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Passive and dynamic gait measures for biped mechanism: formulation and simulation analysis

Published online by Cambridge University Press:  15 October 2012

Carlotta Mummolo  and
Joo H. Kim
Carlotta Mummolo
Affiliation:
Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University (NYU-Poly), Brooklyn, New York, USA Department of Mechanical and Management Engineering, Polytechnic of Bari, Bari, Italy
Joo H. Kim*
Affiliation:
Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University (NYU-Poly), Brooklyn, New York, USA
*
*Corresponding Author. E-mail: jhkim@poly.edu
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Summary

Understanding and mimicking human gait is essential for design and control of biped walking robots. The unique characteristics of normal human gait are described as passive dynamic walking, whereas general human gait is neither completely passive nor always dynamic. To study various walking motions, it is important to quantify the different levels of passivity and dynamicity, which have not been addressed in the current literature. In this paper, we introduce the initial formulations of Passive Gait Measure (PGM) and Dynamic Gait Measure (DGM) that quantify passivity and dynamicity, respectively, of a given biped walking motion, and the proposed formulations will be demonstrated for proof-of-concepts using gait simulation and analysis. The PGM is associated with the optimality of natural human walking, where the passivity weight functions are proposed and incorporated in the minimization of physiologically inspired weighted actuator torques. The PGM then measures the relative contribution of the stance ankle actuation. The DGM is associated with the gait stability, and quantifies the effects of inertia in terms of the Zero-Moment Point and the ground projection of center of mass. In addition, the DGM takes into account the stance foot dimension and the relative threshold between static and dynamic walking. As examples, both human-like and robotic walking motions during single support phase are generated for a planar biped system using the passivity weights and proper gait parameters. The calculated PGM values show more passive nature of human-like walking as compared with the robotic walking. The DGM results verify the dynamic nature of normal human walking with anthropomorphic foot dimension. In general, the DGMs for human-like walking are greater than those for robotic walking. The resulting DGMs also demonstrate their dependence on the stance foot dimension as well as the walking motion; for a given walking motion, smaller foot dimension results in increased dynamicity. Future work on experimental validation and demonstration will involve actual walking robots and human subjects. The proposed results will benefit the human gait studies and the development of walking robots.

Keywords

Biped systemDynamic gait measure (DGM)OptimizationPassive dynamic walkingPassive gait measure (PGM)Passivity weightStabilityStatic walkingZero-moment point (ZMP)
Type
Articles
Information
Robotica , Volume 31 , Issue 4 , July 2013 , pp. 555 - 572
Copyright
Copyright © Cambridge University Press 2012 

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References

1.Xiang, Y., Arora, J. S. and Abdel-Malek, K., “Physics-based modeling and simulation of human walking: A review of optimization-based and other approaches,” Struct. Multidiscip. Optim. 42, 1–23 (2010).CrossRefGoogle Scholar
2.Racic, V., Pavic, A. and Brownjohn, J. M. W., “Experimental identification and analytical modelling of human walking forces: Literature review,” J. Sound Vib. 326, 1–49 (2009).CrossRefGoogle Scholar
3.Kuo, A. D., Donelan, J. M. and Ruina, A., “Energetic consequences of walking like an inverted pendulum: Step-to-Step transitions,” Exercise Sport Sci. Rev., 33 (2), 88–97 (2005).CrossRefGoogle Scholar
4.Kuo, A. D., “The six determinant of gait and the inverted pendulum analogy: A dynamic walking perspective,” Hum. Mov. Sci. 26, 617–656 (2007).CrossRefGoogle ScholarPubMed
5.Vaughan, C. L., “Theories of bipedal walking: An odyssey,” J. Biomech. 36, 513–523 (2003).CrossRefGoogle ScholarPubMed
6.Albert, A. and Gerth, W., “Analytic path planning algorithms for bipedal robots without a trunk,” J. Intell. Robot. Syst. 36, 109–127 (2003).CrossRefGoogle Scholar
7.Park, J. H. and Kim, K. D., “Biped Robot Walking Using Gravity-Compensated Inverted Pendulum Mode and Computed Torque Control,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium (May 1998), vol. 4, pp. 3528–3533.Google Scholar
8.Ha, T. and Choi, C.-H., “An effective trajectory generation method for bipedal walking,” Robot. Auton. Syst. 55, 795–810 (2007).CrossRefGoogle Scholar
9.Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Yokoi, K. and Hirukawa, H., “A Realtime Pattern Generator for Biped Walking,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, DC (May 2002).Google Scholar
10.Li, J. and Chen, W., “Energy-efficient gait generation for biped robot based on the passive inverted pendulum model,” Robotica 29 (4), 595–605 (2011).CrossRefGoogle Scholar
11.Braun, D. J. and Goldfarb, M., “A control approach for actuated dynamic walking in biped robots,” IEEE Trans. Robot. 25 (5), 1292–1303 (Dec. 2009).CrossRefGoogle Scholar
12.McGeer, T., “Passive dynamic walking,” The Int. J. Robot. Res. 9, 62–82 (1990).CrossRefGoogle Scholar
13.Collins, S. H., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307, 1082–1085 (Feb. 2005).CrossRefGoogle ScholarPubMed
14.Collins, S. H. and Ruina, A., “A Bipedal Walking Robot with Efficient and Human-Like Gait,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005).Google Scholar
15.Font-Llagunes, J. M. and Kövecses, J., “Dynamics and energetics of a class of bipedal walking systems,” Mech. Mach. Theory 44 (11), 1999–2019 (Nov. 2009).CrossRefGoogle Scholar
16.Kuo, A. D., “Energetics of actively powered locomotion using the simplest walking model,” J. Biomech. Eng. 124, 113–120 (Feb. 2002).CrossRefGoogle ScholarPubMed
17.Rostami, M. and Bessonnet, G., “Sagittal gait of a biped robot during the single support phase. Part 1: Passive motion,” Robotica 19, 163–176 (2001).CrossRefGoogle Scholar
18.Wisse, M., Schwab, A. L. and van der Helm, F. C. T, “Passive dynamic walking model with upper body,” Robotica 22, 681–688 (2004).CrossRefGoogle Scholar
19.Vukobratovic, M. and Borovac, B., “Zero-moment point – thirty five years of its life,” Int. J. Humanoid Robot. 1 (1), 157–173 (2004).CrossRefGoogle Scholar
20.Popovic, M. B., Goswami, A. and Herr, H., “Ground reference points in legged locomotion: Definitions, biological trajectories and control implications,” Int. J. Robot. Res. 24 (12), 1013–1032 (Dec. 2005).CrossRefGoogle Scholar
21.Mitobe, K., Capi, G. and Nasu, Y., “Control of walking robots based on manipulation of the zero moment point,” Robotica 18 (6), 651–657 (2000).CrossRefGoogle Scholar
22.Czarnetzki, S., Kerner, S. and Urbann, O., “Observer-based dynamic walking control for biped robots,” Robot. Auton. Syst. 57, 839–845 (2009).CrossRefGoogle Scholar
23.Vanderborght, B., Verrelst, B., Van Ham, R., Van Damme, M. and Lefeber, D., “Objective locomotion parameters based inverted pendulum trajectory generator,” Robot. Auton. Syst. 56, 738–750 (2008).CrossRefGoogle Scholar
24.Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18 (6), 523–533 (Jun. 1999).CrossRefGoogle Scholar
25.Azevedo, C., Andreff, N. and Arias, S., “Bipedal walking: From gait design to experimental analysis,” Mechatronics 14, 639–665 (2004).CrossRefGoogle Scholar
26.Mrozowski, J., Awrejcewicz, J. and Bamberski, P., “Analysis of stability of the human gait,” J. Theor. Appl. Mech. 45 (1), 91–98 (2007).Google Scholar
27.Beletskii, V. V. and Chudinov, P. S., “Parametric optimization in the problem of bipedal locomotion,” Izv. An SSSR. Mekhanika Tverdogo Tela (Mech. Solids), 1, 25–35 (1977).Google Scholar
28.Chevallereau, C. and Sardain, P., “Design and Actuation Optimization of a 4 Axes Biped Robot for Walking and Running,” Proceedings of the 2000 IEEE International Conference on Robotics and Automation, San Francisco, CA (Apr. 2000).Google Scholar
29.Djoudi, D., Chevallereau, C. and Aoustin, Y., “Optimal Reference Motions for Walking of a Biped Robot,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005).Google Scholar
30.Liu, R. and Ono, K., “Energy Optimal Trajectory Planning of Biped Walking Motion,” Proceedings of the International Symposium on Adaptive Motion of Animals and Machines, Montreal, Canada (Aug. 2000).Google Scholar
31.Anderson, F. C. and Pandy, M. G., “Dynamic optimization of human walking,” J. Biomech. Eng. 123 (5), 381–390 (2001).CrossRefGoogle ScholarPubMed
32.Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19 (5), 557–569 (2001).CrossRefGoogle Scholar
33.Bessonnet, G., Chessé, S. and Sardain, P., “Optimal gait synthesis of a seven-link planar biped,” Int. J. Robot. Res. 123 (10–11), 1059–1073 (Oct. 2004).CrossRefGoogle Scholar
34.Srinivasan, M. and Ruina, A., “Computer optimization of a minimal biped model discovers walking and running,” Nature 439, 72–75 (Jan. 2006).CrossRefGoogle ScholarPubMed
35.Xiang, Y., Chung, H. J., Kim, J. H., Bhatt, R., Rahmatalla, S., Yang, J., Marler, T., Arora, J. S. and Abdel-Malek, K., “Predictive dynamics: An optimization-based novel approach for human motion simulation,” Struct. Multidiscip. Optim. 41 (3), 465–479 (Apr. 2010).CrossRefGoogle Scholar
36.Bessonnet, G., Seguin, P. and Sardain, P., “A parametric optimization approach to walking pattern synthesis,” Int. J. Robot. Res. 24, 523–536 (Jul. 2005).CrossRefGoogle Scholar
37.Alba, M., Prada, J. C. G., Meneses, J. and Rubio, H., “Center of percussion and gait design of biped robots,” Mech. Mach. Theory 45, 1681–1693 (2010).CrossRefGoogle Scholar
38.Zielinska, T., Chew, C.-M., Kryczka, P. and Jargilo, T., “Robot gait synthesis using the scheme of human motions skills development,” Mech. Mach. Theory 44, 541–558 (2009).CrossRefGoogle Scholar
39.Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N. and Tanie, K., “Planning walking patterns for a biped robot,” IEEE Trans. Robot. Autom. 17 (3), 280–289 (2001).CrossRefGoogle Scholar
40.Vaughan, C. L., Davis, B. L. and O'Connor, J. C., Dynamics of Human Gait (Kiboho Publishers, Cape Town, South Africa, 1992).Google Scholar
41.Yamaguchi, J., Inoue, S., Nishino, D. and Takanishi, A., “Development of a Bipedal Humanoid Robot having Antagonistic Driven Joints and Three DOF Trunk,” Proceedings of the 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, Victoria, B.C., Canada (Oct. 1998).Google Scholar
42.Park, J. H. and Rhee, Y. K., “ZMP trajectory generation for reduced trunk motions of biped robots,” Proceedings of the 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, Victoria, B.C., Canada (Oct. 1998).Google Scholar
43.Kuo, A. D., “A simple model of bipedal walking predicts the preferred speed–step length relationship,” J. Biomech. Eng. 123, 264–269 (2001).CrossRefGoogle ScholarPubMed
44.Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., Robotics – Control, Sensing, Vision, and Intelligence (McGraw Hill, Columbus, OH, 1987).Google Scholar
45.Inman, V. T., Ralston, H. J. and Todd, F., Human Walking (Williams Wilkins, Baltimore, MD, 1981).Google Scholar
46.Sardain, P. and Bessonnet, G., “Forces acting on a biped robot. Center of pressure-zero moment point,” IEEE Trans. Syst. Man Cybern. A 34 (5), 630–637 (Sep. 2004).CrossRefGoogle Scholar
47.Hase, K. and Yamazaki, N., “Development of three-dimensional whole-body musculoskeletal model for various motion analyses,” JSME Int. J. C 40 (1), 25–32 (Mar. 1997).Google Scholar
48.Anderson, F. C. and Pandy, M. G., “Static and dynamic optimization solutions for gait are practically equivalent,” J. Biomech. 34 (2), 153–161 (Feb. 2001).CrossRefGoogle ScholarPubMed
49.Kim, J. H., Abdel-Malek, K., Yang, J. and Marler, T., “Prediction and analysis of human motion dynamics performing various tasks,” Int. J. Hum. Factors Model. Simul. 1 (1), 69–94 (2006).CrossRefGoogle Scholar
50.Kim, J. H., Yang, J. and Abdel-Malek, K., “A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators with DH representation,” Multibody Syst. Dyn. 19 (4), 427–451 (May 2008).CrossRefGoogle Scholar
51.Kim, J. H., Yang, J. and Abdel-Malek, K., “Planning load-effective dynamic motions of highly articulated human model for generic tasks,” Robotica 27 (5), 739–747 (Sep. 2009).CrossRefGoogle Scholar
52.Saunders, J. B., Inman, V. T. and Eberhart, H. D., “The major determinants in normal and pathological gait,” The J. Bone Joint Surg. 35, 543–558 (1953).CrossRefGoogle ScholarPubMed
53.Xiang, Y., Arora, J. S. and Abdel-Malek, K., “Optimization-based prediction of asymmetric human gait,” J. Biomech. 44, 683–693 (2011).CrossRefGoogle ScholarPubMed
54.Collins, S. H. and Ruina, A., “A Bipedal Walking Robot with Efficient and Human-Like Gait,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 1983–1988.Google Scholar
55.Ruina, A., Bertram, J. E. and Srinivasan, M., “A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition,” J. Theor. Biol. 237 (2), 170–192 (2005).CrossRefGoogle ScholarPubMed
56.Flynn, L., Jafari, R., Hellum, A. and Mukherjee, R., “An Energy Optimal Gait for the MSU Active Synthetic Wheel Biped,” Proceedings of the ASME 2010 Dynamic Systems and Control Conference, Cambridge, MA, USA (2010).Google Scholar
57.Venture, G., Ayusawa, K. and Nakamura, Y., “Human and Humanoid Identification from Base-Link Dynamics,” In: Proceedings of the 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, Scottsdale, AZ, USA (October 2008) pp. 445–450.CrossRefGoogle Scholar