Low-dimensional modeling and analysis of human gait with application to the gait of transtibial prosthesis users

This dissertation uses a robotics-inspired approach to develop a low-dimensional forward dynamic model of normal human walking. The analytical model captures the dynamics of walking over a complete gait cycle in the sagittal plane. The model for normal walking is extended to model asymmetric gait. The asymmetric model is applied to study the gait dynamics of a transtibial prosthesis user.; Modeling human walking is complex because walking involves (i) the body's many degrees of freedom (DOF), (ii) constraints that change, and (iii) intermittent contact with the environment that may be impulsive. Complex forward dynamic models that attempt to capture details such as joints with multiple DOF, musculature, etc., are analytically intractable; it is impossible to describe the model's behavior in mathematically manageable terms because of the enormous number of variables and redundancies involved. Observation of human walking from a systems point of view reveals that the human body coordinates its many DOF in a parsimonious manner to accomplish the task of moving the body's center of mass from one point to another. This dissertation's approach exploits this parsimony to derive an analytically tractable model that has the minimum DOF necessary to describe the task of walking in the sagittal plane.; The low-dimensional hybrid model is derived as an exact sub-dynamic of a higher-dimensional anthropomorphic hybrid model. The hybrid nature is the result of continuous sub-models of single support (SS) and double support (DS), and discrete maps that model the transitions from SS to DS and DS to SS. The modeling is validated using existing gait data.; To extend the clinical usefulness of the modeling approach, the model for normal walking is extended to model asymmetric gait. The asymmetric model can accommodate asymmetries in the parameters and joint motions of the left and right legs. The asymmetric model is applied to analyze the gait dynamics of a transtibial prosthesis user. Cost functions are used to evaluate the effect of varying prosthetic alignment, prosthesis mass distribution, and prosthetic foot stiffness. The results agree well with clinical observations and the results of related gait studies reported in the literature.