The Simplest Walking Model: Stability, Complexity, and Scaling

Journal of Biomechanical Engineering

Volumn 120, Issue 2, 1998, Pages 281-288

  Garcia, Mariano ^a   Chatterjee, Anindya ^a   Ruina, Andy ^a   Coleman, Michael ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAVITATIONAL EFFECTS; MATHEMATICAL MODELS;

GAIT CYCLES;

GAIT ANALYSIS;

ARTICLE; BIOMECHANICS; ENERGY; GAIT; HUMAN; LEG MOVEMENT; MATHEMATICAL MODEL; WALKING;

ALGORITHMS; BIOMECHANICS; ENERGY METABOLISM; FOOT; FORECASTING; GAIT; GRAVITATION; HIP JOINT; HUMANS; LEG; MODELS, BIOLOGICAL; POSTURE; WALKING;

EID: 0032054337     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.2798313     Document Type: Article

References (22)

1. Alexander, R. M., 1991, “Energy-saving mechanisms in walking and running,”.J. Exp. Biol, 160:55-69.
2. Alexander, R. M., 1995, “Simple models of human motion,” Applied Mechanics Review, 48:461-469.
3. Bloch, A. M., Krishnaprasad, P. S., Marsden, J. E., and Murray, R. M., 1996, “Nonholonomic mechanical systems with symmetry,” Arch. Rat. Mech. An., 136:21-99.
4. Coleman, M., Chatterjee, A., and Ruina, A., 1997, “Motions of a rimless spoked wheel: A simple 3D system with impacts,” Dynamics and Stability of Systems, 12(3): 139-160.
5. Coleman, M., and Ruina, A., 1997, “An uncontrolled toy that can walk but cannot stand still,” Physical Review Letters, in press.
6. Garcia, M., Ruina, A., and Chatterjee, A., 1997, “Speed, efficiency, and stability of small-slope 2D passive-dynamic bipedal walking,” International Conference on Robotics and Automation, accepted.
7. Goldstein, H., 1980, Classical Mechanics, Addison-Wesley Publishing Company Inc.
8. Goswami, A., Espiau B., and Keramane, A., 1996a, “Limit cycles and their stability in a passive bipedal gait,” Proc. International Conference on Robotics and Automation.
9. Goswami, A., Thuilot, B., and Espiau B., 1996b, “Compass-like bipedal robot part I: Stability and bifurcation of passive gaits,” INRIA Research Report No. 2996.
10. Goswami, A., Espiau B., and Keramane, A., 1997, “Limit cycles in a passive compass gait biped and passivity-mimicking control laws,” Journal of Autonomous Robots, in press.
11. Hand, R. S., 1988, “Comparisons and stability analysis of linearized equations of motion for a basic bicycle model,” Master’s thesis, Cornell University, Ithaca, NY.
12. Hubbard, M., 1979, “Lateral dynamics and stability of the skateboard,” ASME Journal of Applied Mechanics, 46:931-936.
13. Hurmuzlu, Y., and Moskowitz, G., 1986, “The role of impact in the stability of bipedal locomotion,” Dynamics and Stability of Systems, 1:217-234.
14. Katoh, R., and Mori, M., 1984, “Control method of biped locomotion giving asymptotic stability of trajectory,” Automatica, 20:405-414.
15. Lattanzio, H., Kuenzler, G., and Reading, M., 1992, “Passive dynamic walking,” Project Report, Human Power Lab., Cornell University.
16. McGeer, T., 1990a, “Passive dynamic walking,” International Journal of Robotics Research, 9:62-82.
17. McGeer, T., 1990b, “Passive walking with knees,” Proc. IEEE Conference on Robotics and Automation, 2:1640-1645.
18. Mochon, S., and McMahon, T., 1980, “Ballistic walking: An improved model,” Mathematical Biosciences, 52:241-260.
19. Ruina, A., 1997, “Non-holonomic stability aspects of piecewise holonomic systems,” Reports on Mathematical Physics, accepted.
20. Strogatz, S., 1994, Nonlinear Dynamics and Chaos, Addison-Wesley, Reading, MA.
21. Thuilot, B., Goswami, A., and Espiau B., 1997, “Bifurcation and chaos in a simple passive bipedal gait,” Proc. IEEE International Conference on Robotics and Automation.
22. Zenkov, D., Bloch, A., and Marsden, J., 1997, “The energy-momentum method for the stability of nonholonomic systems,” Technical report, University of Michigan.