Journal of Intelligent & Robotic Systems

, Volume 76, Issue 3–4, pp 461–474 | Cite as

Improving Finite State Impedance Control of Active-Transfemoral Prosthesis Using Dempster-Shafer Based State Transition Rules

  • Ming LiuEmail author
  • Fan Zhang
  • Philip Datseris
  • He (Helen) Huang


Finite state impedance (FSI) control is a widely used approach to control active-transfemoral prostheses (ATP). Current design of state transition rules depends on hard thresholding of intrinsic mechanical measurements, which cannot cope well with uncertainty related with intra- and inter-subject variations of these intrinsic recordings. In this study, we aimed to generate more robust FSI control of ATP against these variations by using Dempster-Shafer theory (DST)-based transition rules. The FSI control with DST-based rules was implemented on an instrumented ATP, evaluated on five able-bodied subjects and one patient with a unilateral transfemoral amputation. Then the DSP based transition rules were compared to the control with hard threshold (HT)-based transition rules. The results showed that when compared to the hard thresholding approach, the DST yielded enhanced accuracy in state transition timing and reduced control errors when intra- and inter-subject variations were presented. Additionally, the parameters of DST-based rules were uniform for all the subjects tested, allowing for easy and efficient transition rule design and calibration. The outcome of this study can lead to further improvement of robust, practical, and self-contained ATP design, which in turn will advance the motor function of patients with lower limb amputations.


Impedance control Finite state machine Uncertainty Amputee gait 


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  1. 1.
    Grimes, D., Flowers, W., Donath, M.: Feasibility of an active control scheme for above-knee prostheses. J. Biomech. Eng. 99, 215–221 (1977)CrossRefGoogle Scholar
  2. 2.
    Stein, J.L., Flowers, W.C.: Stance Phase-control of above-knee prostheses—knee control versus Sach foot design. J. Biomech. 20(1), 19–28 (1987)CrossRefGoogle Scholar
  3. 3.
    Au, S., Berniker, M., Herr, H.: Powered ankle-foot prosthesis to assist level-ground and stair-descent gaits. Neural Netw. 21(4), 654–666 (2008)CrossRefGoogle Scholar
  4. 4.
    Sup, F., Bohara, A., Goldfarb, M.: Design and control of a powered transfemoral prosthesis. Int. J. Robot. Res. 27(2), 263–273 (2008)CrossRefGoogle Scholar
  5. 5.
    Martinez-Villalpando, E.C., Herr, H.: Agonist-antagonist active knee prosthesis: a preliminary study in level-ground walking. J. Rehabil. Res. Dev. 46(3), 361–373 (2009)CrossRefGoogle Scholar
  6. 6.
    Sup, F., Varol, H.A., Mitchell, J., Withrow, T.J., Goldfarb, M.: Preliminary evaluations of a self-contained anthropomorphic transfemoral prosthesis. IEEE/ASME Trans. Mech. 14(6), 667–676 (2009)CrossRefGoogle Scholar
  7. 7.
    Highsmith, M.J., Kahle, J.T., Carey, S.L., Lura, D.J., Dubey, R.V., Quillen, W.S.: Kinetic differences using a power knee and C-Leg while sitting down and standing up: a case report. J. Prosthet. Orthot. 22(4), 237–243 (2010)CrossRefGoogle Scholar
  8. 8.
    Aaron, R.K., Herr, H.M., Ciombor, D.M., Hochberg, L.R., Donoghue, J.P., Briant, C.L., Morgan, J.R., Ehrlich, M.G.: Horizons in prosthesis development for the restoration of limb function. J. Am. Acad. Orthop. Surg. 14(10), 198–204 (2006)Google Scholar
  9. 9.
    Lambrecht, B.G.A., Kazerooni, H.: Design of a semiactive knee prosthesis. In: IEEE International Conference on Robotics and Automation, 2009. ICRA ’09, pp. 639–645, 12–17 May 2009Google Scholar
  10. 10.
    Vallery, H., Burgkart, R., Hartmann, C., Mitternacht, J., Riener, R., Buss, M.: Complementary limb motion estimation for the control of active knee prostheses. Biomed. Tech. (Berl) 56(1), 45–51 (2011)CrossRefGoogle Scholar
  11. 11.
    Borjian, R., Lim, J., Khamesee, M.B., Melek, W.: The design of an intelligent mechanical active prosthetic knee. In: Industrial Electronics, 2008. IECON 2008. 34th Annual Conference of IEEE, pp. 3016–3021, 10–13 Nov 2008Google Scholar
  12. 12.
    Donath, M.: Proportional EMG Control for Above-Knee Prosthesis. MIT Press, Cambridge (1974)Google Scholar
  13. 13.
    Zlatnik, D., Steiner, B., Schweitzer, G.: Finite-state control of a trans-femoral (TF) prosthesis. IEEE Trans. Control Syst. Technol. 10(3), 408–420 (2002)CrossRefGoogle Scholar
  14. 14.
    Soares, A.S.O.D., Yamaguti, E.Y., Mochizuki, L., Amadio, A.C., Serrao, J.C.: Biomechanical parameters of gait among transtibial amputees: a review. Sao Paulo Med. J. 127(5), 302–309 (2009)CrossRefGoogle Scholar
  15. 15.
    Sagawa, Y. Jr., Turcot, K., Armand, S., Thevenon, A., Vuillerme, N., Watelain, E.: Biomechanics and physiological parameters during gait in lower-limb amputees: a systematic review. Gait Posture 33(4), 511–526 (2011)CrossRefGoogle Scholar
  16. 16.
    Yeung, L.F., Leung, A.K., Zhang, M., Lee, W.C.: Long-distance walking effects on trans-tibial amputees compensatory gait patterns and implications on prosthetic designs and training. Gait Posture 35(2) (2011)Google Scholar
  17. 17.
    Dundass, C., Yao, G.Z., Mechefske, C.K.: Initial biomechanical analysis and modeling of transfemoral amputee gait. J. Prosthet. Orthot. 15(1), 20–26 (2003)CrossRefGoogle Scholar
  18. 18.
    Jakeman, J., Eldred, M., Xiu, D.: Numerical approach for quantification of epistemic uncertainty. J. Comput. Phys. 229(12), 4648–4663 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  20. 20.
    Hogan, N.: Impedance control: an approach to manipulation: Part II-implementation. J. Dyn. Syst. Meas. Control. 107, 8–16 (1985)CrossRefzbMATHGoogle Scholar
  21. 21.
    Hogan, N.: Impedance control: an approach to manipulation: Part I - theory. J. Dyn. Syst. Meas. Control. 107, 1–7 (1985)CrossRefzbMATHGoogle Scholar
  22. 22.
    Hogan, N.: Impedance control: an approach to manipulation: Part III - applications. J. Dyn. Syst. Meas. Control. 107, 17–24 (1985)CrossRefzbMATHGoogle Scholar
  23. 23.
    Sup, F., Bohara, A., Goldfarb, M.: Design and control of a powered transfemoral prosthesis. Int. J. Robot. Res. 27(2), 263–273 (2008). doi: 10.1177/0278364907084588 CrossRefGoogle Scholar
  24. 24.
    Sup, F.C.: A Powered Self-Contianed Knee and Ankle Prosthesis for Near Normal Gait in Transfemoral Amputees. Vanderbilt University (2009)Google Scholar
  25. 25.
    Perry, J., Burnfield, J.M.: Gait Analysis: Normal and Pathological Function, 2nd edn. SLACK, Thorofare (2010)Google Scholar
  26. 26.
    Bejek, Z., Paroczai, R., Illyes, A., Kiss, R.M.: The influence of walking speed on gait parameters in healthy people and in patients with osteoarthritis. Knee Surg. Sports Traumatol. Arthrosc. 14(7), 612–622 (2006). doi: 10.1007/s00167-005-0005-6 CrossRefGoogle Scholar
  27. 27.
    Zeni, J.A., Jr., Richards, J.G., Higginson, J.S.: Two simple methods for determining gait events during treadmill and overground walking using kinematic data. Gait Posture 27(4), 710–714 (2008)CrossRefGoogle Scholar
  28. 28.
    Walley, P.: Towards a unified theory of imprecise probability. Int. J. Approx. Reason. 24(2–3), 125–148 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Sentz, K., Ferson, S.: Combination of Evidence in Dempster-Shafer Theory. In: vol. SAND2002-0835. Sandia National Laboratories (2002)Google Scholar
  31. 31.
    Basir, O., Yuan, X.: Engine fault diagnosis based on multi-sensor information fusion using Dempster–Shafer evidence theory. Inform. Fusion 8(4), 379–386 (2007)CrossRefGoogle Scholar
  32. 32.
    Chen, Q., Aickelin, U.: Anomaly detection using the Dempster-Shafer method. In: DMIN06, International Conference on Data Mining 2006, pp. 232–240, Las Vegas, Nevada, USA, 26–29 June 2006Google Scholar
  33. 33.
    Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 28, 325–339 (1967)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ming Liu
    • 1
    • 2
    Email author
  • Fan Zhang
    • 1
    • 2
  • Philip Datseris
    • 3
  • He (Helen) Huang
    • 1
    • 2
  1. 1.The Neuromuscular Rehabilitation Engineering Laboratory, Department of Electrical, Computer, and Biomedical EngineeringUniversity of Rhode IslandKingstonUSA
  2. 2.The Neuromuscular Rehabilitation Engineering Laboratory, Department of Biomedical EngineeringNorth Carolina State UniversityRaleighUSA
  3. 3.Department of Mechanical, Industrial and Systems EngineeringUniversity of Rhode IslandKingstonUSA

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