Comparing Legged Locomotion With a Sprung-Knee and Telescoping-Spring When Hip Torque is Applied

Legged locomotion has been a subject of study for many years. However, the role of the knee in whole-body dynamics of locomotion is not well understood, especially for non-conservative dynamics. Based upon a hip actuated Spring-Loaded Inverted Pendulum (Hip-actuated SLIP) model, we develop a more human-like, two-segment leg model with a pin-jointed springy knee, to see what effects a knee has in the context of an applied hip torque. Overall, we find that the governing equations for the two-segment (knee) version have a distinct structure when compared to the telescoping version of SLIP. The two-segment model with a knee spring influences forces acting on the mass center in a more complex way than a telescoping spring. While a wide variation of behavior is possible for the two-segment model, here we focus on comparing the dynamics for a special case when the knee spring resting angle is 90°. For this particular choice of resting knee angle we find that the knee version of actuated SLIP can have similar locomotion dynamics to the telescoping version of actuated SLIP. This result provides one explanation for how animals and robots with multi-segmented legs could produce overall center-of-mass dynamics that are similar to models with telescoping legs. Nonetheless, despite overall similarities for this special case, small differences in the stability of locomotion are still observed. In particular, we find that the knee version tends to be slightly more stable than the telescoping SLIP in terms of the allowable size of perturbations, while requiring higher input power.