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Two walking gaits for a planar bipedal robot equipped with a four-bar mechanism for the knee joint

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Abstract

The design of a knee joint is a key issue in robotics and biomechanics to improve the compatibility between prosthesis and human movements, and to improve the bipedal robot performances. We propose a novel design for the knee joint of a planar bipedal robot, based on a four-bar linkage. The dynamic model of the planar bipedal robot is calculated. Two kinds of cyclic walking gaits are considered. The first gait is composed of successive single support phases with stance flat-foot on the ground separated by impacts. The second gait is a succession of finite time double support phases, single support phases, and impacts. During the double support phase, both feet rotate. This phase is ended by an impact of the toe of the forward foot, while the rear foot is taking off. The single support phase is ended by an impact of the swing foot heel, the other foot keeping contact with the ground through its toe. For both gaits, the reference trajectories of the rotational joints are prescribed by cubic spline functions in time. A parametric optimization problem is presented for the determination of the parameters corresponding to the optimal cyclic walking gaits. The main contribution of this paper is the design of a dynamical stable walking gait with double support phases with feet rotation, impacts, and single support phases for this bipedal robot.

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References

  1. Wilson, D.R., Feikes, J.D., O’Connor, J.: Ligaments and articular contact guide passive knee flexion. J. Biomech. 31, 1127–1136 (1998)

    Article  Google Scholar 

  2. Leardini, A., O’Connor, J., Catani, F., Giannini, S.: A geometric model of the human ankle joint. J. Biomech. 32(6), 585–591 (1999)

    Article  Google Scholar 

  3. Dye, S.: An evolutionary perspective of the knee. J. Bone Jt. Surg. 69(7), 976–983 (1987)

    Google Scholar 

  4. Fuss, F.K.: Anatomy of the cruciate ligaments and their function in extension and flexion of the human knee joint. Am. J. Anat. 184(2), 165–176 (1989)

    Article  Google Scholar 

  5. Landjerit, B., Bisserie, M.: Cinématique spatiale de l’articulation fémoro-tibiale du genou humain: caractérisation expérimentale et implications chirurgicales. Acta Orthop. Belg. 58(2), 147–158 (1992)

    Google Scholar 

  6. Herrmann, S., Woernie, C., Kaehler, M., Rachholz, R., Souffrant, R., Zierath, J., Kluess, D., Bader, R.: Hil simulation for testing joint stability after total knee arthroplasty. Multibody Syst. Dyn. 67, 28–55 (2012). doi:10.1007/s11044-011-9283-6

    Google Scholar 

  7. Guess, T.: Forward dynamics simulation using a natural knee with menisci in the multibody framework. Multibody Syst. Dyn. 53, 28–37 (2012). doi:10.1007/s11044-011-9293-4

    Google Scholar 

  8. Argatov, I.: Development of an asymptotic modeling methodology for tibia-femoral contact in multibody dynamic simulations of the human knee joint. Multibody Syst. Dyn. 28, 3–20 (2012). doi:10.1007/s111044-011-9275-6

    Article  MATH  MathSciNet  Google Scholar 

  9. Ribeiro, A., Rasmussen, J., Flores, P., Silva, L.: Modeling of the condyle elements within a biomechanical knee model. Multibody Syst. Dyn. 28, 181–197 (2012). doi:10.1007/s11044-011-9280-9

    Article  MathSciNet  Google Scholar 

  10. Strasser, H.: Lehrbuch der Muskel und Gelenkmechanik (1917)

    Google Scholar 

  11. Gard, S.A., Childress, D.S., Uellendahl, J.E.: The influence of four-bar linkage knees on prosthetic swing-phase floor clearance. J. Prosthet. Orthot. 8(2), 34–40 (1996)

    Article  Google Scholar 

  12. Menschik, A.: Mechanics of the knee-joint. Part I. Z. Orthop. Grendgeb. 112(3), 481–495 (1974)

    Google Scholar 

  13. Feikes, J.D., O’Connor, J.J., Zavatsky, A.B.: A constraint-based approach to modelling the mobility of the human knee joint. J. Biomech. 36(1), 125–129 (2003)

    Article  Google Scholar 

  14. Kaneko, K., Kanehiro, F., Kajita, S., Hirukawa, H., Kawasaki, T., Hirita, M., Akachi, K., Isozumi, T.: Humanoid robot hrp-2. In: Proceedings of the International Conference on Robotics and Automation 2004, pp. 1083–1090 (2004)

    Google Scholar 

  15. Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E., Canuddas-de Wit, C., Grizzle, J.: Rabbit: a testbed for advanced control theory. IEEE Control Syst. Mag. 23(5), 57–79 (2003)

    Article  Google Scholar 

  16. Grishin, A., Formal’sky, A., Lensky, A., Zhitomirsky, S.: Dynamic walking of a vehicle with two telescopic legs controlled by two drives. Int. J. Robot. Res. 13(2), 137–147 (1994)

    Article  Google Scholar 

  17. Yang, T., Westervelt, E., Schmideler, J., Bockbrader, R.: Design and control of a planar bipedal robot Ernie with parallel knee compliance. Auton. Robots 25, 317–333 (2008)

    Article  Google Scholar 

  18. Kajita, S., Kaneko, K., Morisawa, M., Nakaoka, S., Hirukawa, H.: Zmp-based biped running enhanced by toe springs. In: 2007 IEEE International Conference on Robotics and Automation, pp. 3963–3969 (2007)

    Chapter  Google Scholar 

  19. Tajima, R., Honda, D., Suga, K.: Fast running experiments involving a humanoid robot. In: 2009 IEEE Conference on Robotics and Automation, pp. 1571–1576 (2009)

    Chapter  Google Scholar 

  20. Tlalolini Romero, D., Aoustin, Y., Chevallereau, C.: Design of a walking cyclic gait with single support phases and impacts for the locomotor system of a thirteen-link 3d biped using the parametric optimization. Multibody Syst. Dyn. 23(1), 33–56 (2009)

    Article  Google Scholar 

  21. Gini, G., Scarfogliero, U., Folgheraiter, M.: Human-oriented biped robot design: insights into the development of a truly antropomophic leg. In: IEEE International Conference on Robotics and Automation, pp. 2910–2915 (2007)

    Google Scholar 

  22. Wang, F., Wu, C., Zhang, Y., Xu, X.: Design and implementation of coordinated control strategy for biped robot with heterogeneous legs. In: IEEE International Conference on Mechatronics and Automation, pp. 1559–1564 (2007)

    Google Scholar 

  23. Hamon, A., Aoustin, Y.: Cross four-bar linkage for the knees of a planar bipedal robot. In: 2010 IEEE-RAS International Conference on Humanoid Robots, pp. 379–384 (2010)

    Chapter  Google Scholar 

  24. Tlalolini Romero, D., Chevallereau, C., Aoustin, Y.: Comparison of different gaits with rotation of the feet for a planar biped. Robot. Auton. Syst. 57(4), 371–383 (2009)

    Article  Google Scholar 

  25. Bradley, J., FitzPatrick, D., Daniel, D., Shercliff, T., O’Connor, J.: Orientation of the cruciate ligament in the sagittal plane. J. Bone Jt. Surg. 70-B, 94–99 (1988)

    Google Scholar 

  26. Freudenstein, F.: Harmonic analysis of crank rocker mechanism with applications. J. Appl. Mech. ASME, Ser. E 26, 673–675 (1959)

    MATH  Google Scholar 

  27. Paul, R.: Robot Manipulators: Mathematics, Programming, and Control. MIT Press, Cambridge (1981)

    Google Scholar 

  28. Bourelle, J., Chen, C., Caro, S., Angeles, J.: Graphical user interface to solve the burmester problem. In: 12th IFToMM World Congress, Besancon, June (2007)

    Google Scholar 

  29. Khalil, W., Dombre, E.: Modeling, Identification and Control of Robots. Hermes Sciences Europe, Paris (2002)

    Google Scholar 

  30. Appell, P.: Dynamique des Systèmes – Mécanique Analytique. Gauthiers-Villars, Paris (1931)

    Google Scholar 

  31. Vukobratovic, M., Stepanenko, J.: On the stability of anthropomorphic systems. Math. Biosci. 15(1), 1–37 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  32. Formal’skii, A.: Locomotion of Anthropomorphic Mechanisms. Nauka, Moscow (1982) [In Russian]

    Google Scholar 

  33. Boor, C.D.: A Practical Guide to Splines. Springer, Berlin (1978).

    Book  MATH  Google Scholar 

  34. Gill, P., Murray, W., Wright, M.: Practical Optimization. Academic Press, London (1981)

    MATH  Google Scholar 

  35. Powell, M.: Variable Metric Methods for Constrained Optimization. Lecture Notes in Mathematics, pp. 62–72. Springer, Berlin (1977)

    Google Scholar 

  36. Chevallereau, C., Bessonnet, G., Abba, G., Aoustin, Y.: Bipedal Robots. ISTE Wiley, New York (2009)

    Book  Google Scholar 

Download references

Acknowledgements

This work is supported by ANR grants for the R2A2.

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Correspondence to Y. Aoustin.

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Hamon, A., Aoustin, Y. & Caro, S. Two walking gaits for a planar bipedal robot equipped with a four-bar mechanism for the knee joint. Multibody Syst Dyn 31, 283–307 (2014). https://doi.org/10.1007/s11044-013-9382-7

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