Multibody System Dynamics

, Volume 43, Issue 1, pp 71–96 | Cite as

Walking of biped with passive exoskeleton: evaluation of energy consumption

  • Y. AoustinEmail author
  • A. M. Formalskii


The paper aims to theoretically show the feasibility and efficiency of a passive exoskeleton for a human walking and carrying a load. The human is modeled using a planar bipedal anthropomorphic mechanism. This mechanism consists of a trunk and two identical legs; each leg consists of a thigh, shin, and foot (massless). The exoskeleton is considered also as an anthropomorphic mechanism. The shape and the degrees of freedom of the exoskeleton are identical to the biped (to human)—the topology of the exoskeleton is the same as of the biped (human). Each model of the human and exoskeleton has seven links and six joints. The hip-joint connects the trunk and two thighs of the two legs. If the biped is equipped with an exoskeleton, then the links of this exoskeleton are attached to the corresponding links of the biped and the corresponding hip, knee, and ankle joints coincide. We compare the walking gaits of a biped alone (without exoskeleton) and of a biped equipped with exoskeleton; for both cases the same load is transported. The problem is studied in the framework of a ballistic walking model. During ballistic walking of the biped with exoskeleton, the knee of the support leg is locked, but the knee of the swing leg is unlocked. The locking and unlocking can be realized in the knees of the exoskeleton by any mechanical brake devices without energy consumption. There are no actuators in the exoskeleton. Therefore, we call it a passive exoskeleton. The walking of the biped consists of alternating single- and double-support phases. In our study, the double-support phase is assumed instantaneous. At the instant of this phase, the knee of the previous swing leg is locked and the knee of the previous support leg is unlocked. Numerical results show that during the load transport the human with the exoskeleton spends less energy than human alone. For transportation of a load with mass 40 kg, the economy of the energy is approximately 28%, if the length of the step and its duration are equal to 0.5 m and 0.5 s, respectively.


Human Bipedal model Massless feet Passive Exoskeleton Ballistic walking Single-support phase Instantaneous double-support Impulsive torque Optimization Energy consumption 



This work is supported by Ministry of Education and Science of Russian Federation, Project No. 7.524.11.4012, and by Région des Pays de la Loire, Project LMA and Gérontopôle Autonomie Longévité des Pays de la Loire.


  1. 1.
    Dollar, A., Herr, H.: Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Trans. Robot. 24(1), 144–158 (2008) CrossRefGoogle Scholar
  2. 2.
    Hayashi, T., Sakurai, T., Eguchi, K.: Development of single leg version of HAL for hemiplegia. In: Proc. Int. Conf. of the IEEE Engineering in Medicine and Biology Society, Minneapolis, USA, pp. 5038–5043 (2009). doi: 10.1109/IEMBS.2009.5333698 Google Scholar
  3. 3.
    Viteckova, S., Kutilek, P., Jirina, M.: Wearable lower limb robotics: a review. Biocybern. Biomed. Eng. 33(2), 96–105 (2013) CrossRefGoogle Scholar
  4. 4.
    Talaty, M., Esquenazi, A., Briceno, J.E.: Differentiating ability in users of the ReWalk(TM) powered exoskeleton: an analysis of walking kinematics. In: Proc. IEEE Int. Conf. on Rehabilitation Robotics (ICORR), Seattle, USA, pp. 1–5 (2013). doi: 10.1109/ICORR.2013.6650469 Google Scholar
  5. 5.
    Rupala, B.S., Singla, A., Virk, G.S.: Lower limb exoskeletons: a brief review. In: Proc. Int. Conf. on Mechanical Engineering & Technology COMET, Varanasi, Pradesh, Utter, pp. 18–24 (2016) Google Scholar
  6. 6.
    Farris, R.J., Quintero, H.A., Murray, S.A., Ha, K.H., Hartigan, C., Goldfarb, M.: A preliminary assessment of legged mobility provided by a lower limb exoskeleton for persons with paraplegia. IEEE Trans. Neural Syst. Rehabil. Eng. 22(3), 482–490 (2014) CrossRefGoogle Scholar
  7. 7.
    Aoustin, Y.: Walking gait of a biped with a wearable walking assist device. Int. J. Humanoid Robot. 12(2), 1550018 (2015). doi: 10.1142/S0219843615500188 CrossRefGoogle Scholar
  8. 8.
    Zaroodny, S.J.: Bumpusher: A Powered Aid to Locomotion. Tech. Note 1524, U.S. Army Ballistic Res. Lab., Aberdeen Proving Ground, MD (1963) Google Scholar
  9. 9.
    Vukobratovic, M., Hristic, D., Stojiljkovic, Z.: Development of active anthropomorphic exoskeletons. Med. Biol. Eng. 12(1), 66–80 (1974) CrossRefGoogle Scholar
  10. 10.
    Main, J.: Exoskeletons for human performance augmentation. In: DARPA Project, 3701 North Fairfax Drive, Arlington (2005) Google Scholar
  11. 11.
    Zoss, A., Kazerooni, H., Chu, H.: On the mechanical design of the Berkeley lower extremity exoskeleton (BLEEX). In: Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Alberta, Canada, pp. 3465–3472 (2005) Google Scholar
  12. 12.
    Kazerooni, H., Steger, R.: The Berkeley lower extremity exoskeleton. Trans. Am. Soc. Mech. Eng., J. Dyn. Syst. Meas. Control 128(1), 14–25 (2006) CrossRefGoogle Scholar
  13. 13.
    Marcheschi, S., Salsedo, F., Fontana, M., Bergamasco, M.: Body extended: whole body exoskeleton for human power augmentation. In: Proc. IEEE Int. Conf. on Robotics and Automation, Shanghai China, pp. 611–616 (2011) Google Scholar
  14. 14.
    Yana, T., Cempini, M., Oddo, C.M., Vitiello, N.: Review of assistive strategies in powered lower-limb orthoses and exoskeletons. Robot. Auton. Syst. 64, 120–136 (2015) CrossRefGoogle Scholar
  15. 15.
    Herr, H.: Exoskeletons and orthoses: classification, design, design challenges and future directions. J. NeuroEng. Rehabil. 6(21), 1–9 (2009). doi: 10.1186/1743-0003-6-21 Google Scholar
  16. 16.
    Strausser, K.A., Kazerooni, H.: The development and testing of a human machine interface for a mobile medical exoskeleton. In: IEEE. Int. Conf. on Intelligent Robots and Systems, San Francisco, USA, pp. 4911–4916 (2011) Google Scholar
  17. 17.
    van den Bogert, A.J.: Exotendons for assistance of human locomotion. Biomed. Eng. Online 2–17 (2003) Google Scholar
  18. 18.
    Walsh, C.J., Pasch, K., Herr, H.: An autonomous, under actuated exoskeleton for load-carrying augmentation. In: Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Beijing China, pp. 1410–1415 (2006) Google Scholar
  19. 19.
    Agrawal, S.K., Banala, S.K., Fattah, A., Scholz, J.P., Krishnamoorthy, V., Hsu, W.-L.: A gravity balancing passive exoskeleton for the human leg. In: Robotics: Science and Systems (2006) Google Scholar
  20. 20.
    Agrawal, S.K., Banala, S.K., Fattah, A., Sangwan, V., Krishnamoorthy, V., Scholz, J.P., Hsu, W.L.: Assessment of motion of a swing leg and gait rehabilitation with a gravity balancing exoskeleton. IEEE Trans. Neural Syst. Rehabil. Eng. 15(3), 410–420 (2007) CrossRefGoogle Scholar
  21. 21.
    Dariush, B.: Analysis and simulation of an exoskeleton controller that accommodates static and reactive loads. In: Proc. IEEE Conf. on Robotics and Automation, Barcelona, Spain, pp. 2350–2355 (2005) Google Scholar
  22. 22.
    van Dijk, W., van der Kooij, H., Heckman, E.: A passive exoskeleton with artificial tendons. In: IEEE. Int. Conf. on Rehabilitation Robotics, Rehab Week Zürich, ETH Zürich Science City, Switzerland, June 29–July 1 (2011) Google Scholar
  23. 23.
    Xi, R., Zhu, Z., Du, F., Yang, M., Wang, X., Wu, Q.: Deign concept of the quasi-passive energy-efficient power-assisted lower-limb exoskeleton based on the theory of passive dynamic walking. In: Proc. Int. Conf. of the 23rd IEEE on Mechatronics and Machine Vision in Practice (M2VIP), Nanjing, China, pp. 1–5 (2016) Google Scholar
  24. 24.
    Collo, A., Bonnet, V., Venturei, G.: A quasi-passive lower limb exoskeleton for partial body weight support. In: Proc. Int. Conf. of the 6th IEEE RAS/EMBS Engineering on Biomedical Robotics and Biomechatronics (BioRob), pp. 643–648. UTown, Singapore (2016) Google Scholar
  25. 25.
    Aoustin, Y., Formalskii, A.M.: Strategy to lock the knee of exoskeleton stance leg: study in the framework of ballistic walking model. In: Wenger, P., Chevallereau, C., Pisla, D., Bleuler, H., Rodic, A. (eds.) New Trends in Medical and Service Robots: Human Walking (2016), 275p Google Scholar
  26. 26.
    Dumas, R., Chèze, L., Verriest, J.P.: Adjustments to McConville et al. and Young et al. body segment inertial parameters. J. Biomech. 40(3), 543–553 (2007) CrossRefGoogle Scholar
  27. 27.
    Formal’skii, A.M.: Motion of anthropomorphic biped under impulsive control. In: Proc. of Institute of Mechanics, Moscow State Lomonosov University: “Some Questions of Robot’s Mechanics and Biomechanics”, pp. 17–34 (1978) (in Russian) Google Scholar
  28. 28.
    Formalskii, A.M.: Locomotion of Anthropomorphic Mechanisms. Nauka, Moscow (1982) (in Russian) Google Scholar
  29. 29.
    Formal’sky, A.: Ballistic locomotion of a biped. In: Morecki, A., Waldron, K. (eds.): Design and Control of Two Biped Machines. Springer, Berlin (1997) Google Scholar
  30. 30.
    Formal’skii, A.M.: Ballistic walking design via impulsive control. J. Aerosp. Eng. 23(2), 129–138 (2010) CrossRefGoogle Scholar
  31. 31.
    Mochon, S., McMahon, T.: Ballistic walking: an improved model. Math. Biosci. 52, 241–260 (1981) MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990) CrossRefGoogle Scholar
  33. 33.
    Aoustin, Y., Formalskii, A.M.: 3D walking biped: optimal swing of the arms. Multibody Syst. Dyn. 32(1), 55–66 (2014). doi: 10.1007/s11044-013-9378-3 MathSciNetCrossRefGoogle Scholar
  34. 34.
    Wisse, M.: Essentials of Dynamic Walking, Analysis and Design of Two Legged Robots. PhD thesis, ISBN 90-77595-82-1 (2004) Google Scholar
  35. 35.
    Collins, S., Ruina, S., Tedrake, R., Wisse, M.: Efficient bipedal robots based on passive-dynamic walkers. Sci. Mag. 19, 1082–1085 (2005) Google Scholar
  36. 36.
    Geursen, J.B., Altena, D., Massen, C.H.: A model of the standing man for the description of his dynamic behaviour. Agressologie 17(12), 63–69 (1976) Google Scholar
  37. 37.
    Fenn, W.O.: Work against gravity and work due to velocity changes in running. Am. J. Physiol. 93, 433–462 (1930) Google Scholar
  38. 38.
    Cavagna, G.A., Thys, H., Zamboni, A.: The sources of external work in level walking and running. J. Physiol. 261(3), 639–657 (1976) CrossRefGoogle Scholar
  39. 39.
    Patton, J.L., Pai, Y.C., Lee, W.A.: Evaluation of a model that determines the stability limits of dynamic balance. Gait Posture 9(1), 38–49 (1999) CrossRefGoogle Scholar
  40. 40.
    Ikeuchi, Y., Ashihara, J., Hiki, Y., Kudoh, H., Noda, T.: Walking assist device with bodyweight support system. In: Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, St Louis, USA, pp. 4073–4079. (2010) Google Scholar
  41. 41.
    Appell, P.: Dynamique des Systèmes. Mécanique Analytique. Gauthier-Villars, Paris (1931) Google Scholar
  42. 42.
    Vukobratovic, M., Borovac, B.: Zero-moment point-thirty five years of its life. Int. J. Humanoid Robot. 1(1), 157–173 (2004) CrossRefGoogle Scholar
  43. 43.
    Devie, S., Sakka, S.: Effects of the rolling mechanism of the stance foot on the generalized inverted pendulum definition. In: Wenger, P., Chevallereau, C., Pisla, D., Bleuler, H., Rodic, A. (eds.) New Trends in Medical and Service Robots: Human Walking (2016), 275p Google Scholar
  44. 44.
    Rosenblatt, N.J., Grabiner, M.D.: Measures of frontal plane stability during treadmill and overground walking. Gait Posture 31(3), 380–384 (2010) CrossRefGoogle Scholar
  45. 45.
    Lugade, V., Kaufman, K.: Center of pressure trajectory during gait: a comparison of four foot positions. Gait Posture 40(1), 252–254 (2014) CrossRefGoogle Scholar
  46. 46.
    Font-Llagunes, J.M., Barjau, A.M., Pàmies, R., Kövecses, V.J.: Dynamic analysis of impact in swing-through crutch gait using impulsive and continuous contact models. Multibody Syst. Dyn. 28(3), 257–282 (2012) MathSciNetCrossRefGoogle Scholar
  47. 47.
    Hurmuzlu, Y., Chang, T.-H.: Rigid body collisions of a special class of planar kinematic chains. IEEE Trans. Syst. Man Cybern. Syst. 22(5), 964–971 (1992) CrossRefzbMATHGoogle Scholar
  48. 48.
    Formal’skii, A., Chevallereau, C., Perrin, B.: On ballistic walking locomotion of a quadruped. Int. J. Robot. Res. 19(8), 743–761 (2000) CrossRefGoogle Scholar
  49. 49.
    Beletskii, V.V.: Biped Walking. Nauka, Moscow (1984) (in Russian) Google Scholar
  50. 50.
    Gill, P., Murray, W., Wright, M.: Practical Optimization. Academic Press, London (1981) zbMATHGoogle Scholar
  51. 51.
    Powell, M.: Variable Metric Methods for Constrained Optimization. Lecture Notes in Mathematics, pp. 62–72. Springer, Berlin/Heidelberg (1977) Google Scholar
  52. 52.
    Jung, Y., Jung, M., Lee, K., Koo, S.: Ground reaction force estimation using an insole-type pressure mat and joint kinematics during walking. J. Biomech. 47, 2693–2699 (2014) CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.NantesFrance
  2. 2.Laboratoire des Sciences du Numérique de Nantes, UMR 6004, CNRSÉcole Centrale de NantesUniversité de NantesFrance
  3. 3.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

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