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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Wilson, D.R., Feikes, J.D., O’Connor, J.: Ligaments and articular contact guide passive knee flexion. J. Biomech. 31, 1127–1136 (1998)
Leardini, A., O’Connor, J., Catani, F., Giannini, S.: A geometric model of the human ankle joint. J. Biomech. 32(6), 585–591 (1999)
Dye, S.: An evolutionary perspective of the knee. J. Bone Jt. Surg. 69(7), 976–983 (1987)
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)
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)
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
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
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
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
Strasser, H.: Lehrbuch der Muskel und Gelenkmechanik (1917)
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)
Menschik, A.: Mechanics of the knee-joint. Part I. Z. Orthop. Grendgeb. 112(3), 481–495 (1974)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Freudenstein, F.: Harmonic analysis of crank rocker mechanism with applications. J. Appl. Mech. ASME, Ser. E 26, 673–675 (1959)
Paul, R.: Robot Manipulators: Mathematics, Programming, and Control. MIT Press, Cambridge (1981)
Bourelle, J., Chen, C., Caro, S., Angeles, J.: Graphical user interface to solve the burmester problem. In: 12th IFToMM World Congress, Besancon, June (2007)
Khalil, W., Dombre, E.: Modeling, Identification and Control of Robots. Hermes Sciences Europe, Paris (2002)
Appell, P.: Dynamique des Systèmes – Mécanique Analytique. Gauthiers-Villars, Paris (1931)
Vukobratovic, M., Stepanenko, J.: On the stability of anthropomorphic systems. Math. Biosci. 15(1), 1–37 (1972)
Formal’skii, A.: Locomotion of Anthropomorphic Mechanisms. Nauka, Moscow (1982) [In Russian]
Boor, C.D.: A Practical Guide to Splines. Springer, Berlin (1978).
Gill, P., Murray, W., Wright, M.: Practical Optimization. Academic Press, London (1981)
Powell, M.: Variable Metric Methods for Constrained Optimization. Lecture Notes in Mathematics, pp. 62–72. Springer, Berlin (1977)
Chevallereau, C., Bessonnet, G., Abba, G., Aoustin, Y.: Bipedal Robots. ISTE Wiley, New York (2009)
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This work is supported by ANR grants for the R2A2.
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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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DOI: https://doi.org/10.1007/s11044-013-9382-7