On the manipulability of swing foot and stability of human locomotion

  • Behnam Miripour FardEmail author
  • Sjoerd M Bruijn


Manipulability is a measure that quantifies the range of possible motions of a robotic end-effector and it is also an important measure in the study of coordination of human upper body and grasping tasks. This measure, which is defined on both the kinematic and dynamic level, could be useful in gait, as it could be used to determine potential foot placement possibilities. Kinematic manipulability is defined based on the Jacobian and dynamic manipulability on both the Jacobian and mass-inertia matrix. The main purpose of this study was to evaluate the manipulability of human walking and to explore a possible relation between the manipulability and dynamic stability of walking at different speeds. A 37-DoF tree-like model of the human body was developed to evaluate the manipulability index of human walking. We measured kinematics of 11 healthy male subjects while walking on a treadmill, and mapped the data to the model using inverse kinematics. Jacobian based kinematic/dynamic manipulability measures of walking were evaluated for the swing phase of walking. Manipulability ellipsoids were drawn for geometric determination of this measure in all directions during early, mid- and late swing phases. As stability metrics, the local divergence exponent and Floquet Multipliers were calculated. The results indicated a high kinematic manipulability of the swing foot during early and late swing phases and a drop in kinematic manipulability during mid-swing. Kinematic manipulability of the swing leg during early and late (but not mid-) swing phases increased with walking speed but the average kinematic manipulability of the center of mass and dynamic manipulability of swing foot decreased with increasing walking speed. Moreover, the results showed a weak relation between the manipulability and local and orbital stability.


Bipedal walking Manipulability Stability Optimization 



S. M Bruijn was funded by a VIDI grant (016.Vidi.178.014) from the Dutch Organization for Scientific Research (NWO).


  1. 1.
    Acasio, J., Fey, N.P., Gordon, K.E., et al.: Stability-maneuverability trade-offs during lateral steps. Gait Posture 52, 171–177 (2017) Google Scholar
  2. 2.
    Baetz, G., Scheint, M., Wollherr, D.: Toward dynamic manipulation for humanoid robots: experiments and design aspects. Int. J. Humanoid Robot. 8(03), 513–532 (2011) Google Scholar
  3. 3.
    Bauby, C.E., Kuo, A.D.: Active control of lateral balance in human walking. J. Biomech. 33(11), 1433–1440 (2000) Google Scholar
  4. 4.
    Bruijn, S., Meijer, O., Beek, P., Van Dieën, J.: Assessing the stability of human locomotion: a review of current measures. J. R. Soc. Interface 10(83), 20120999 (2013) Google Scholar
  5. 5.
    Chiaacchio, P., Concilio, M.: The dynamic manipulability ellipsoid for redundant manipulators. In: Proceedings. 1998 IEEE International Conference on Robotics and Automation, vol. 1, pp. 95–100. IEEE Press, New York (1998) Google Scholar
  6. 6.
    Cotton, S., Fraisse, P., Murray, A.P.: On the manipulability of the center of mass of humanoid robots: application to design. In: ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1259–1267 (2010). American Society of Mechanical Engineers Google Scholar
  7. 7.
    Endo, H.: Application of robotic manipulability indices to evaluate thumb performance during smartphone touch operations. Ergonomics 58(5), 736–747 (2015) Google Scholar
  8. 8.
    Gen, M., Zhang, W., Lin, L., Yun, Y.: Recent advances in hybrid evolutionary algorithms for multiobjective manufacturing scheduling. Comput. Ind. Eng. 112, 616–633 (2017) Google Scholar
  9. 9.
    Gravagne, I.A., Walker, I.D.: Manipulability, force, and compliance analysis for planar continuum manipulators. IEEE Trans. Robot. Autom. 18(3), 263–273 (2002) Google Scholar
  10. 10.
    Gu, Y., Lee, C.G., Yao, B.: Feasible center of mass dynamic manipulability of humanoid robots. In: 2015 IEEE International Conference on Robotics and Automation, ICRA, pp. 5082–5087. IEEE Press, New York (2015) Google Scholar
  11. 11.
    Hof, A.L., van Bockel, R.M., Schoppen, T., Postema, K.: Control of lateral balance in walking: experimental findings in normal subjects and above-knee amputees. Gait Posture 25(2), 250–258 (2007) Google Scholar
  12. 12.
    Huang, Q., Yu, Z., Zhang, W., Xu, W., Chen, X.: Design and similarity evaluation on humanoid motion based on human motion capture. Robotica 28(5), 737–745 (2010) Google Scholar
  13. 13.
    Inoue, K., Yoshida, H., Arai, T., Mae, Y.: Mobile manipulation of humanoids-real-time control based on manipulability and stability. In: IEEE International Conference on Robotics and Automation, 2000. Proceedings, ICRA’00, vol. 3, pp. 2217–2222. IEEE Press, New York (2000) Google Scholar
  14. 14.
    Jacquier-Bret, J., Gorce, P., Rezzoug, N.: The manipulability: a new index for quantifying movement capacities of upper extremity. Ergonomics 55(1), 69–77 (2012) Google Scholar
  15. 15.
    Jacquier-Bret, J., Rezzoug, N., Gorce, P.: Effect of spinal cord injury at c6–c7 on global upper-limb coordination during grasping: manipulability approach. IRBM 34(1), 69–73 (2013) Google Scholar
  16. 16.
    Klein, C.A., Blaho, B.E.: Dexterity measures for the design and control of kinematically redundant manipulators. Int. J. Robot. Res. 6(2), 72–83 (1987) Google Scholar
  17. 17.
    Kobayashi, Y., Minami, M., Yanou, A., Maeba, T.: Dynamic reconfiguration manipulability analyses of humanoid bipedal walking. In: 2013 IEEE International Conference on Robotics and Automation, ICRA, pp. 4779–4784. IEEE Press, New York (2013) Google Scholar
  18. 18.
    Lee, I., Oh, J.H.: Humanoid posture selection for reaching motion and a cooperative balancing controller. J. Intell. Robot. Syst. 81(3–4), 301–316 (2016) Google Scholar
  19. 19.
    Lenarčič, J., Klopčar, N.: Positional kinematics of humanoid arms. Robotica 24(1), 105–112 (2006) Google Scholar
  20. 20.
    Maneewarn, T., Boonprakob, A.: Walking pattern modification using manipulability ellipsoid for biped robot. In: IEEE International Conference on Robotics and Biomimetics, 2008, ROBIO 2008, pp. 160–165. IEEE Press, New York (2009). Google Scholar
  21. 21.
    Minami, M., Takahara, M.: Avoidance manipulability for redundant manipulators. In: Proceedings. 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM 2003, vol. 1, pp. 314–319. IEEE Press, New York (2003) Google Scholar
  22. 22.
    Minami, M., Zhang, T., Yu, F., Nakamura, Y., Yasukura, O., Song, W., Yanou, A., Deng, M.: Reconfiguration manipulability analyses for redundant robots in view of structure and shape. In: SCIS & ISIS, SCIS & ISIS 2010, pp. 971–976 (2010). Japan Society for Fuzzy Theory and Intelligent Informatics Google Scholar
  23. 23.
    Müller, A.: Manipulability and static stability of parallel manipulators. Multibody Syst. Dyn. 9(1), 1–23 (2003) MathSciNetzbMATHGoogle Scholar
  24. 24.
    Nagatani, K., Hirayama, T., Gofuku, A., Tanaka, Y.: Motion planning for mobile manipulator with keeping manipulability. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, 2002, vol. 2, pp. 1663–1668. IEEE Press, New York (2002) Google Scholar
  25. 25.
    Naksuk, N., Lee, C.G.: Zero moment point manipulability ellipsoid. In: Proceedings 2006 IEEE International Conference on Robotics and Automation, ICRA 2006, pp. 1970–1975. IEEE Press, New York (2006) Google Scholar
  26. 26.
    Ota, Y., Yoneda, K., Muramatsu, Y., Hirose, S.: Development of walking and task performing robot with bipedal configuration. In: Proceedings. 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 1, pp. 247–252. IEEE Press, New York (2001) Google Scholar
  27. 27.
    Padois, V., Ivaldi, S., Babič, J., Mistry, M., Peters, J., Nori, F.: Whole-body multi-contact motion in humans and humanoids: advances of the CoDyCo European project. Robot. Auton. Syst. 90, 97–117 (2017) Google Scholar
  28. 28.
    Pataky, T.C.: Generalized \(n\)-dimensional biomechanical field analysis using statistical parametric mapping. J. Biomech. 43(10), 1976–1982 (2010) Google Scholar
  29. 29.
    Pataky, T.C., Vanrenterghem, J., Robinson, M.A.: Zero- vs. one-dimensional, parametric vs. non-parametric, and confidence interval vs. hypothesis testing procedures in one-dimensional biomechanical trajectory analysis. J. Biomech. 48(7), 1277–1285 (2015) Google Scholar
  30. 30.
    Perry, J.A., Srinivasan, M.: Walking with wider steps changes foot placement control, increases kinematic variability and does not improve linear stability. R. Soc. Open Sci. 4(9), 160627 (2017) Google Scholar
  31. 31.
    Pianosi, F., Sarrazin, F., Wagener, T.: A Matlab toolbox for global sensitivity analysis. Environ. Model. Softw. 70, 80–85 (2015) Google Scholar
  32. 32.
    Samy, V., Kheddar, A.: Falls control using posture reshaping and active compliance. In: 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pp. 908–913. IEEE Press, New York (2015) Google Scholar
  33. 33.
    Shen, K., Li, X., Tian, H., Matsuno, T., Minami, M.: Analyses of biped walking posture by dynamical-evaluating index. Artif. Life Robot., 1–10 (2017) Google Scholar
  34. 34.
    Spong, M.W., Hutchinson, S., Vidyasagar, M., et al.: Robot Modeling and Control, vol. 3. Wiley, New York (2006) Google Scholar
  35. 35.
    Tagawa, Y., Yamashita, T.: Controllability of body motion in bipedal locomotion. In: Proceedings. IEEE/RSJ International Workshop on Intelligent Robots and Systems’ 89. The Autonomous Mobile Robots and Its Applications, IROS’89, pp. 180–186. IEEE Press, New York (1989) Google Scholar
  36. 36.
    Tripp, B.P., McIlroy, W.E., Maki, B.E.: Online mutability of step direction during rapid stepping reactions evoked by postural perturbation. IEEE Trans. Neural Syst. Rehabil. Eng. 12(1), 140–152 (2004) Google Scholar
  37. 37.
    Vahrenkamp, N., Asfour, T., Metta, G., Sandini, G., Dillmann, R.: Manipulability analysis. In: 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids), pp. 568–573. IEEE Press, New York (2012) Google Scholar
  38. 38.
    Yoshikawa, T.: Dynamic manipulability of robot manipulators. Trans. Soc. Instrum. Control Eng. 21(9), 970–975 (1985) Google Scholar
  39. 39.
    Wang, Y., Srinivasan, M.: Stepping in the direction of the fall: the next foot placement can be predicted from current upper body state in steady-state walking. Biol. Lett. 10(9), 20140405 (2014) Google Scholar
  40. 40.
    Winter, D.A.: Biomechanics and Motor Control of Human Movement. Wiley, New York (2009) Google Scholar
  41. 41.
    Xiao, T., Li, M., Huang, Q., Zhang, W., He, L.: Analysis of pushing manipulation by humanoid robot BHR-2 during dynamic walking. In: 2007 IEEE International Conference on Automation and Logistics, pp. 3000–3005. IEEE Press, New York (2007) Google Scholar
  42. 42.
    Yoshikawa, T.: Manipulability of robotic mechanisms. Int. J. Robot. Res. 4(2), 3–9 (1985) Google Scholar
  43. 43.
    Yoshikawa, T.: Foundations of Robotics: Analysis and Control. MIT Press, Cambridge (1990) Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of GuilanRashtIran
  2. 2.Department of Human Movement ScienceVU universityAmsterdamNetherlands

Personalised recommendations