical control
  • Inverse dynamics
  • Force control
  • Humanoid