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Multibody System Dynamics

, Volume 43, Issue 4, pp 349–367 | Cite as

Stability improvement of a dynamic walking system via reversible switching surfaces

  • Ali Tehrani Safa
  • Somaye Mohammadi
  • Mahyar Naraghi
  • Aria Alasty
Article
  • 215 Downloads

Abstract

Inspired by the effects of a switching surface on the stability of passive dynamic walking (Safa and Naraghi in Robotica 33(01):195–207, 2015; Safa et al. in Nonlinear Dyn. 81(4):2127–2140, 2015), this paper suggests a new control strategy for stabilization of dynamic bipedal locomotion. It verifies that the stability improvement of a dynamic walking system is feasible while preserving the speed, step-length, period, natural dynamics, and the energy effectiveness of the gait. The proposed control policy goes behind the three primary principles: (i) The system’s switching surface has to be replaced by a new one if an external disturbance is induced. (ii) The new switching surface has to be reshaped back into its old style, together with the disturbance rejection. (iii) The stabilization procedure has to be performed with as small energy consumption as possible. Because of the reversibility effects of the switching surfaces in the above rules, the terminology of “Reversible Switching Surfaces” (RSS) is employed to address the control scheme; so the control objective would be the implementation of RSS for a bipedal robotic system. In this paper, this aim is achieved by a kinematically controlled foot scheme that is implemented on a simple structured biped. The presented idea is validated by a commercial version of MSC Adams software.

Keywords

Biped Dynamic walking Stability Switching surface Hybrid limit cycle 

Notes

Acknowledgements

The first and last authors are grateful to Iran National Science Foundation (INSF) for partially supporting the research.

Supplementary material

11044_2017_9593_MOESM1_ESM.mp4 (6.7 mb)
(MP4 6.7 MB)

References

  1. 1.
  2. 2.
    Ames, A.D., Galloway, K., Sreenath, K., Grizzle, J.W.: Rapidly exponentially stabilizing control Lyapunov functions and hybrid zero dynamics. IEEE Trans. Autom. Control 59(4), 876–891 (2014) MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bhounsule, P.: A controller design framework for bipedal robots: trajectory optimization and event-based stabilization. PhD thesis, Cornell University (2012) Google Scholar
  4. 4.
    Bhounsule, P.A.: Control of a compass gait walker based on energy regulation using ankle push-off and foot placement. Robotica 33(06), 1314–1324 (2015) CrossRefGoogle Scholar
  5. 5.
    Bhounsule, P.A., Cortell, J., Grewal, A., Hendriksen, B., Karssen, J.D., Paul, C., Ruina, A.: Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge. Int. J. Robot. Res. 33(10), 1305–1321 (2014) CrossRefGoogle Scholar
  6. 6.
    Collins, S., Ruina, A., Tedrake, R., Wisse, M.: Efficient bipedal robots based on passive-dynamic walkers. Science 307(5712), 1082–1085 (2005) CrossRefGoogle Scholar
  7. 7.
    Consolini, L., Maggiore, M.: Control of a bicycle using virtual holonomic constraints. Automatica 49(9), 2831–2839 (2013) MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Freidovich, L., Robertsson, A., Shiriaev, A., Johansson, R.: Periodic motions of the pendubot via virtual holonomic constraints: theory and experiments. Automatica 44(3), 785–791 (2008) MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Garcia, M., Chatterjee, A., Ruina, A., Coleman, M.: The simplest walking model: stability, complexity, and scaling. J. Biomech. Eng. 120(2), 281–288 (1998) CrossRefGoogle Scholar
  10. 10.
    Giesbers, J.: Contact mechanics in MSC ADAMS—a technical evaluation of the contact models in multibody dynamics software MSC ADAMS. BSc thesis, University of Twente (2012) Google Scholar
  11. 11.
    Goswami, A., Thuilot, B., Espiau, B.: A study of the passive gait of a compass-like biped robot symmetry and chaos. Int. J. Robot. Res. 17(12), 1282–1301 (1998) CrossRefGoogle Scholar
  12. 12.
    Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: analysis via systems with impulse effects. IEEE Trans. Autom. Control 46(1), 51–64 (2001) MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hamed, K.A., Grizzle, J.W.: Robust event-based stabilization of periodic orbits for hybrid systems: application to an underactuated 3d bipedal robot. In: 2013 American Control Conference, pp. 6206–6212. IEEE Press, New York (2013) CrossRefGoogle Scholar
  14. 14.
    Hamed, K.A., Grizzle, J.W.: Event-based stabilization of periodic orbits for underactuated 3-d bipedal robots with left-right symmetry. IEEE Trans. Robot. 30(2), 365–381 (2014) CrossRefGoogle Scholar
  15. 15.
    Hamed, K.A., Grizzle, J.W.: Iterative robust stabilization algorithm for periodic orbits of hybrid dynamical systems: application to bipedal running. IFAC-PapersOnLine 48(27), 161–168 (2015) CrossRefGoogle Scholar
  16. 16.
    Hasaneini, S.J., Macnab, C.J., Bertram, J.E., Leung, H., et al.: Optimal relative timing of stance push-off and swing leg retraction. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3616–3623 (2013) Google Scholar
  17. 17.
    Hobbelen, D.G.: Limit cycle walking (2008) Google Scholar
  18. 18.
    Hürmüzlü, Y., Moskowitz, G.D.: The role of impact in the stability of bipedal locomotion. Dyn. Stab. Syst. 1(3), 217–234 (1986) zbMATHGoogle Scholar
  19. 19.
    Hürmüzlü, Y., Moskowitz, G.D.: Bipedal locomotion stabilized by impact and switching: I. Two-and three-dimensional, three-element models. Dyn. Stab. Syst. 2(2), 73–96 (1987) zbMATHGoogle Scholar
  20. 20.
    Hürmüzlü, Y., Moskowitz, G.D.: Bipedal locomotion stabilized by impact and switching: II. Structural stability analysis of a four-element bipedal locomotion model. Dyn. Stab. Syst. 2(2), 97–112 (1987) zbMATHGoogle Scholar
  21. 21.
    Iqbal, S., Zang, X., Zhu, Y., Zhao, J.: Bifurcations and chaos in passive dynamic walking: a review. Robot. Auton. Syst. 62(6), 889–909 (2014) CrossRefGoogle Scholar
  22. 22.
    Kuo, A.D.: Energetics of actively powered locomotion using the simplest walking model. J. Biomech. Eng. 124(1), 113–120 (2002) CrossRefGoogle Scholar
  23. 23.
    Maggiore, M., Consolini, L.: Virtual holonomic constraints for Euler–Lagrange systems. IEEE Trans. Autom. Control 58(4), 1001–1008 (2013) MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990) CrossRefGoogle Scholar
  25. 25.
    Montanari, M., Ronchi, F., Rossi, C., Tonielli, A.: Control of a camless engine electromechanical actuator: position reconstruction and dynamic performance analysis. IEEE Trans. Ind. Electron. 51(2), 299–311 (2004) CrossRefGoogle Scholar
  26. 26.
    Raibert, M., Blankespoor, K., Nelson, G., Playter, R.: Bigdog, the rough-terrain quadruped robot. IFAC Proc. Vol. 41(2), 10,822–10,825 (2008) CrossRefGoogle Scholar
  27. 27.
    Raibert, M.H.: Legged Robots that Balance. MIT Press, Cambridge (1986) CrossRefzbMATHGoogle Scholar
  28. 28.
    Ramezani, A., Hurst, J.W., Hamed, K.A., Grizzle, J.: Performance analysis and feedback control of ATRIAS, a three-dimensional bipedal robot. J. Dyn. Syst. Meas. Control 136(2), 1–12 (2014) Google Scholar
  29. 29.
    Rezazadeh, S., Hubicki, C., Jones, M., Peekema, A., Van Why, J., Abate, A., Hurst, J.: Spring-mass walking with ATRIAS in 3D: robust gait control spanning zero to 4.3 kph on a heavily underactuated bipedal robot. In: ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, New York (2015) Google Scholar
  30. 30.
    Safa, A., Naraghi, M., Aalasty, A.: Application of local slopes in the study of metastable walking. In: Assistive Robotics: 18th International Conference on Climbing and Walking Robots (CLAWAR), pp. 337–344. World Scientific, Singapore (2015) CrossRefGoogle Scholar
  31. 31.
    Safa, A.T., Alasty, A., Naraghi, M.: A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory. Nonlinear Dyn. 81(4), 2127–2140 (2015) MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Safa, A.T., Mohammadi, S., Hajmiri, S.E., Naraghi, M., Alasty, A.: How local slopes stabilize passive bipedal locomotion? Mech. Mach. Theory 100, 63–82 (2016) CrossRefGoogle Scholar
  33. 33.
    Safa, A.T., Naraghi, M.: The role of walking surface in enhancing the stability of the simplest passive dynamic biped. Robotica 33(01), 195–207 (2015) CrossRefGoogle Scholar
  34. 34.
    Safa, A.T., Naraghi, M., Alasty, A.: Optimization of the switching surface for the simplest passive dynamic biped. In: International Conference on Advanced Robotics (ICAR), pp. 363–368 (2015) Google Scholar
  35. 35.
    Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N., Fujimura, K.: The intelligent ASIMO: system overview and integration. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2478–2483 (2002) CrossRefGoogle Scholar
  36. 36.
    Shiriaev, A.S., Freidovich, L.B., Robertsson, A., Johansson, R., Sandberg, A.: Virtual-holonomic-constraints-based design of stable oscillations of furuta pendulum: theory and experiments. IEEE Trans. Robot. 23(4), 827–832 (2007) CrossRefGoogle Scholar
  37. 37.
    Sreenath, K., Park, H.W., Poulakakis, I., Grizzle, J.W.: A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL. Int. J. Robot. Res. 30(9), 1170–1193 (2011) CrossRefGoogle Scholar
  38. 38.
    Vukobratović, M., Borovac, B.: Zero-moment point—thirty five years of its life. Int. J. Humanoid Robot. 1(01), 157–173 (2004) CrossRefGoogle Scholar
  39. 39.
    Vukobratović, M., Juricic, D.: Contribution to the synthesis of biped gait. IEEE Trans. Biomed. Eng. 1, 1–6 (1969) CrossRefGoogle Scholar
  40. 40.
    Westervelt, E., Morris, B., Farrell, K.: Analysis results and tools for the control of planar bipedal gaits using hybrid zero dynamics. Auton. Robots 23(2), 131–145 (2007) CrossRefGoogle Scholar
  41. 41.
    Westervelt, E.R., Grizzle, J.W., Koditschek, D.E.: Hybrid zero dynamics of planar biped walkers. IEEE Trans. Autom. Control 48(1), 42–56 (2003) MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Ylikorpi, T., Peralta, J.L., Halme, A.: Comparing passive walker simulators in Matlab and Adams. J. Struct. Mech. 44(1), 65–92 (2011) Google Scholar

Copyright information

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

Authors and Affiliations

  • Ali Tehrani Safa
    • 1
  • Somaye Mohammadi
    • 1
  • Mahyar Naraghi
    • 1
  • Aria Alasty
    • 2
  1. 1.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Mechanical EngineeringSharif University of TechnologyTehranIran

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