Inheritance of SLIP running stability to a single-legged and bipedal model with leg mass and damping

Spring-like leg behavior is found in the global dynamics of human and animal running. The corresponding template model, the conservative spring-loaded inverted pendulum (SLIP), shows stability for a large range of speeds and, therefore, is a promising concept for the design of legged robots. However, an anchoring of this template is needed in order to provide functions of biological structures (e.g. mass configuration, leg design) and to provide engineers with detailed guidelines for robot construction. We extend the template model by adding considerable leg mass (M-SLIP) to investigate the influence of leg inertia on running stability. We question whether the model with mass distributed to leg and trunk inherits stable running patterns of the underlying SLIP model. Separately, we investigate single-legged running and alternating bipedal running like humans. Here, we ask for the mass effect of the swing leg on running stability. The results show that the domain of stable SLIP running is anchored in the M-SLIP model. The stability domain is almost completely conserved for bipedal human-like running and reduces slightly for single-legged running. Our study reveals clearly that the SLIP can be anchored in a leg mass model with minimal control effort in using simple hip actuation policies. Our model enhances the theoretical foundation of biologically inspired robotic systems and is a promising candidate for nature-inspired engineering.