On the energetics of quadrupedal running: predicting the metabolic cost of transport via a flexible-torso model

In this paper, the effect of torso flexibility on the energetics of quadrupedal bounding is examined in a template setting. Two reductive sagittal-plane models, one with a rigid, non-deformable torso and one with a flexible, unactuated torso are proposed. Both models feature non-trivial leg mass and inertia to capture the energy associated with repositioning the legs after liftoff as well as the energy lost due to impacts. Bounding motions that minimize the cost of transport are generated for both models via a simple controller that coordinates leg recirculation. Comparisons reveal that torso compliance promotes locomotion efficiency by facilitating leg recirculation in anticipation of touchdown at speeds that are sufficiently high. Furthermore, by considering non-ideal torque generating and compliant elements with biologically reasonable efficiency values, it is shown that the flexible-torso model can predict the metabolic cost of transport for different animals, estimated using measurements of oxygen consumption. This way, the proposed model offers a means for approximating the energetic cost of transport of running quadrupeds in a simple and direct fashion.