The spine plays important roles in the quadruped locomotion. To investigate the effects of the spine on the quadruped trotting motion, firstly, a sagittal passive model is proposed which contains four massless springy legs and two passive spinal joints. To generate the trotting gait of the model, the multibody hybrid dynamics model is established based on the defined events. The combination of optimization tools is used to find the suitable solution space in which the model can maintain a periodic motion. It reveals that the quadruped trotting motion results from the coordinated features of the spine and the legs. By comparing the model with the rigid body, it is proven that the spinal joints can reduce the effect of the ground reaction forces on the body in a special velocity range. Then, a hybrid controller whose objective is to maintain the kinematic coordination between the spinal joints is applied and it replaces the passive spinal joints, and the results prove that it can make the model achieve a stable periodic motion. Finally, the prototype of the quadruped robot with two spinal joints based on the model is established and its trotting motion is achieved successfully. The experiment results also indicate the compliant effect of the spine on the motion performance. Consequently, the effects of the spine at trotting gait are helpful to guide the development of the quadruped robots.
Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction
