Abstract: Abstract: Goat is a typical quadrupedal animal which can walk steady and fast on complex terrain environment. The irregular surface topography of goat's hoof bottom is one of the key factors affecting the stability of goat walking on the rough terrain. The study on the irregular surface characteristics of the goat's hoof bottom will help to apply this superior feature to the 4-legged walking robots of goat-like agricultural, in order to solve the problem of poor walking stability of the agricultural 4-legged walking robots on rough pavement. In this study, male Boer goat's hoofs of 6 months were selected. In order to get the exact surface of the hoof, the hoof was sprayed with contrast intensifying agent and pasted mark points before the experiments, and the hoof point cloud data was obtained by using a 3D stereo scanner. The Geomagic Studio software was used to perform point cloud denoising, sampling, encapsulation and surface treatment to obtain the precise surface of the goat's hoof. The surface deviation analysis was carried out. The bottom surface of goat's hoof were divided into 2 parts according to the goat's hoof structure. The Digitized Shape Editor module in Catia software was used to filter the dense point clouds of the 2 surfaces and preserve the features of the curved surface, and the three-dimensional coordinate data of 2 regional feature points were derived. The 3D coordinate data of point cloud of feature surface were fitted by using cftool toolbox of Matlab software. The fitting equations of 2 surfaces, the residual square (SSE), standard deviation (RMSE) and the determination coefficient R2 were obtained respectively. In order to verify the mathematical model of irregular surface at the bottom of goat's hoof, other 3 goat's hoof of the model were selected as the verification sample. The x and y coordinates of the characteristic surfaces of the three samples were substituted into the mathematical model respectively, and the mathematical model was validated. Research results show that the standard deviation for the surface of the hoof was 1.402 2 mm. The fitting result of the left curved surface on the bottom of the goat's hoof showed that the sum of squares for residuals (SSE), the standard deviation (RMSE) and the determination coefficient (R2) were 359, 0.792 9 and 0.988 9, respectively. The fitting result of the right curved surface on the bottom of the goat's hoof showed that the residual square (SSE), the root mean square error (RMSE) and the determination coefficient (R2) were 256.2, 0.725 3 and 0.987 9, respectively. The mathematical model validated results showed that the residual of model 1 ranged from 0.18 to 4.86, the residual of model 2 ranged from 0.13 to 5.25. The maximum relative error between the fitted and the actual values of the model were 8.63% and 9.58%, respectively, The error were 4.32% and 4.73%, respectively. The relative error was range of ±5%, which means the calculated values of the 2 mathematical models were in good agreement with the actual values. The validity of the model was verified and the transformation of irregular surface from biological model to mathematical model at the bottom of goat's hoof was realized. This research will provide theoretical foundation for the application of bionics to the surface morphology of the surface of goat's hoofs, and provide references for the study of the agricultural quadruped walking robots using bionics technology.