Dynamic stability of passive dynamic walking on an irregular surface

Falls that occur during walking are a significant problem in the elderly. Previous research has quantified how the human locomotor system responds to perturbations by observing the variability in the system. Walking on irregular surfaces increases walking variability and increased walking variability predicts increased risk of falls in the elderly. However, measures of variability do not quantify how the locomotor system responds to perturbations and are not correlated with measures of local dynamic stability that do. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and locomotor stability. We modified a previously published irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. We then examined how the kinematic variability, local stability, and orbital stability of the walker changed as the amplitude of these perturbations was varied. We generated 10 simulations of 300 consecutive strides of walking at each of 6 perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the system could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., “local”) perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the system. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating the local exponential rates of divergence for the system. The variability of the walker’s kinematics increased exponentially with increases in perturbation amplitude. Although all simulations were run under conditions where the walker was orbitally stable (since it did not fall over), the walker still exhibited significant local instability under all conditions examined. Orbital and local stability measures of the model were generally not strongly correlated with increases in perturbation amplitude. Furthermore, increases in kinematic variability were generally not good predictors of either local or orbital stability. We concluded that observed increases in kinematic variability do not necessarily correspond to a loss of locomotor stability. The implications of these findings for understanding the mechanisms that may be responsible for falls and for interpreting the increases in variability that humans exhibit when walking over irregular surfaces are discussed.