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Walking of biped with passive exoskeleton: evaluation of energy consumption

Abstract

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.

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References

  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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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

    Article  Google 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)

  9. 9.

    Vukobratovic, M., Hristic, D., Stojiljkovic, Z.: Development of active anthropomorphic exoskeletons. Med. Biol. Eng. 12(1), 66–80 (1974)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

  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)

    Article  Google 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)

    Article  Google 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)

    Article  Google Scholar 

  31. 31.

    Mochon, S., McMahon, T.: Ballistic walking: an improved model. Math. Biosci. 52, 241–260 (1981)

    MathSciNet  Article  MATH  Google Scholar 

  32. 32.

    McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990)

    Article  Google 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

    MathSciNet  Article  Google Scholar 

  34. 34.

    Wisse, M.: Essentials of Dynamic Walking, Analysis and Design of Two Legged Robots. PhD thesis, ISBN 90-77595-82-1 (2004)

  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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    MathSciNet  Article  Google 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)

    Article  MATH  Google 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)

    Article  Google 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)

    MATH  Google 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)

    Article  Google Scholar 

Download references

Acknowledgements

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.

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Correspondence to Y. Aoustin.

Appendix: Energy consumption at the instantaneous double-support phase

Appendix: Energy consumption at the instantaneous double-support phase

If the impulsive torques described by Dirac delta-functions are applied at the interlink joints of the biped, then each interlink angular velocity undergoes a discontinuous change.

For a sake of clarity and without loss of generality, we consider only one actuated joint of the biped. The joint variable is defined with \(\theta \). An impulsive torque \(\varGamma \) applied at this joint is defined to be as follows:

$$ \varGamma (t)=I\delta (t-T). $$
(45)

Expression (45) describes the Dirac delta-function; the magnitude \(I\) describes the intensity of the torque \(\varGamma \) such that

$$ \displaystyle \int _{T^{-}}^{T^{+}}I\delta (t-T) \,\mathrm{d} t=I. $$

We want to evaluate the energy expended during the operation of the impulsive torque (45). The chosen energy criterion is as follows:

$$ W = \displaystyle \int _{T^{-}}^{T{+}} \bigl\vert I\delta (t-T) (t) \dot{\theta }(t) \bigr\vert \,\mathrm{d} t. $$
(46)

Now instead of the delta-function (45) let us consider the following distributed in time piecewise constant function:

$$ \varGamma_{\Delta }(t)=\left \{ \textstyle\begin{array}{l@{\quad}l} \dfrac{I}{2\Delta } & \text{if}\ t \in [T-\Delta ,T+\Delta ], \\ \\ 0 & \text{if}\ t\notin [T-\Delta ,T+\Delta ]. \\ \end{array}\displaystyle \right . $$
(47)

Here \(\Delta =\mbox{const}>0\); function (47) is shown in Fig. 13. If \(\Delta \to 0\), then function \(\varGamma_{\Delta }(t)\) “tends” to Dirac delta-function (45).

Fig. 13
figure13

Function \(\varGamma_{\Delta }(t)\)

Let us assume that in each interlink joint the distributed in time torque (similar to (47)) is applied. And let value \(\Delta \) be the same for each joint.

The joint velocity \(\dot{\theta }\) undergoes discontinuity at the instant \(T\) (as in each joint), when the impulsive torques (similar to torque (45)) are applied in the joints of our biped. Let equality \(\dot{\theta }=\dot{\theta }^{-}\) be valid just before the applying of the impulsive torques and equality \(\dot{\theta }= \dot{\theta }^{+}\) be valid just after the applying of these impulsive torques.

If interval \([T-\Delta ,~T+\Delta ]\) is “small”, then velocity \(\dot{\theta }(t)\) can be distributed in this interval by the following way (function \(O(\Delta )\) is a magnitude of the first order with respect to magnitude \(\Delta \))

$$ \dot{\theta }_{\Delta }(t)=\dot{\theta }^{-}+ \dfrac{\dot{\theta }^{+}- \dot{\theta }^{-}}{2\Delta }(t-T+\Delta )+O(\Delta ). $$
(48)

If \(\Delta \to 0\), then, according to expression (48), \(O(\Delta )\to 0\) and \(\dot{\theta }_{\Delta }(T-\Delta )\to \dot{\theta }^{-}\), \(\dot{\theta }(T+\Delta )\to \dot{\theta }^{+}\).

Now let us consider instead of (46) the following integral using expressions (47) and (48):

$$ W_{\Delta }=\displaystyle \int _{T-\Delta }^{T+\Delta } \bigl\vert \varGamma_{ \Delta }(t)\dot{\theta }_{\Delta }(t) \bigr\vert \,\mathrm{d} t= \biggl\vert \dfrac{I}{2 \Delta } \biggr\vert \displaystyle \int _{T-\Delta }^{T+\Delta } \biggl\vert \dot{\theta }^{-}+\dfrac{\dot{\theta }^{+}-\dot{\theta }^{-}}{2\Delta }(t-T+\Delta )+O(\Delta ) \biggr\vert \,\mathrm{d} t. $$
(49)

To calculate integral (49), we consider two cases. The first case is as follows:

$$ \dot{\theta }^{-}\dot{\theta }\geqslant 0 \quad \text{and} \quad \dot{\theta }^{-}\neq 0 \quad \text{or} \quad \dot{ \theta }^{+}\neq 0. $$
(50)

It is possible to show that under condition (50),

$$ \textstyle\begin{array}{ccl} \lim_{\Delta \to 0}W_{\Delta }&=&\lim_{\Delta \to 0} \biggl\vert \dfrac{I}{2\Delta } \biggr\vert \displaystyle \int _{T-\Delta }^{T+ \Delta } \biggl\vert \dot{\theta }^{-}+\dfrac{\dot{\theta }^{+}- \dot{\theta }^{-}}{2\Delta }(t-T+\Delta )+O(\Delta )\biggr\vert \,\mathrm{d} t \\ \\ &=& \biggl\vert \dfrac{I}{2\Delta } \biggr\vert \displaystyle \int _{T-\Delta }^{T+ \Delta } \biggl\vert \dot{\theta }^{-}+\dfrac{\dot{\theta }^{+}- \dot{\theta }^{-}}{2\Delta }(t-T+\Delta ) \biggr\vert \,\mathrm{d} t = \biggl\vert I\dfrac{ \dot{\theta }^{+}+\dot{\theta }^{-}}{2} \biggr\vert . \end{array} $$
(51)

The expression of the last integral in (51) contains value \(\Delta \). However, the result of its calculation does not depend on this value and this result looks like (34) or (37) for the joint \(i\).

Let us consider now the second case, when

$$ \dot{\theta }^{-}\dot{\theta }^{+}< 0. $$
(52)

Function (48) becomes zero at the instant

$$ t_{0}=T-\Delta +\dfrac{2\dot{\theta }^{-}}{\dot{\theta }^{-}- \dot{\theta }^{+}}\Delta +O\bigl( \Delta^{2}\bigr). $$
(53)

Function (48) has different signs in intervals \([T-\Delta ,~t_{0})\) and \((t_{0},T+\Delta ]\). Therefore, integral (49) can be written as follows:

$$ \textstyle\begin{array}{ccl} W_{\Delta } &=& \biggl\vert \dfrac{I}{2\Delta } \biggr\vert \biggl\vert \displaystyle \int _{T-\Delta }^{t_{0}} [ \dot{\theta }^{-}+\dfrac{ \dot{\theta }^{+}-\dot{\theta }^{-}}{2\Delta }(t-T+\Delta )+O(\Delta ) ] \,\mathrm{d} t \\ \\ &&{} -\displaystyle \int _{t_{0}}^{T+\Delta } \biggl[ \dot{\theta }^{-}+\dfrac{ \dot{\theta }^{+}-\dot{\theta }^{-}}{2\Delta }(t-T+\Delta )+O(\Delta ) \biggr] \,\mathrm{d} t \biggr\vert . \end{array} $$
(54)

Straightforward calculations show that

$$ \textstyle\begin{array}{ccl} \lim_{\Delta \to 0}W_{\Delta }&=& \biggl\vert \dfrac{I}{2\Delta } \biggr\vert \biggl\vert \displaystyle \int _{~T-\Delta }^{t_{0} ^{*}}\biggl[ \dot{\theta }^{-}+\dfrac{\dot{\theta }^{+}-\dot{\theta } ^{-}}{2\Delta }(t-T+\Delta ) \biggr] \,\mathrm{d} t \\ \\ &&{} -\displaystyle \int _{t_{0}^{*}}^{T+\Delta } \biggl[ \dot{\theta } ^{-}+\dfrac{\dot{\theta }^{+}-\dot{\theta }^{-}}{2\Delta }(t-T+\Delta ) \biggr] \,\mathrm{d} t \biggr\vert = \biggl\vert \dfrac{I}{2} \dfrac{( \dot{\theta }^{+})^{2}+(\dot{\theta }^{-})^{2}}{\dot{\theta }^{+}- \dot{\theta }^{-}} \biggr\vert . \end{array} $$
(55)

Here \(t_{0}^{*}=T-\Delta +\dfrac{2\dot{\theta }^{-}}{\dot{\theta } ^{-}-\dot{\theta }^{+}}\Delta \). The expression of each integral in (55) contains value \(\Delta \), but the calculations show that the difference between these two integrals does not depend on this value. The result of these calculations looks like (35) and (38) for the joint \(i\).

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Aoustin, Y., Formalskii, A.M. Walking of biped with passive exoskeleton: evaluation of energy consumption. Multibody Syst Dyn 43, 71–96 (2018). https://doi.org/10.1007/s11044-017-9602-7

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Keywords

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