山羊蹄底部非规则曲面仿生形貌数学模型构建及验证

山羊蹄底部非规则曲面形貌是影响山羊在崎岖路面稳定行走的关键因素之一,研究山羊蹄底部曲面特征将有助于将其这一优越特征应用到仿山羊农业四足行走机器人上,以解决目前农业四足行走机器人在崎岖地面上行走稳定性差的难题。该研究选取6个月的雄性波尔山羊蹄,采用三维立体扫描仪获取山羊蹄点云数据,并导入Geomagic Studio软件中进行点云去噪声、采样、封装、表面处理,得出山羊蹄的精确曲面,进行曲面偏差分析,最后根据山羊蹄偶型结构把山羊蹄底部曲面划分为2部分,利用Catia软件中的Digitized Shape Editor模块,对2个曲面的密集点云进行过滤,保留曲面形貌的特征点,并导出2个区域特征点云三维坐标数据。运用Matlab软件中的cftool工具箱对特征曲面的点云三维坐标数据进行3次多项式拟合,分别得到2个曲面的拟合方程、残差平方(SSE)、均方差(RMSE)和决定系数R2,研究结果表明:山羊蹄曲面标准偏差为1.402 2 mm,山羊蹄底部左侧曲面拟合残差平方(SSE)是359,均方差(RMSE)是0.792 9,决定系数(R2)是0.988 9;山羊蹄底部右侧曲面拟合残差平方(SSE)是256.2,均方差(RMSE)是0.7253,决定系数(R2)是0.987 9。对构建的数学模型进行验证发现,模型的拟合值与实际值的相对误差最大值分别为8.63%和9.58%,相对误差均值分别为4.32%和4.73%,相对误差均值能满足工程设计允许的误差范围±5%,验证了模型的有效性,实现了山羊蹄底部非规则曲面由生物模型到数学模型的转化。该研究为将山羊蹄底部曲面形貌进行仿生学应用奠定了理论基础,并为利用仿生学技术研究农业四足行走机器人提供参考依据。

Mathematical model establishment and validation of bionic irregular plantar surface of goat's hoof

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.