The inherent dynamics of bipedal, kneed mechanisms are studied with emphasis on the existence and stability of repetitive gait in a three-dimensional environment, in the absence of external, active control. The investigation is motivated by observations that sustained anthropomorphic locomotion is largely a consequence of geometric and inertial properties of the mechanism. While the modeling excludes active control, the energy dissipated in ground and knee collisions is continuously re-injected by considering gait down slight inclines. The paper describes the dependence of the resulting passive gait in vertically constrained and unconstrained mechanisms on model parameters, such as ground compliance and ground slope. We also show the possibility of achieving statically unstable gait with appropriate parameter choices.

1.
Bach, T. M., Evans, O. M., and Robinson, I. G. A., 1994, “Optimization of Inertial Characteristics of the Transfemoral Limb Prostheses Using a Computer Simulation of Human Walking,” Proc. Eighth Biennial Conference of the Canadian Society for Biomechanics, pp. 212–213.
2.
Tsai
,
C.-S.
, and
Mansour
,
J. M.
,
1986
, “
Swing Phase Simulation and Design of Above Knee Prostheses,
ASME J. Biomech. Eng.
,
108
, p.
65
65
.
3.
Kay, B. A., 1998, private communication, Brown University, Providence, RI.
4.
Diedrich
,
F. J.
, and
Warren
,
W. H.
, Jr.
,
1995
, “
Why Change Gaits? Dynamics of the Walk–Run Transition
,”
J. Exp. Psychol. Hum. Percept Perform
,
21
, No.
1
, pp.
183
202
.
5.
Warren
, Jr.,
W. H.
,
Young
,
D. S.
, and
Lee
,
D. N.
,
1986
, “
Visual Control of Step Length During Running Over Irregular Terrain
,”
J. Exp. Psychol. Hum. Percept Perform
,
12
, No.
3
, pp.
259
266
.
6.
Hurmuzlu
,
Y.
,
Basdogan
,
C.
, and
Stoianovici
,
D.
,
1996
, “
Kinematics and Dynamic Stability of the Locomotion of Post-Polio Patients
,”
ASME J. Biomech. Eng.
,
118
, pp.
405
411
.
7.
Basmajian, J. V., and Tuttle, R., 1973, “EMG of Locomotion in Gorilla and Man,” in: Control of Posture and Locomotion, Plenum Press, New York, pp. 599–609.
8.
McGeer
,
T.
,
1990
, “
Passive Dynamic Walking
,”
Int. J. Robot. Res.
,
9
, pp.
62
82
.
9.
McGeer, T., 1990, “Passive Walking With Knees,” Proc. IEEE Conference on Robotics and Automation, Vol. 2, pp. 1640–1645.
10.
Chatterjee, A., and Garcia, M., 1998, “Small Slope Implies Low Speed in Passive Dynamic Walking, ” submitted to Dynamics and Stability of Systems.
11.
Coleman
,
M.
, and
Ruina
,
A.
,
1998
, “
An Uncontrolled Toy That Can Walk But Cannot Stand Still
,”
Phys. Rev. Lett.
,
80
, No.
16
, pp.
3658
3661
.
12.
Garcia
,
M.
,
Chatterjee
,
A.
,
Ruina
,
A.
, and
Coleman
,
M.
,
1998
, “
The Simplest Walking Model: Stability, Complexity, and Scaling
,”
ASME J. Biomech. Eng.
,
120
, pp.
281
288
.
13.
Garcia, M., Chatterjee, A., and Ruina, A., 1998, “Efficiency, Speed, and Scaling of Passive Dynamic Bipedal Walking,” submitted to Dynamics and Stability of Systems.
14.
Brogliato, B., 1999, Nonsmooth Mechanics: Models, Dynamic and Control, Springer-Verlag, London–New York.
15.
Ju
,
M.-S.
, and
Mansour
,
J. M.
,
1988
, “
Simulations of the Double Limb Support Phase of Human Gait,
ASME J. Biomech. Eng.
,
110
, pp.
223
229
.
16.
Lesser, M., 1995, The Analysis of Complex Nonlinear Mechanical Systems, World Scientific, Singapore.
17.
Press, W. H., Teukolsky, S. A., Vettering, W. T., and Flannery, B. P ., 1992, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, Cambridge–New York.
18.
Guckenheimer, J., and Holmes, P., 1990, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York.
19.
Adolfsson, J., Dankowicz, H., and Nordmark, A. B., 2000, “3D Passive Walkers: Stability Analysis in the Presence of Discontinuities,” Nonlinear Dyn., in press.
20.
Rose, J., and Gamble, J. G., 1994, Human Walking, Williams & Wilkins, Baltimore, MD.
21.
Formal’sky, A. M., 1996, “Ballistic Locomotion of a Biped. Design and Control of Two Biped Machines,” CISM Advanced School on Modelling and Simulation of Human and Walking Robots Locomotion, Udine.
22.
Mochon
,
S.
, and
McMahon
,
T.
,
1980
, “
Ballistic Walking: An Improved Model
,”
Math. Biosci.
,
52
, pp.
241
260
.
23.
McGeer
,
T.
,
1993
, “
Dynamics and Control of Bipedal Locomotion
,”
J. Theor. Biol.
,
163
, pp.
277
314
.
24.
Howell, G. W., and Baillieul, J., 1998, “Simple Controllable Walking Mechanisms Which Exhibit Bifurcations,” in: Proc. 37th IEEE Conference on Decision and Control, pp. 3027–3032.
25.
Fowble, J. V., and Kuo, A. D., 1996, “Stability and Control of Passive Locomotion in 3D, ” in: Proc. Conference on Biomechanics and Neural Control of Movement, pp. 28–29.
26.
Pratt, J. E., 1995, “Virtual Model Control of a Biped Walking Robot,” M. Eng. thesis, MIT.
27.
Pratt, J., and Pratt G., 1998 “Intuitive Control of a Planar Bipedal Walking Robot,” in: Proc. IEEE International Conference on Robotics and Automation (ICRA ’98), Leuven, Belgium.
You do not currently have access to this content.