Phase Relationship between Spinal Motion and Limb Support Determines High-speed Running Performance in a Cheetah Model with Asymmetric Spinal Stiffness

Abstract

Cheetahs are characterized by large spinal flexion and extension during high-speed running, yet the dynamical role of the phase relationship between spinal motion and limb support remains unclear. We aimed to clarify how this phase relationship affects running performance, focusing on the effect of asymmetric spinal stiffness. Using a simple planar cheetah model with asymmetric torsional spinal stiffness, we numerically searched for periodic bounding solutions over a range of stiffness parameters and compared their ground reaction forces, horizontal velocities, and stability. We obtained both cheetah-like solutions, in which the spine extends after hindlimb liftoff and flexes after forelimb liftoff, and non-cheetah-like solutions, in which the spine flexes after hindlimb liftoff and extends after forelimb liftoff. Under asymmetric spinal stiffness, cheetah-like solutions reduced ground reaction forces while maintaining horizontal velocity more effectively than non-cheetah-like solutions. The phase relationship between spinal motion and stance timing is a key determinant of high-speed running performance. These findings provide a dynamical understanding of cheetah locomotion and suggest design principles for spined legged robots.

Figures (10)

• Figure 1: Sequence of the cheetah gait: extended flight (the spine is extended and the fore and hind limbs are apart), forelimb stance, gathered flight (the spine is flexed and the fore and hind limbs are close), and hindlimb stance.
• Figure 2: Simple model of cheetah. (A) Flight phase. (B) Forelimb (Leg 1) stance. (C) Hindlimb (Leg 2) stance.
• Figure 3: Classification of periodic solutions. Type EG: the spine is extended after the hindlimb stance, as in cheetahs. Type GE: the spine is extended after the forelimb stance. Type EE: the spine is extended after both the forelimb and hindlimb stance. Type E: the spine is extended during the flight.
• Figure 4: Time profiles of variables and relative leg angle $\psi_i$ ($i=1,2$) between the Body $i$ and the Leg $i$, and stick diagrams of typical solutions of (A) type EG ($[y^*, \dot{\theta}^*]=[0.67,-1.0]$, 'a2' in Fig. \ref{['fig:sol_distri']}) and (B) type GE ($[y^*, \dot{\theta}^*]=[0.67,1.0]$, 'b2' in Fig. \ref{['fig:sol_distri']}). Red and blue shaded areas indicate fore and hindlimb stance, respectively. Stick diagrams highlight the initial state, touchdown and liftoff of forelimb, mid-gait, touchdown and liftoff of hindlimb, and terminal state.
• Figure 5: Time profiles of (A) GRF and (B) horizontal velocity of solutions with $[y^*, \dot{\theta}^*]=[0.67, -1.0]$ (type EG) and $[0.67, 1.0]$ (type GE). Dashed lines in (B) indicate average horizontal velocity.