A fundamental mechanism of legged locomotion with hip torque and leg damping

New models and theories of legged locomotion are needed to better explain and predict the robustly stable legged locomotion of animals and some bio-inspired robots. In this paper we observe that a hip-torque and leg-damping mechanism is fundamental to many legged robots and some animals and determine its affect on locomotion dynamics. We discuss why this hip-torque-and-leg-damping mechanism is not so easily understood. We investigate how hip-torque and leg-damping affect the stability and robustness of locomotion using a mathematical model: First, we extend the canonical spring-loaded-inverted-pendulum model to include constant hip torque and leg damping proportional to leg length speed. Then, we calculate the stability and robustness of locomotion as a function of increasing levels of torque and damping, starting from zero-the energy conserving and marginally stable special case-to high levels of torque and damping. We find that the stabilizing effects of hip-torque and leg-damping occur in the context of the piecewise-continuous dynamics of legged locomotion, and so linear intuition does not apply. We discover that adding hip torque and leg damping changes the stability of legged locomotion in an unexpected way. When a small amount of torque and damping are added, legged locomotion is initially destabilized. As more torque and damping are added, legged locomotion turns stable and becomes increasingly more stable and more robust the more torque and damping are added. Also, stable locomotion becomes more probable over the biologically-relevant region of the parameter space, indicating greater prediction and explanatory capabilities of the model. These results provide a more clear understanding of the hip-torque-and-leg-damping mechanism of legged locomotion, and extend existing theory of legged locomotion towards a greater understanding of robustly stable locomotion.