Autonomous Robots

, Volume 34, Issue 4, pp 347–361 | Cite as

Reflexive stability control framework for humanoid robots

  • Tadej PetričEmail author
  • Andrej Gams
  • Jan Babič
  • Leon Žlajpah


In this paper we propose a general control framework for ensuring stability of humanoid robots, determined through a normalized zero-moment-point (ZMP). The proposed method is based on the modified prioritized kinematic control, which allows smooth and continuous transition between priorities. This, as long as the selected criterion is met, allows arbitrary joint movement of a robot without any regard of the consequential movement of the ZMP. On the other hand, it constrains the movement when the criterion approaches a critical condition. The critical condition thus triggers a reflexive, subconscious behavior, which has a higher priority than the desired, conscious movement. The transition between the two is smooth and reversible. Furthermore, the switching is encapsulated in a single modified prioritized task control equation. We demonstrate the properties of the algorithm on two human-inspired robots developed in our laboratory; a human-inspired leg-robot used for imitating human movement and a skiing robot.


Humanoids Stability Skiing robot 



This paper was partially funded by the European Community’s Seventh Framework Programme FP7/2007-2013 (Specific Programme Cooperation, Theme 3, Information and Communication Technologies) under grant agreement no. 269959, IntellAct.

Supplementary material

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  1. Antonelli, G. (2009). Stability analysis for prioritized closed-loop inverse kinematic algorithms for redundant robotic systems. IEEE Transactions on Robotics, 25(5), 985–994.CrossRefGoogle Scholar
  2. Asfour, T., & Dillmann, R. (2003). Human-like motion of a humanoid robot arm based on a closed-form solution of the inverse kinematics problem. In Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), (Vol. 2, pp. 1407–1412).Google Scholar
  3. Atkeson, C., Hale, J., Pollick, F., Riley, M., Kotosaka, S., Schaul, S., et al. (2000). Using humanoid robots to study human behavior. IEEE on Intelligent Systems and their Applications, 15(4), 46–56.CrossRefGoogle Scholar
  4. Babic, J., & Lenarcic, J. (2006). Optimization of biarticular gastrocnemius muscle in humanoid jumping robot simulation. International Journal of Humanoid Robotics, 3(2), 219–234.zbMATHCrossRefGoogle Scholar
  5. Babič, J., Bokman, L., Omrčen, D., Lenarčič, J., & Park, F. (2009). A biarticulated robotic leg for jumping movements: theory and experiments. Journal of Mechanisms and Robotics, 1, 1–9.Google Scholar
  6. Babič, J., Hale, J. G., & Oztop, E. (2011). Human sensorimotor learning for humanoid robot skill synthesis. Adaptive Behavior, 19(4), 250–263.Google Scholar
  7. Babič, J., & Škorja, G. (2012). Analysis of musculoskeletal system responses to perturbations during standing posture. Elektrotehniki vestnik, 79(1/2), 7–12.Google Scholar
  8. Baerlocher, P., & Boulic, R. (1998). Task-priority formulations for the kinematic control of highly redundant articulated structures. In Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (Vol. 1, pp. 323–329).Google Scholar
  9. Chen, T.-H., Cheng, F.-T., Sun, Y.-Y., & Hung, M.-H. (1994). Torque optimization schemes for kinematically redundant manipulators. Journal of Robotic Systems, 11(4), 257–269.zbMATHCrossRefGoogle Scholar
  10. Cherubini, A., & Chaumette, F. (2010). A redundancy-based approach for obstacle avoidance in mobile robot navigation. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), (pp. 5700–5705).Google Scholar
  11. Federolf, P.A. (2005). Finite element simulation of a carving alpine ski. PhD thesis, Swiss Federal Institute of Technology Zurich.Google Scholar
  12. Gams, A., Ijspeert, A. J., Schaal, S., & Lenarčič, J. (2009). On-line learning and modulation of periodic movements with nonlinear dynamical systems. Autonomous Robots, 27(1), 3–23.CrossRefGoogle Scholar
  13. Gams, A., Petrič, T., Babič, J., Žlajpah, L., & Ude, A. (2011). Constraining movement imitation with reflexive behavior: Robot squatting. In 11th IEEE-RAS International Conference on Humanoid Robots (Humanoids), (pp. 294–299).Google Scholar
  14. Grillner, S. (1975). Locomotion in vertebrates: central mechanisms and reflex interaction. Physiological Reviews, 55(2), 247–304.CrossRefGoogle Scholar
  15. Harada, K., Kajita, S., Kaneko, K., & Hirukawa, H. (2003). Zmp analysis for arm/leg coordination. In Proceedings of 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), (Vol. 1, pp. 75–81).Google Scholar
  16. Hirai, K., Hirose, M., Haikawa, Y., & Takenaka, T. (1998). The development of honda humanoid robot. In Proceedings of 1998 IEEE International Conference on Robotics and Automation, (Vol. 2, pp. 1321–1326).Google Scholar
  17. Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N., et al. (2001). Planning walking patterns for a biped robot. Robotics and Automation, IEEE Transactions, 17(3), 280–289.Google Scholar
  18. Hutter, M., Hoepflinger, M. A., Gehring, C., Bloesch, M., Remy, C. D., & Siegwart, R. (2012). Hybrid operational space control for compliant legged systems. RSS: In Robotics Science and Systems VIII.Google Scholar
  19. Hyon, S.-H., Hale, J., & Cheng, G. (2007). Full-body compliant human-humanoid interaction: Balancing in the presence of unknown external forces. Robotics, IEEE Transactions, 23(5), 884–898.CrossRefGoogle Scholar
  20. Ijspeert, A. J. (2008). Central pattern generators for locomotion control in animals and robots: A review. Neural Networks, 21(4), 642–653.CrossRefGoogle Scholar
  21. Ijspeert, A. J., Nakanishi, J., & Schaal, S. (2002). Movement imitation with nonlinear dynamical systems in humanoid robots. In Proceedings of IEEE International Conference on Robotics and Automation, (pp. 1398–1403). Washington, DC.Google Scholar
  22. Khatib, O. (1987). A unified approach for motion and force control of robot manipulators: The operational space formulation. IEEE Journal of Robotics and Automation, 3(1), 43–53.CrossRefGoogle Scholar
  23. Komoguchi, Y., Yano, K., Peer, A., & Buss, M. (2008). Redundancy resolution of a 7 dof haptic interface considering collision and singularity avoidance. In IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2008, pp. 3513–3518.Google Scholar
  24. Lahajnar, L. (2009). Avtonomno smucanje humanoidnega robota. PhD thesis, Faculty of Electrical Engineering, University of Ljubljana.Google Scholar
  25. Lahajnar, L., Kos, A., & Nemec, B. (2009). Skiing robot-design, control, and navigation in unstructured environment. Robotica, 27, 567–577.CrossRefGoogle Scholar
  26. Liegeois, A. (1977). Automatic supervisory control of the configuration and behavior of multibody mechanisms. IEEE Transactions on Systems Man and Cybernetics, 7(12), 868–871.zbMATHCrossRefGoogle Scholar
  27. Maciejewski, A. A., & Klein, C. A. (1985). Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments. The International Journal of Robotics Research, 4(3), 109–117.CrossRefGoogle Scholar
  28. Mansard, N., Khatib, O., & Kheddar, A. (2009). A unified approach to integrate unilateral constraints in the stack of tasks. IEEE Transactions on Robotics, 25(3), 670–685.CrossRefGoogle Scholar
  29. Murphy, R. R. (2000). Introduction to AI robotics (1st ed.), MIT Press, Cambridge.Google Scholar
  30. Nakamura, Y. (1990). Advanced Robotics: Redundancy and Optimization (1st ed.), Addison-Wesley Longman Publishing Co., Inc., Boston.Google Scholar
  31. Nemec, B., & Lahajnar, L. (2009). Control and navigation of the skiing robot. In Proceedings of the 2009 IEEE/RSJ international conference on Intelligent Robots and Systems IROS’09, (pp. 2321–2326). IEEE Press: Piscataway.Google Scholar
  32. Nemec, B., Žlajpah, L., & Omrčen, D. (2007). Comparison of null-space and minimal null-space control algorithms. Robotica, 25(05), 511–520.CrossRefGoogle Scholar
  33. Oberegger, U. F., Kaps, P., Mssner, M., Heinrich, D., & Nachbauer, W. (2010). Simulation of turns with a 3d skier model. Procedia Engineering, 2(2):3171–3177. The Engineering of Sport 8 - Engineering Emotion.Google Scholar
  34. Omrčen, D., & Ude, A. (2010). Redundancy control of a humanoid head for foveation and three-dimensional object tracking: A virtual mechanism approach. Advanced Robotics, 24(15), 2171–2197.CrossRefGoogle Scholar
  35. Peternel, L., Petrič, T., & Nemec, B. (2011). Skiing robot navigation learning. In Zbornik 14. Mednarodne multikonference Informacijska druba-IS 2011, (vol. A). Institut Jozef Stefan.Google Scholar
  36. Petrič, T., Curk, B., Cafuta, P., & Žlajpah, L. (2010). Modeling of the robotic powerball: A nonholonomic, underactuated, and variable structure-type system. Mathematical and Computer Modelling of Dynamical Systems, 16(4), 327–346.zbMATHCrossRefMathSciNetGoogle Scholar
  37. Petrič, T., Gams, A., Ijspeert, A. J., & Žlajpah, L. (2011a). On-line frequency adaptation and movement imitation for rhythmic robotic tasks. The International Journal of Robotics Research, 30(14), 1775–1788Google Scholar
  38. Petrič, T., Nemec, B., Babič, J., & Žlajpah, L. (2011b). Multilayer control of skiing robot. In International Conference on Intelligent Robots and Systems (IROS), 2011 IEEE/RSJ, (pp. 4832–4837). Google Scholar
  39. Righetti, L., & Ijspeert, A. J. (2006). Programmable central pattern generators: an application to biped locomotion control. In Proceedings of the 2006 IEEE International Conference on Robotics and Automation.Google Scholar
  40. Samson, C., Espiau, B., & Borgne, M. L. (1991). Robot control: The task function approach. Oxford: Oxford University Press.Google Scholar
  41. Schaal, S., Mohajerian, P., & Ijspeert, A. (2007). Dynamics systems vs. optimal control: A unifying view. Progress in Brain Research, 165(6), 425–445.CrossRefGoogle Scholar
  42. Sciavicco, L., & Siciliano, B. (2005). Modelling and control of robot manipulators (advanced textbooks in control and signal processing). Advanced textbooks in control and signal processing (2nd ed.). Heidelberg: Springer.Google Scholar
  43. Sentis, L., Park, J., & Khatib, O. (2010). Compliant control of multicontact and center-of-mass behaviors in humanoid robots. IEEE Transactions on Robotics, 26(3), 483–501.CrossRefGoogle Scholar
  44. Shin, D., Sardellitti, I., Park, Y.-L., Khatib, O., & Cutkosky, M. (2010). Design and control of a bio-inspired human-friendly robot. The International Journal of Robotics Research, 29(5), 571–584.CrossRefGoogle Scholar
  45. Siciliano, B., & Khatib, O. (Eds.). (2008). Springer Handbook of Robotics. Heidelberg: Springer.Google Scholar
  46. Siciliano, B., & Slotine, J.-J. (1991). A general framework for managing multiple tasks in highly redundant robotic systems. In 5th International Conference on Advanced Robotics,’Robots in Unstructured Environments’, 91 ICAR, (Vol. 2, pp. 1211–1216).Google Scholar
  47. Sugiura, H., Gienger, M., Janssen, H., & Goerick, C. (2007). Real-time collision avoidance with whole body motion control for humanoid robots. In IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2007, (pp. 2053–2058).Google Scholar
  48. Suleiman, W., Kanehiro, F., Miura, K., & Yoshida, E. (2009). Improving zmp-based control model using system identification techniques. In 9th IEEE-RAS International Conference on Humanoid Robots, Humanoids 2009, (pp. 74–80).Google Scholar
  49. Ude, A., Atkeson, C. G., & Riley, M. (2004). Programming full-body movements for humanoid robots by observation. Robotics and Autonomous Systems, 47(2–3), 93–108. Robot Learning from Demonstration.Google Scholar
  50. Ude, A., Gams, A., Asfour, T., & Morimoto, J. (2010). Task-specific generalization of discrete and periodic dynamic movement primitives. IEEE Transactions on Robotics, 26(5), 800–815.CrossRefGoogle Scholar
  51. Ukidve, C., McInroy, J., & Jafari, F. (2008). Using redundancy to optimize manipulability of stewart platforms. IEEE/ASME Transactions on Mechatronics, 13(4), 475–479.CrossRefGoogle Scholar
  52. Vukobratovic, M., & Borovac, B. (2004). Zero-moment point: Thirty five years of its life. International Journal of Humanoid Robotics, 1(1), 157–173.CrossRefGoogle Scholar
  53. Vukobratovic, M., & Juricic, D. (1969). Contribution to the synthesis of biped gait. IEEE Transactions on Biomedical Engineering, 16(1), 1–6.CrossRefGoogle Scholar
  54. Žlajpah, L. (2006). Robotic yo-yo: Modelling and control strategies. Robotica, 24(2), 211–220.CrossRefGoogle Scholar
  55. Žlajpah, L., & Nemec, B. (2002). Kinematic control algorithms for on-line obstacle avoidance for redundant manipulators. In IEEE/RSJ International Conference on Intelligent Robots and Systems, (Vol. 2, pp. 1898–1903).Google Scholar
  56. Yoneyama, T., Kagawa, H., Unemoto, M., Iizuka, T., & Scott, N. (2009). A ski robot system for qualitative modelling of the carved turn. Sports Engineering, 11, 131–141. doi: 10.1007/s12283-009-0018-3.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tadej Petrič
    • 1
    Email author
  • Andrej Gams
    • 1
    • 2
  • Jan Babič
    • 1
  • Leon Žlajpah
    • 1
  1. 1.Department of Automation, Biocybernetics and RoboticsJožef Stefan InstituteLjubljanaSlovenia
  2. 2.Biorobotics LaboratoryÉcole Polytechnique Fédérale de LausanneVaudSwitzerland

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