Passive dynamic walking is an excellent tool for evaluating biped stability measures, due to its simplicity, but an understanding of the stability, in the classical definition, is required. The focus of this paper is on analyzing the stability of the passive dynamic gait. The stability of the passive walking model, validated in Part I, was analyzed with Lyapunov exponents, and the geometry of the basin of attraction was determined. A novel method was created to determine the 2D projection of the basin of attraction of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of gait was examined. The angular momentum of the passive walker was not found to correlate to the stability of the gait.
Issue Section:
Research Papers
References
1.
Vukobratovic
, M.
, and Borovac
, B.
, 2004
, “Zero-Moment Point – Thirty-Five Years of Its Life
,” Int. J. Human. Robot.
, 1
(1
), pp. 157
–173
.10.1142/S02198436040000832.
Goswami
, A.
, 1999
, “Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point
,” Int. J. Robot. Res.
, 18
(6
), pp. 523
–533
.10.1177/027836499220663763.
Herr
, H.
, and Popovic
, M.
, 2008
, “Angular Momentum in Human Walking
,” J. Exp. Biol.
, 211
, pp. 467
–481
.10.1242/jeb.0085734.
Silverman
, A.
, Wilken
, J.
, Sinitski
, E.
, and Neptune
, R.
, 2012
, “Whole-Body Angular Momentum in Incline and Decline Walking
,” J. Biomech.
, 45
, pp. 965
–971
.10.1016/j.jbiomech.2012.01.0125.
Popovic
, M.
, Hofmann
, A.
, and Herr
, H.
, 2004
, “Angular Momentum Regulation During Human Walking: Biomechanics and Control
,” Proc. of the 2004 IEEE International Conference on Robotics and Automation
, New Orleans, LA
, Vol. 3, pp. 2405
–2411
.6.
Goswami
, A.
, and Kallem
, V.
, 2004
, “Rate of Change of Angular Momentum and Balance Maintenance of Biped Robots
,” Proc. of the 2004 IEEE International Conference on Robotics and Automation
, New Orleans, LA
, pp. 3785
–3790
.7.
Popovic
, M.
, Hofmann
, A.
, and Herr
, H.
, 2004
, “Zero Spin Angular Momentum Control: Definition and Applicability
,” Proc. of the 2004 IEEE RAS/RSJ International Conference on Humanoid Robots
, Los Angeles, CA
, Vol. 1, pp. 478
–493
.8.
Popovic
, M.
, Goswami
, A.
, and Herr
, H.
, 2005
, “Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications
,” Int. J. Robot. Res.
, 24
(12
), pp. 1013
–1032
.10.1177/02783649050583639.
Wight
, D.
, Kubica
, E.
, and Wang
, D.
, 2008
, “Introduction of the Foot Placement Estimator: A Dynamic Measure of Balance for Bipedal Robotics
,” ASME J. Comput. Nonlinear Dyn.
, 3
(1
), p. 011009
.10.1115/1.281533410.
Millard
, M.
, McPhee
, J.
, and Kubica
, E.
, 2012
, “Foot Placement and Balance in 3D
,” ASME J. Comput. Nonlinear Dyn.
, 7
(2
), p. 021015
.10.1115/1.400546211.
Schwab
, A.
, and Wisse
, M.
, 2001
, “Basin of Attraction of the Simplest Walking Model
,” Proc. of the ASME Design Engineering Technical Conferences
, pp. 531
–539
.12.
Ning
, L.
, Junfeng
, L.
, and Tianshu
, W.
, 2009
, “The Effects of Parameter Variation on the Gaits of Passive Walking Models: Simulations and Experiments
,” Robotica
, 27
(4
), pp. 511
–528
.10.1017/S026357470800490613.
Zhang
, P.
, Tian
, Y.
, and Liu
, Z.
, 2009
, “Bisection Method for Evaluation of Attraction Region of Passive Dynamic Walking
,” Proc. of the 4th International Conference on Autonomous Robots and Agents
, Wellington, New Zealand
, pp. 692
–697
.14.
Wolf
, A.
, Swift
, J.
, Swinney
, H.
, and Vastano
, J.
, 1985
, “Determining Lyapunov Exponents From a Time Series
,” Phys. D
, 16
, pp. 285
–317
.10.1016/0167-2789(85)90011-915.
Sobczyk
, M.
, Perondi
, E.
, and Cunha
, M. A.
, 2010
, “A Continuous Approximation of the LuGre Friction Model
,” ABCM Symposium Series in Mechatronics
, Vol. 4, ABCM
, Ouro Preto
, pp. 218
–228
.16.
Jarvis
, R.
, 1973
, “On the Identification of the Convex Hull of a Finite Set of Points in the Plane
,” Inf. Process. Lett.
, 2
, pp. 18
–21
.10.1016/0020-0190(73)90020-317.
Dempster
, W.
, 1955
, Space Requirements of the Seated Operator: Geometrical, Kinematic, and Mechanical Aspects of the Body, With Special Reference to the Limbs
, WADC
, Ohio
, pp. 55
–159
.18.
Collins
, S.
, Wisse
, M.
, and Ruina
, A.
, 2001
, “A Three Dimensional Passive-Dynamic Walking Robot With Two Legs and Knee
,” Int. J. Robot. Res.
, 20
(7
), pp. 607
–615
.10.1177/0278364012206756119.
Borzova
, E.
, and Hurmuzlu
, Y.
, 2004
, “Passively Walking Five-Link Robot
,” Automatica
, 40
(4
), pp. 621
–629
.10.1016/j.automatica.2003.10.015Copyright © 2013 by ASME
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