Simple Models of Legged Locomotion based on Compliant Limb Behavior Grundmodelle pedaler Lokomotion basierend auf nachgiebigem Beinverhalten

In this dissertation, simple models of legged locomotion are developed mainly following the hypothesis that rather than reflecting two distinct phenomena, the fundamental gait patterns of walking and running can be described within a single conceptual framework that is based on compliant limb behavior. In Chapter 1, the most prominent mechanical paradigms of walking and running, namely the stiff-legged inverted pendulum and the compliant spring-mass model, are introduced by demonstrating their importance for investigating legged locomotion. However, it is also discussed that both models must be ranked differently when assessing their value as basic gait templates that encode parsimoniously the strikingly uniform whole body dynamics observed during animal and human locomotion. Whereas the spring-mass model can describe the characteristic motion of the center of mass in running, the inverted pendulum fails to reproduce the corresponding pattern in walking. By contrast, walking experiments show that, instead of vaulting over rigid legs as suggested by the inverted pendulum motion, the center of mass experiences much less vertical excursion requiring substantial stance-leg compressions. Inspired by this observation, in the following chapters, the general significance of limb compliance for biological legged locomotion is explored utilizing simple mechanical and neuromechanical models. Here, the spring-mass model for running is used as starting point since it not only represents a known gait template, but also embodies limb compliance in its simplest form. In Chapter 2, a limitation of the spring-mass model is addressed. Although with a Hooke’s law spring attached to a point mass the planar spring-mass model may appear trivial, it describes a nonlinear system whose equations of motion are nonintegrable. In light of the model’s growing importance for basic research on legged locomotion and for applications in robotics, the lack of a closed form solution of its system dynamics has prompted scientists to seek suitable approximations. However, as of today, no approximation could be found that combines mathematical tractability with sufficient accuracy in the physiologically relevant parameter domain. The former would allow to extract parametric dependencies of the model’s behavior by analytical means, the latter is required to verify resulting hypotheses on legged locomotion, in experiments.