Showing papers by "James J. Collins published in 1993"

Open-loop and closed-loop control of posture: A random-walk analysis of center-of-pressure trajectories

Abstract: A new conceptual and theoretical framework for studying the human postural control system is introduced. Mathematical techniques from statistical mechanics are developed and applied to the analysis and interpretation of stabilograms. This work was based on the assumption that the act of maintaining an erect posture could be viewed, in part, as a stochastic process. Twenty-five healthy young subjects were studied under quite-standing conditions. Center-of-pressure (COP) trajectories were analyzed as one-dimensional and two-dimensional random walks. This novel approach led to the extraction of repeatable, physiologically meaningful parameters from stabilograms. It is shown that although individual stabilograms for a single subject were highly variable and random in appearance, a consistent, subject-specific pattern emerged with the generation of averaged stabilogram-diffusion plots (mean square COP displacement vs time interval). In addition, significant inter-subject differences were found in the calculated results. This suggests that the steady-state behavior of the control mechanisms involved in maintaining erect posture can be quite variable even amongst a population of age-matched, anthropometrically similar, healthy individuals. These posturographic analyses also demonstrated that COP trajectories could be modelled as fractional Brownian motion and that at least two control systems-a short-term mechanism and a long-term mechanism-were operating during quit standing. More specifically, the present results suggest that over short-term intervals open-loop control schemes are utilized by the postural control system, whereas over long-term intervals closed-loop control mechanisms are called into play. This work strongly supports the position that much can be learned about the functional organization of the postural control system by studying the steady-state behavior of the human body during periods of undisturbed stance.

Coupled Nonlinear Oscillators and the Symmetries of Animal Gaits

Abstract: Animal locomotion typically employs several distinct periodic patterns of leg movements, known as gaits. It has long been observed that most gaits possess a degree of symmetry. Our aim is to draw attention to some remarkable parallels between the generalities of coupled nonlinear oscillators and the observed symmetries of gaits, and to describe how this observation might impose constraints on the general structure of the neural circuits, i.e. central pattern generators, that control locomotion. We compare the symmetries of gaits with the symmetry-breaking oscillation patterns that should be expected in various networks of symmetrically coupled nonlinear oscillators. We discuss the possibility that transitions between gaits may be modeled as symmetry-breaking bifurcations of such oscillator networks. The emphasis is on general model-independent features of such networks, rather than on specific models. Each type of network generates a characteristic set of gait symmetries, so our results may be interpreted as an analysis of the general structure required of a central pattern generator in order to produce the types of gait observed in the natural world. The approach leads to natural hierarchies of gaits, ordered by symmetry, and to natural sequences of gait bifurcations. We briefly discuss how the ideas could be extended to hexapodal gaits.

Hexapodal gaits and coupled nonlinear oscillator models

Abstract: The general, model-independent features of different networks of six symmetrically coupled nonlinear oscillators are investigated. These networks are considered as possible models for locomotor central pattern generators (CPGs) in insects. Numerical experiments with a specific oscillator network model are briefly described. It is shown that some generic phase-locked oscillation-patterns for various systems of six symmetrically coupled nonlinear oscillators correspond to the common forward-walking gaits adopted by insects. It is also demonstrated that transitions observed in insect gaits can be modelled as standard symmetry-breaking bifurcations occurring in such systems. The present analysis, which leads to a natural classification of hexapodal gaits by symmetry and to natural sequences of gait bifurcations, relates observed gaits to the overall organizational structure of the underlying CPG. The implications of the present results for the development of simplified control systems for hexapodal walking robots are discussed.