Comparison of Two Measures of Dynamic Stability During Treadmill Walking

Stability of biped walking is an important characteristic of legged locomotion. Whereas clinical investigations often relate increased variability to decreased stability, there are only few studies examining stability aspects directly. On the other hand, various papers from the field of robotics are dedicated to the question: how can the stability of legged locomotor systems be quantified? Particularly, when it comes to realizing fast motions in robots, the question of maintaining dynamic stability is of utmost importance. The current paper presents a theoretical comparison of several measures for dynamic stability - namely Floquet multipliers and Local Divergence Exponents (LDE). The sensitivity of these parameters to changes in speed of human treadmill locomotion is investigated. Experimental results show that two different types of stability with respect to speed dependence seem to exist. Short term LDE and Floquet multipliers consider the stability over a period of one stride, which seems to be optimal at intermediate walking speeds. Long term LDE quantify stability of movement trajectories over multiple strides. This type of stability decreases with speed and may be one reason for changing gaits from walking to running at a certain speed value.

[1]  J. Hamill,et al.  Energetic Cost and Stability during Human Walking at the Preferred Stride Frequency , 1995 .

[2]  N. Stergiou,et al.  Nonlinear dynamics indicates aging affects variability during gait. , 2003, Clinical biomechanics.

[3]  Y. Hurmuzlu,et al.  On the measurement of dynamic stability of human locomotion. , 1994, Journal of biomechanical engineering.

[4]  J. Dingwell,et al.  Nonlinear time series analysis of normal and pathological human walking. , 2000, Chaos.

[5]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[6]  M. Vukobratovic,et al.  On the stability of anthropomorphic systems , 1972 .

[7]  Michael E Hahn,et al.  Can motion of individual body segments identify dynamic instability in the elderly? , 2003, Clinical biomechanics.

[8]  T. Oberg,et al.  Basic gait parameters: reference data for normal subjects, 10-79 years of age. , 1993, Journal of rehabilitation research and development.

[9]  Dagmar Sternad,et al.  Debates in dynamics: A dynamical systems perspective on action and perception , 2000 .

[10]  J. Brisswalter,et al.  Energy cost and stride duration variability at preferred transition gait speed between walking and running. , 1996, Canadian journal of applied physiology = Revue canadienne de physiologie appliquee.

[11]  David E Krebs,et al.  Is base of support greater in unsteady gait? , 2002, Physical therapy.

[12]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[13]  Daniel Koditschek,et al.  Quantifying Dynamic Stability and Maneuverability in Legged Locomotion1 , 2002, Integrative and comparative biology.

[14]  T. Oberg,et al.  Joint angle parameters in gait: reference data for normal subjects, 10-79 years of age. , 1994, Journal of rehabilitation research and development.

[15]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[16]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[17]  D. Sternad,et al.  Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. , 2001, Journal of biomechanical engineering.

[18]  W. H. Warren,et al.  Why change gaits? Dynamics of the walk-run transition. , 1995, Journal of experimental psychology. Human perception and performance.

[19]  P. Cavanagh,et al.  Increased variability of continuous overground walking in neuropathic patients is only indirectly related to sensory loss. , 2001, Gait & posture.

[20]  M P Kadaba,et al.  Measurement of lower extremity kinematics during level walking , 1990, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[21]  Li Li.  Stability Landscapes of Walking and Running Near Gait Transition Speed , 2000 .

[22]  C Basdogan,et al.  Presenting joint kinematics of human locomotion using phase plane portraits and Poincaré maps. , 1994, Journal of biomechanics.

[23]  Mitchell Batavia,et al.  Dynamic stability during walking following unilateral total hip arthroplasty. , 2004, Gait & posture.

[24]  C Basdogan,et al.  Kinematics and dynamic stability of the locomotion of post-polio patients. , 1996, Journal of biomechanical engineering.

[25]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[26]  L E Larsson,et al.  The phases of the stride and their interaction in human gait. , 1980, Scandinavian journal of rehabilitation medicine.