In order to improve the slope movement stability and flexibility of quadruped robot, a theoretical design method of a flexible spine of a robot that was based on bionics was proposed. The kinematic characteristics of the spine were analyzed under different slopes with a Saanen goat as the research object. A Qualisys track manager (QTM) gait analysis system was used to obtain the trunk movement of goats under multiple slopes, and linear time normalization (LTN) was used to calibrate and match typical gait cycles to characterize the goat locomotion gait under slopes. Firstly, the spatial angle changes of cervical thoracic vertebrae, thoracolumbar vertebrae, and lumbar vertebrae were compared and analyzed under 0°, 5°, 10°, and 15° slopes, and it was found that the rigid and flexible coupling structure between the thoraco-lumbar vertebrae played an obvious role when moving on the slope. Moreover, with the increase in slope, the movement of the spine changed to the coupling movement of thoraco-lumbar coordination movement and a flexible swing of lumbar vertebrae. Then, the Gaussian mixture model (GMM) clustering algorithm was used to analyze the changes of the thoraco-lumbar vertebrae and lumbar vertebrae in different directions. Combined with anatomical knowledge, it was found that the motion of the thoraco-lumbar vertebrae and lumbar vertebrae in the goat was mainly manifested as a left-right swing in the coronal plane. Finally, on the basis of the analysis of the maximin and variation range of the thoraco-lumbar vertebrae and lumbar vertebrae in the coronal plane, it was found that the coupling motion of the thoraco-lumbar cooperative motion and flexible swing of the lumbar vertebrae at the slope of 10° had the most significant effect on the motion stability. SSE, R2, adjusted-R2, and RMSE were used as evaluation indexes, and the general equations of the spatial fitting curve of the goat spine were obtained by curve fitting of Matlab software. Finally, Origin software was used to obtain the optimal fitting spatial equations under eight movements of the goat spine with SSE and adjusted-R2 as indexes. The research will provide an idea for the bionic spine design with variable stiffness and multi-direction flexible bending, as well as a theoretical reference for the torso design of a bionic quadruped robot.
Keywords: Gaussian mixture model clustering algorithm; coupling motion; linear time normalization; quadruped robot; rigid and flexible coupling structure; the kinematic characteristics of the spine.