Species-specific effects of spinal stiffness on gait and actuation-cost proxy in simulated cheetah and horse galloping.

Abstract

Cursorial quadrupeds employ distinct mechanical strategies for high-speed locomotion, with felids relying more strongly on axial motion than equids. The biomechanical role of spinal stiffness, however, is difficult to isolate experimentally because it is coupled to limb mechanics, morphology, and coordination. Here, we used comparative three-dimensional trajectory optimization to test how spinal stiffness influences gait mechanics and actuation-demand proxies in simulated cheetah-like and horse-like galloping. Homologous cheetah and horse models were evaluated across spinal-stiffness values, prescribed rotary and transverse footfall sequences, and target speeds. The cheetah rotary gallop exhibited a favourable intermediate-stiffness region in the actuation-demand proxies, whereas the horse model was less sensitive to spinal stiffness and more strongly influenced by distal limb compliance. Peak spring-energy summaries indicated greater spinal elastic participation in the cheetah and stronger distal-limb dominance in the horse. Secondary torque-capacity and distal-stiffness sensitivity analyses showed that the exact location and magnitude of the favourable stiffness region were objective- and parameter-dependent, but did not eliminate the intermediate-stiffness pattern in the cheetah rotary case. High-speed cheetah transverse solutions were sensitive to initialization and were interpreted cautiously. Overall, spinal compliance was not generically beneficial: within the present model framework, it produced the clearest favourable stiffness response in the cheetah-like rotary-gallop morphology, while the horse-like model remained more distal-limb dominated. Comparative simulation can therefore isolate how axial and distal elasticity interact with morphology, while highlighting that the reported trajectories are plausible local optima rather than certified global optima or direct predictions of metabolic economy.