Exploring the Effect of Pitching and Rolling Spine Angle for a Galloping Quadruped Robot via Trajectory Optimization

Existing research into the spinal morphology of quadruped robots predominantly simplifies it to a single degree of freedom (DOF) structure, a simplification that is valid for most locomotion gaits, but not optimally suited for a galloping gait where complex spinal movements could confer benefits. Observations of running cheetahs show that the elevation of the hips on the opposing sides of the torso is often uneven, suggesting a potential role of spinal torsion in locomotion. In this paper, a three DOF spine morphology is proposed, in which the front and rear torso have relative pitching DOF in the sagittal plane, while each has its own DOF in a rolling motion. Dynamic models are established for the front and rear torso separately, taking the rigid connection of the torso as constraints, and then motion planning is executed based on trajectory optimization. We adopt a galloping gait and compare this spinal morphology with the rigid torso and single DOF spinal morphology during the locomotion's rapid acceleration, constant high-speed running, and rapid deceleration phases. The results indicate that the DOF of the spine's pitch motion increases the stride between the front and rear legs, while the DOF of the rolling motion increases the stride between the left and right legs. It can be inferred that when the pitch joint angle of the spine is limited, the stride length can be further improved by adding the roll motion joints.