Multibody System Dynamics

, Volume 45, Issue 4, pp 379–401 | Cite as

Rigid vs compliant contact: an experimental study on biped walking

  • Majid KhadivEmail author
  • S. Ali A. Moosavian
  • Aghil Yousefi-Koma
  • Majid Sadedel
  • Abbas Ehsani-Seresht
  • Saeed Mansouri


Contact modeling plays a central role in motion planning, simulation and control of legged robots, as legged locomotion is realized through contact. The two prevailing approaches to model the contact consider rigid and compliant premise at interaction ports. Contrary to the dynamics model of legged systems with rigid contact (without impact) which is straightforward to develop, there is no consensus among researchers to employ a standard compliant contact model. Our main goal in this paper is to study the dynamics model structure of bipedal walking systems with rigid contact and a novel compliant contact model, and to present experimental validation of both models. For the model with rigid contact, after developing the model of the articulated bodies in flight phase without any contact with environment, we apply the holonomic constraints at contact points and develop a constrained dynamics model of the robot in both single and double support phases. For the model with compliant contact, we propose a novel nonlinear contact model and simulate motion of the robot using this model. In order to show the performance of the developed models, we compare obtained results from these models to the empirical measurements from bipedal walking of the human-size humanoid robot Surena III, which has been designed and fabricated at CAST, University of Tehran. This analysis shows the merit of both models in estimating dynamic behavior of the robot walking on a semi-rigid surface. The model with rigid contact, which is less complex and independent of the physical properties of the contacting bodies, can be employed for model-based motion optimization, analysis as well as control, while the model with compliant contact and more complexity is suitable for more realistic simulation scenarios.


Bipedal locomotion Dynamics modeling Contact modeling Rigid and compliant contact models Foot–ground contact 



The authors would like to express deep gratitude to the Industrial Development and Renovation Organization of Iran (IDRO) and Iran National Science Foundation (INSF) for their financial support (Project Number: 95849278) to develop the Surena III humanoid robot. We further thank to the members of CAST for their valuable participation in the design and fabrication of the robot.


  1. 1.
    Baruh, H.: Analytical Dynamics. WCB/McGraw-Hill, Boston (1999) Google Scholar
  2. 2.
    Brown, P., McPhee, J.: A 3d ellipsoidal volumetric foot–ground contact model for forward dynamics. Multibody Syst. Dyn. 42(4), 447–467 (2018) MathSciNetGoogle Scholar
  3. 3.
    Buschmann, T.: Simulation and control of biped walking robots. PhD thesis, Technical University of Munich (TUM) (2010) Google Scholar
  4. 4.
    Buschmann, T., Lohmeier, S., Ulbrich, H.: Humanoid robot Lola: design and walking control. J. Physiol. 103(3), 141–148 (2009) zbMATHGoogle Scholar
  5. 5.
    Carpentier, J., Tonneau, S., Naveau, M., Stasse, O., Mansard, N.: A versatile and efficient pattern generator for generalized legged locomotion. In: IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden (2016) Google Scholar
  6. 6.
    Dai, H., Tedrake, R.: Planning robust walking motion on uneven terrain via convex optimization. In: 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pp. 579–586. IEEE Press, New York (2016) Google Scholar
  7. 7.
    Dashkhaneh, A.: Modeling of the behavior of the lower-extremity joints in human walking and using it for the control of rehabilitation robots in the case of sci and stroke patients. PhD thesis, Tarbiat Modares University (2014) Google Scholar
  8. 8.
    Englsberger, J., Ott, C., Albu-Schäffer, A.: Three-dimensional bipedal walking control based on divergent component of motion. IEEE Trans. Robot. 31(2), 355–368 (2015) Google Scholar
  9. 9.
    Ezati, M., Khadiv, M., Moosavian, S.A.A.: Effects of toe-off and heel-off motions on gait performance of biped robots. In: 2015 3rd RSI International Conference on Robotics and Mechatronics (ICROM), pp. 007–012. IEEE Press, New York (2015) Google Scholar
  10. 10.
    Faraji, S., Pouya, S., Ijspeert, A.: Robust and agile 3d biped walking with steering capability using a footstep predictive approach. In: Robotics Science and Systems (RSS), EPFL-CONF-198512 (2014) Google Scholar
  11. 11.
    Featherstone, R.: Rigid Body Dynamics Algorithms. Springer, Berlin (2014) zbMATHGoogle Scholar
  12. 12.
    Feng, S., Xinjilefu, X., Atkeson, C.G., Kim, J.: Robust dynamic walking using online foot step optimization. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5373–5378. IEEE Press, New York (2016) Google Scholar
  13. 13.
    Herdt, A., Diedam, H., Wieber, P.B., Dimitrov, D., Mombaur, K., Diehl, M.: Online walking motion generation with automatic footstep placement. Adv. Robot. 24(5–6), 719–737 (2010) Google Scholar
  14. 14.
    Herzog, A., Rotella, N., Schaal, S., Righetti, L.: Trajectory generation for multi-contact momentum control. In: 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pp. 874–880. IEEE Press, New York (2015) Google Scholar
  15. 15.
    Herzog, A., Rotella, N., Mason, S., Grimminger, F., Schaal, S., Righetti, L.: Momentum control with hierarchical inverse dynamics on a torque-controlled humanoid. Auton. Robots 40(3), 473–491 (2016) Google Scholar
  16. 16.
    Herzog, A., Schaal, S., Righetti, L.: Structured contact force optimization for kino-dynamic motion generation. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2703–2710. IEEE Press, New York (2016) Google Scholar
  17. 17.
    Hopkins, M.A., Leonessa, A., Lattimer, B.Y., Hong, D.W.: Optimization-based whole-body control of a series elastic humanoid robot. Int. J. Humanoid Robot. 13(01), 1550034 (2016) Google Scholar
  18. 18.
    Jackson, J., Hass, C., Fregly, B.: Development of a subject-specific foot–ground contact model for walking. J. Biomech. Eng. 138(9), 091002 (2016) Google Scholar
  19. 19.
    Jia, Y.B., Mason, M.T., Erdmann, M.A.: Multiple impacts: a state transition diagram approach. Int. J. Robot. Res. 32(1), 84–114 (2013) Google Scholar
  20. 20.
    Juhász, T., Urbancsek, T.: Beyond the limits of kinematics in planning keyframed biped locomotion. Period. Polytech., Electr. Eng. 53(1–2), 3–9 (2011) Google Scholar
  21. 21.
    Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K., Hirukawa, H.: The 3D linear inverted pendulum mode: a simple modeling for a biped walking pattern generation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 239–246. IEEE Press, New York (2001) Google Scholar
  22. 22.
    Khadiv, M., Moosavian, S.A.A., Sadedel, M.: Dynamics modeling of fully-actuated humanoids with general robot–environment interaction. In: 2014 Second RSI/ISM International Conference on Robotics and Mechatronics (ICRoM), pp. 233–238. IEEE Press, New York (2014) Google Scholar
  23. 23.
    Khadiv, M., Moosavian, S.A.A., Yousefi-Koma, A., Sadedel, M., Mansouri, S.: Optimal gait planning for humanoids with 3d structure walking on slippery surfaces. Robotica 35(3), 1–19 (2015) Google Scholar
  24. 24.
    Khadiv, M., Herzog, A., Moosavian, S.A.A., Righetti, L.: Step timing adjustment: a step toward generating robust gaits. In: 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pp. 35–42. IEEE Press, New York (2016) Google Scholar
  25. 25.
    Khadiv, M., Kleff, S., Herzog, A., Moosavian, S.A., Schaal, S., Righetti, L.: Stepping stabilization using a combination of dcm tracking and step adjustment. In: 2016 4th International Conference on Robotics and Mechatronics (ICROM) (2016) Google Scholar
  26. 26.
    Khadiv, M., Moosavian, S.A.A., Yousefi-Koma, A., Maleki, H., Sadedel, M.: Online adaptation for humanoids walking on uncertain surfaces. Proc. Inst. Mech. Eng., Part I, J. Syst. Control Eng. (2017, accepted). Available: arXiv:1703.10337
  27. 27.
    Kim, J.H., Joo, C.B.: Numerical construction of balanced state manifold for single-support legged mechanism in sagittal plane. Multibody Syst. Dyn. 31(3), 257–281 (2014) MathSciNetGoogle Scholar
  28. 28.
    Komoda, K., Wagatsuma, H.: Energy-efficacy comparisons and multibody dynamics analyses of legged robots with different closed-loop mechanisms. Multibody Syst. Dyn. 40(2), 123–153 (2017) MathSciNetGoogle Scholar
  29. 29.
    Koolen, T., Bertrand, S., Thomas, G., De Boer, T., Wu, T., Smith, J., Englsberger, J., Pratt, J.: Design of a momentum-based control framework and application to the humanoid robot atlas. Int. J. Humanoid Robot. 13(01), 1650007 (2016) Google Scholar
  30. 30.
    Lim, I.s., Kwon, O., Park, J.H.: Gait optimization of biped robots based on human motion analysis. Robot. Auton. Syst. 62(2), 229–240 (2014) Google Scholar
  31. 31.
    Lopes, D., Neptune, R., Ambrósio, J., Silva, M.: A superellipsoid-plane model for simulating foot-ground contact during human gait. Comput. Methods Biomech. Biomed. Eng. 19(9), 954–963 (2016) Google Scholar
  32. 32.
    Marques, F., Isaac, F., Dourado, N., Souto, A.P., Flores, P., Lankarani, H.M.: A study on the dynamics of spatial mechanisms with frictional spherical clearance joints. J. Comput. Nonlinear Dyn. 12(5), 051,013 (2017) Google Scholar
  33. 33.
    Mazumdar, A., Spencer, S.J., Hobart, C., Salton, J., Quigley, M., Wu, T., Bertrand, S., Pratt, J., Buerger, S.P.: Parallel elastic elements improve energy efficiency on the STEPPR bipedal walking robot. IEEE/ASME Trans. Mechatron. 22(2), 898–908 (2017) Google Scholar
  34. 34.
    McLean, S.G., Su, A., van den Bogert, A.J.: Development and validation of a 3D model to predict knee joint loading during dynamic movement. Trans. Am. Soc. Mech. Eng. J. Biomech. Eng. 125(6), 864–874 (2003) Google Scholar
  35. 35.
    Millard, M., McPhee, J., Kubica, E.: Multi-step forward dynamic gait simulation. In: Multibody Dynamics, pp. 25–43. Springer, Berlin (2009) Google Scholar
  36. 36.
    Nikolić, M., Borovac, B., Raković, M.: Dynamic balance preservation and prevention of sliding for humanoid robots in the presence of multiple spatial contacts. Multibody Syst. Dyn. 42(2), 197–218 (2017) MathSciNetGoogle Scholar
  37. 37.
    Orin, D.E., Goswami, A., Lee, S.H.: Centroidal dynamics of a humanoid robot. Auton. Robots 35(2–3), 161–176 (2013) Google Scholar
  38. 38.
    Park, J.H., Kwon, O.: Reflex control of biped robot locomotion on a slippery surface. In: IEEE International Conference on Robotics and Automation, Proceedings 2001 ICRA, vol. 4, pp. 4134–4139. IEEE Press, New York (2001). 2001 Google Scholar
  39. 39.
    Peasgood, M., Kubica, E., McPhee, J.: Stabilization of a dynamic walking gait simulation. J. Comput. Nonlinear Dyn. 2(1), 65–72 (2007) Google Scholar
  40. 40.
    Ponton, B., Herzog, A., Schaal, S., Righetti, L.: A convex model of humanoid momentum dynamics for multi-contact motion generation. In: 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pp. 842–849. IEEE Press, New York (2016) Google Scholar
  41. 41.
    Pratt, J.E.: Exploiting inherent robustness and natural dynamics in the control of bipedal walking robots. Tech. rep., Massachusetts Inst. of Tech., Cambridge Dept. of Electrical Engineering and Computer Science (2000) Google Scholar
  42. 42.
    Pratt, J., Koolen, T., De Boer, T., Rebula, J., Cotton, S., Carff, J., Johnson, M., Neuhaus, P.: Capturability-based analysis and control of legged locomotion, part 2: application to M2V2, a lower-body humanoid. Int. J. Robot. Res. 31(10), 1117–1133 (2012) Google Scholar
  43. 43.
    Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.: Optimal distribution of contact forces with inverse-dynamics control. Int. J. Robot. Res. 32(3), 280–298 (2013) Google Scholar
  44. 44.
    Sadedel, M., Yousefi-Koma, A., Khadiv, M., Mahdavian, M.: Adding low-cost passive toe joints to the feet structure of Surena III humanoid robot. Robotica 35(11), 1–23 (2017) Google Scholar
  45. 45.
    Sadedel, M., Yousefi-Koma, A., Khadiv, M., Mansouri, S.: Investigation on dynamic modeling of Surena III humanoid robot with heel-off and heel-strike motions. Iran. J. Sci. Technol., Trans. A, Sci. 41(1), 9–23 (2017) Google Scholar
  46. 46.
    Sherman, M.A., Seth, A., Delp, S.L.: Simbody: multibody dynamics for biomedical research. Proc. IUTAM 2, 241–261 (2011) Google Scholar
  47. 47.
    Taghirad, H., Belanger, P.: Modeling and parameter identification of harmonic drive systems. Trans. Am. Soc. Mech. Eng. J. Dyn. Syst. Meas. Control 120, 439–444 (1998) Google Scholar
  48. 48.
    Tassa, Y., Erez, T., Todorov, E.: Synthesis and stabilization of complex behaviors through online trajectory optimization. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4906–4913. IEEE Press, New York (2012) Google Scholar
  49. 49.
    Tlalolini, D., Aoustin, Y., Chevallereau, C.: Design of a walking cyclic gait with single support phases and impacts for the locomotor system of a thirteen-link 3D biped using the parametric optimization. Multibody Syst. Dyn. 23(1), 33–56 (2010) MathSciNetzbMATHGoogle Scholar
  50. 50.
    Wensing, P.M., Orin, D.E.: Improved computation of the humanoid centroidal dynamics and application for whole-body control. Int. J. Humanoid Robot. 13(01), 1550, 039 (2016) Google Scholar
  51. 51.
    Wieber, P.B., Tedrake, R., Kuindersma, S.: Modeling and control of legged robots. In: Springer Handbook of Robotics, pp. 1203–1234. Springer, Berlin (2016) Google Scholar
  52. 52.
    Wojtyra, M.: Multibody Simulation Model of Human Walking (2003) Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Majid Khadiv
    • 1
    Email author
  • S. Ali A. Moosavian
    • 2
  • Aghil Yousefi-Koma
    • 3
  • Majid Sadedel
    • 4
  • Abbas Ehsani-Seresht
    • 5
  • Saeed Mansouri
    • 6
  1. 1.Movement Generation and Control GroupMax Planck Institute for Intelligent SystemsTübingenGermany
  2. 2.Department of Mechanical EngineeringK. N. Toosi University of TechnologyTehranIran
  3. 3.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran
  4. 4.Department of Mechanical EngineeringTarbiat Modares UniversityTehranIran
  5. 5.Department of Mechanical EngineeringHakim Sabzevari UniversitySabzevarIran
  6. 6.Department of Mechanical EngineeringSharif University of TechnologyTehranIran

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