面向振动采收的果树枝干三维重建方法及其动力学特性研究
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摘要
本文的研究对象是山核桃树(Carya cathayensis Sarg.)，由于山核桃的营养价值高，随着生活水平的不断提高，人们对山核桃消费的需求持续增长。但山核桃树生长在陡峭的山坡，树高普遍超过8m，因此人工采摘山核桃具有很高的危险性。机械式振动采摘山核桃是一种行之有效的方法，它不仅能提高果实的采摘效率，减轻劳动强度，更重要的是能保证果农的人身安全。衡量果实采摘机械工作性能的重要依据是果实的采摘率。但由于果树种植环境、果实品种和果树个体的差异，对提升果实采摘机械的性能增添了难度，同时也限制了果实采摘机械在生产上的应用和发展。
解决上述问题的有效办法就是采用自适应采摘方式。本文围绕果树个体结构描述和果树动力学分析，研究了基于立体视觉的果树振动力学参数辨识的相关理论和方法。首先研究了果树枝干的结构参数和材料特性，然后应用立体视觉技术从两幅图像中重建果树的三维枝干，最后把重建的枝干模型应用到动力学仿真，再结合动力学试验获得果树个体的动力学特性。本文的主要研究内容和成果如下：
1)手工测量山核桃树枝干的几何参数，得到截面长/短轴的比例约为1.06，无结点枝干的直径和长度之间呈负线性关系，因此可以把山核桃树枝干认为是直径随长度线性变化的圆形截面梁。用悬臂梁振动试验测量用于动力学分析的山核桃树枝干的弹性模量Ev，比较发现通过测量应力波的传播速度估计弹性模量Ev的方法是不可行的。
2)提出一种基于扫描线的动态跟踪技术提取图像中复杂背景下果树枝干轮廓的方法。扫描线的动态跟踪分为启发式的扫描线搜索和基于梯度二阶导数过零点的扫描线端点的更新。应用“蛇形带状”(Ribbon snake)技术精细化轮廓，获得更加光顺、准确的枝干双轮廓，进而提取枝干区域。根据细化得到的枝干骨架，提出用图论中的二叉树结构描述果树枝干的拓扑结构。基于枝干边缘的连续性和宽度的一致性分别修复分叉点和交叉点附近区域的枝干骨架线。
3)提出一种改进的空间点三维重建的几何方法。应用该方法，以最小化反投影误差为目标，分两步快速优化基于本质矩阵估计的相机外参数。结合极线约束、拓扑结构和形状匹配技术实现双视图中枝干骨架线的对应。首先用动态规划技术搜索同名骨架线上的对应点对，然后用共轭梯度法精细化。
4)以曲线为基元重建枝干的三维骨架线，提出评价空间曲线三维重建性能的2个重要指标：重建曲线的反投影误差和重建曲线的光顺性。根据这两个指标提出一种基于曲率无穷范数约束的空间曲线的三维重建方法。将该方法成功地应用于模拟曲线、圆柱相贯线和枝干骨架线，从而验证了方法的可行性。模拟曲线的重建结果显示提出的曲线重建方法的重建误差约为三角测量法的1/7，表明该方法明显优于三角测量法。分析发现重建误差随着噪声水平的提高而缓慢增大，但并不明显依赖于最大曲率阈值κmax，表明方法具有较强的自适应性和一定的抗干扰能力。圆柱相贯线的重建实例显示重建的曲线在XY平面投影的相对误差仅为2.89%，表明提出的曲线三维重建方法具有比较高的精度。应用植物学的营养管道输送模型，用线性方程参数化枝干的半径。最后以两棵不同山核桃树为对象实现其枝干的三维重建，重建的枝干在视觉上非常接近真实的果树。重建的枝干半径同手工测量值之间的相对误差小于4%，表明重建的山核桃树枝干具有较高的精度。
5)应用拉格朗日方程，建立基于物理杆的果树枝干的动力学模型。分析带2分枝和带3分枝果树的动态响应，结果发现分枝运动和树干运动之间存在一定的独立性，系统第1阶共振频率随着分枝的增加而减小。以三维梁为单元，在欧拉-伯努利(Euler-Bernoulli)梁理论的基础上建立果树枝干的有限元动力学模型，并应用ANSYS软件进行果树枝干的模态分析和谐响应分析。分析结果显示不同分枝的运动存在明显差异，因此很难找到一种简单的振动方式使所有的分枝都能有效地振动起来。在谐响应分析的基础上，进一步分析发现只要激振方向垂直于枝干，其它两个方向对加速度响应的影响都比较小。提出一种用多方向组合力的激振方式，它能同时激发大多数分枝有效地振动，因此能获得比单一激振力更好的振动效果。模拟分析果树枝干半径的精度对动力学特性的影响，结果发现模型精度的相对误差小于5%对固有频率影响很小，对加速度响应的影响也有限，进而验证了重建模型的精度满足动力学分析的需要。
6)分别对室内局部枝干和田间活立木进行试验，获得分枝上不同测试点的加速度响应，并与仿真的结果进行比较。结果表明用本文提出的方法进行果树的动力学仿真能获得比较准确的固有频率，并确定用于振动采摘的最佳激振频率范围。
The object of this paper is the Chinese hickory tree. With the improvement of living standard,the demand for consumption of Chinese hickory nut (Carya cathayensis Sarg.) is also growingdue to its high nutrition. However, the Chinese hickory tree with over8-meters height alwaysgrows in hilly environment, which make it high dangerous to pick fruits by hands. Vibratoryharvesting may improve picking efficiency, reduce labor intensity and prevent fruit grower fromhurting. Therefore, it is the most appropriate and efficient way to harvest Chinese hickory fruits.The evaluation of performance of picking fruit machinery is removal percentage. However,differences in growth condition and variety of individual of tree will increase difficulties inimproving performance of picking fruit machinery, and also restrict its application.
The effective way to solve the above problem is to use an adaptive way of picking. Thispaper focuses on the access to geometrical model and dynamic analysis of individual fruit tree,and studies some new theories and methods about identification of vibratory mechanicalparameters based on stereo vision. Firstly, the geometry parameters and material properties offruit tree were measured; secondly, using stereo vision technology,3D trunk model of wasreconstructed from two images; finally, the dynamic characteristics of individual fruit tree couldbe obtained by combining experiments and simulations. The main contents and achievements areas follows:
1) The ratio between long axis and short axis in the cross-section of Chinese hickory treewas measured about1.06. Therefore, the cross-section can be approximately considered as acircle. Experimental data shows there is a minus linear relationship between the diameter andlength of the branches without node. The modulus of elasticity of trunk used for dynamicanalysis was measured by cantilever vibration experiments. It is not feasible to estimate themodulus of elasticity by measuring the propagation velocity of stress wave in trunk.
2) This paper proposed a method for extracting two contours of trunk under complicatedbackground based on dynamic tracking of scanning line. The dynamic tracking of scanning linewas composed of two steps: heuristically searching of scanning line and updating of end-pointsbased on second derivative gradient zero-crossing point. The―Ribbon snake‖technique wasemployed to refine extracted two contours of trunk synchronously. Resultantly, two refined contours became much more smooth and higher accurate. After thinning image, skeletons oftrunks were obtained, and data structure with binary tree in graph theory was used to describe thetopology of whole tree. Based on the consistency and continuity of trunk, skeleton curves nearthe bifurcation points and intersection points were repaired.
3) An improved method for3D reconstruction with geometrics was proposed. On this basis,the camera extrinsic parameters which were initialized by essential matrix were optimized withtwo fast steps by minimizing the reprojection error. Under the constraints of epipolar andtopology, combining shape matching, all skeletons of trunks in one image could find theircorrespondences in another one. Point correspondences in a pair of corresponding skeletons werefound by dynamic programming firstly, and refined by conjugate gradient method.
4)3D Curve was used as a primitive to reconstruct skeleton of trunk. Two importantindicators: the reprojection errors and the fairing of curve were put forward to evaluate theperformance of reconstructed3D curve. An objective function based on these two indicators wasestablished and improved further. Thus, a method for reconstructing3D space curve under theL-infinity norm of curvatures was proposed. The proposed method was verified to be feasible bysuccessfully applying to reconstruct synthetic space curve, cylindrical intersection curve andskeletons of trunk. The results of synthetic curve reconstruction show that reconstruction errorsgenerated by the proposed method is1/7less than that of triangulation method, which indicatethe proposed method is superior to the triangulation method based on point correspondence. Theproposed method has strong self-adaptability and anti-noise capability, because the effect ofreconstruction does not obviously depends on the maximum curvature threshold κmax. Thereconstruction of cylindrical intersection curve shows that the relative error of projection curvein the XY plane is only2.89%, which indicates that this method has high accuracy and is suitableto be applied in agriculture. Take into consideration of the pipe model of botany, radiuses oftrunks were parameterized as linear equation. Two different Chinese hickory trees werereconstructed by the proposed method, and both reconstructed trees were very similar to theactual one in the visual. Comparisons of estimated radiuses of trunk between3D reconstructionand measurement by hand were made, and their relative derivations are less than4%. Insummary, the Chinese hickory tree can be successfully reconstructed by the proposed methodwith high accuracy.
5) On the basis of Lagrangian equation, a dynamics model of tree with physics-based linkwas built. Two models with two branches and three branches were solved. Results show that theeffect of nonlinear coupling in the dynamics model is to increase a branch modal, the motionbetween branches and the trunk is somewhat independent, and the first-order resonancefrequency of tree decreases with increasing branches. Further, the dynamics of fruit tree wasmodeled by3D beam with Euler-Bernoulli beam theory. Finite element software (ANSYS) wasutilized to do modal analysis and harmonic analysis of a whole fruit tree. Both two results showthat the movements under vibration are obvious different between different branches. Thus, it isdifficult to find a simple vibratory way in which all branches can be moved effectively. On thebasis of harmonic analysis, further analysis showed that as long as the excitation directionperpendicular to the tangent of branch, the influence of rest two directions on accelerationresponse is small. It was found that the combined excitation with multiple directions is superiorto a single excitation, because it can stimulate most of branches in movement. The influence ofgeometry model within5%relative error of radius is small on natural frequencies, and is limitedon acceleration response. Thus, the accuracy of reconstructed3D tree model is sufficient fordynamic analysis.
6) Acceleration responses of test points in different branches could be obtained by twoexperiments both on partial branches indoor and on living tree in the field respectively, and werecompared with which calculated by dynamic simulation. Result shows that the dynamicsimulation by the proposed method can obtain a more accurate natural frequency of fruit tree,and determine the optimal rang of excitation frequency for harvesting.
解决上述问题的有效办法就是采用自适应采摘方式。本文围绕果树个体结构描述和果树动力学分析，研究了基于立体视觉的果树振动力学参数辨识的相关理论和方法。首先研究了果树枝干的结构参数和材料特性，然后应用立体视觉技术从两幅图像中重建果树的三维枝干，最后把重建的枝干模型应用到动力学仿真，再结合动力学试验获得果树个体的动力学特性。本文的主要研究内容和成果如下：
1)手工测量山核桃树枝干的几何参数，得到截面长/短轴的比例约为1.06，无结点枝干的直径和长度之间呈负线性关系，因此可以把山核桃树枝干认为是直径随长度线性变化的圆形截面梁。用悬臂梁振动试验测量用于动力学分析的山核桃树枝干的弹性模量Ev，比较发现通过测量应力波的传播速度估计弹性模量Ev的方法是不可行的。
2)提出一种基于扫描线的动态跟踪技术提取图像中复杂背景下果树枝干轮廓的方法。扫描线的动态跟踪分为启发式的扫描线搜索和基于梯度二阶导数过零点的扫描线端点的更新。应用“蛇形带状”(Ribbon snake)技术精细化轮廓，获得更加光顺、准确的枝干双轮廓，进而提取枝干区域。根据细化得到的枝干骨架，提出用图论中的二叉树结构描述果树枝干的拓扑结构。基于枝干边缘的连续性和宽度的一致性分别修复分叉点和交叉点附近区域的枝干骨架线。
3)提出一种改进的空间点三维重建的几何方法。应用该方法，以最小化反投影误差为目标，分两步快速优化基于本质矩阵估计的相机外参数。结合极线约束、拓扑结构和形状匹配技术实现双视图中枝干骨架线的对应。首先用动态规划技术搜索同名骨架线上的对应点对，然后用共轭梯度法精细化。
4)以曲线为基元重建枝干的三维骨架线，提出评价空间曲线三维重建性能的2个重要指标：重建曲线的反投影误差和重建曲线的光顺性。根据这两个指标提出一种基于曲率无穷范数约束的空间曲线的三维重建方法。将该方法成功地应用于模拟曲线、圆柱相贯线和枝干骨架线，从而验证了方法的可行性。模拟曲线的重建结果显示提出的曲线重建方法的重建误差约为三角测量法的1/7，表明该方法明显优于三角测量法。分析发现重建误差随着噪声水平的提高而缓慢增大，但并不明显依赖于最大曲率阈值κmax，表明方法具有较强的自适应性和一定的抗干扰能力。圆柱相贯线的重建实例显示重建的曲线在XY平面投影的相对误差仅为2.89%，表明提出的曲线三维重建方法具有比较高的精度。应用植物学的营养管道输送模型，用线性方程参数化枝干的半径。最后以两棵不同山核桃树为对象实现其枝干的三维重建，重建的枝干在视觉上非常接近真实的果树。重建的枝干半径同手工测量值之间的相对误差小于4%，表明重建的山核桃树枝干具有较高的精度。
5)应用拉格朗日方程，建立基于物理杆的果树枝干的动力学模型。分析带2分枝和带3分枝果树的动态响应，结果发现分枝运动和树干运动之间存在一定的独立性，系统第1阶共振频率随着分枝的增加而减小。以三维梁为单元，在欧拉-伯努利(Euler-Bernoulli)梁理论的基础上建立果树枝干的有限元动力学模型，并应用ANSYS软件进行果树枝干的模态分析和谐响应分析。分析结果显示不同分枝的运动存在明显差异，因此很难找到一种简单的振动方式使所有的分枝都能有效地振动起来。在谐响应分析的基础上，进一步分析发现只要激振方向垂直于枝干，其它两个方向对加速度响应的影响都比较小。提出一种用多方向组合力的激振方式，它能同时激发大多数分枝有效地振动，因此能获得比单一激振力更好的振动效果。模拟分析果树枝干半径的精度对动力学特性的影响，结果发现模型精度的相对误差小于5%对固有频率影响很小，对加速度响应的影响也有限，进而验证了重建模型的精度满足动力学分析的需要。
6)分别对室内局部枝干和田间活立木进行试验，获得分枝上不同测试点的加速度响应，并与仿真的结果进行比较。结果表明用本文提出的方法进行果树的动力学仿真能获得比较准确的固有频率，并确定用于振动采摘的最佳激振频率范围。
The object of this paper is the Chinese hickory tree. With the improvement of living standard,the demand for consumption of Chinese hickory nut (Carya cathayensis Sarg.) is also growingdue to its high nutrition. However, the Chinese hickory tree with over8-meters height alwaysgrows in hilly environment, which make it high dangerous to pick fruits by hands. Vibratoryharvesting may improve picking efficiency, reduce labor intensity and prevent fruit grower fromhurting. Therefore, it is the most appropriate and efficient way to harvest Chinese hickory fruits.The evaluation of performance of picking fruit machinery is removal percentage. However,differences in growth condition and variety of individual of tree will increase difficulties inimproving performance of picking fruit machinery, and also restrict its application.
The effective way to solve the above problem is to use an adaptive way of picking. Thispaper focuses on the access to geometrical model and dynamic analysis of individual fruit tree,and studies some new theories and methods about identification of vibratory mechanicalparameters based on stereo vision. Firstly, the geometry parameters and material properties offruit tree were measured; secondly, using stereo vision technology,3D trunk model of wasreconstructed from two images; finally, the dynamic characteristics of individual fruit tree couldbe obtained by combining experiments and simulations. The main contents and achievements areas follows:
1) The ratio between long axis and short axis in the cross-section of Chinese hickory treewas measured about1.06. Therefore, the cross-section can be approximately considered as acircle. Experimental data shows there is a minus linear relationship between the diameter andlength of the branches without node. The modulus of elasticity of trunk used for dynamicanalysis was measured by cantilever vibration experiments. It is not feasible to estimate themodulus of elasticity by measuring the propagation velocity of stress wave in trunk.
2) This paper proposed a method for extracting two contours of trunk under complicatedbackground based on dynamic tracking of scanning line. The dynamic tracking of scanning linewas composed of two steps: heuristically searching of scanning line and updating of end-pointsbased on second derivative gradient zero-crossing point. The―Ribbon snake‖technique wasemployed to refine extracted two contours of trunk synchronously. Resultantly, two refined contours became much more smooth and higher accurate. After thinning image, skeletons oftrunks were obtained, and data structure with binary tree in graph theory was used to describe thetopology of whole tree. Based on the consistency and continuity of trunk, skeleton curves nearthe bifurcation points and intersection points were repaired.
3) An improved method for3D reconstruction with geometrics was proposed. On this basis,the camera extrinsic parameters which were initialized by essential matrix were optimized withtwo fast steps by minimizing the reprojection error. Under the constraints of epipolar andtopology, combining shape matching, all skeletons of trunks in one image could find theircorrespondences in another one. Point correspondences in a pair of corresponding skeletons werefound by dynamic programming firstly, and refined by conjugate gradient method.
4)3D Curve was used as a primitive to reconstruct skeleton of trunk. Two importantindicators: the reprojection errors and the fairing of curve were put forward to evaluate theperformance of reconstructed3D curve. An objective function based on these two indicators wasestablished and improved further. Thus, a method for reconstructing3D space curve under theL-infinity norm of curvatures was proposed. The proposed method was verified to be feasible bysuccessfully applying to reconstruct synthetic space curve, cylindrical intersection curve andskeletons of trunk. The results of synthetic curve reconstruction show that reconstruction errorsgenerated by the proposed method is1/7less than that of triangulation method, which indicatethe proposed method is superior to the triangulation method based on point correspondence. Theproposed method has strong self-adaptability and anti-noise capability, because the effect ofreconstruction does not obviously depends on the maximum curvature threshold κmax. Thereconstruction of cylindrical intersection curve shows that the relative error of projection curvein the XY plane is only2.89%, which indicates that this method has high accuracy and is suitableto be applied in agriculture. Take into consideration of the pipe model of botany, radiuses oftrunks were parameterized as linear equation. Two different Chinese hickory trees werereconstructed by the proposed method, and both reconstructed trees were very similar to theactual one in the visual. Comparisons of estimated radiuses of trunk between3D reconstructionand measurement by hand were made, and their relative derivations are less than4%. Insummary, the Chinese hickory tree can be successfully reconstructed by the proposed methodwith high accuracy.
5) On the basis of Lagrangian equation, a dynamics model of tree with physics-based linkwas built. Two models with two branches and three branches were solved. Results show that theeffect of nonlinear coupling in the dynamics model is to increase a branch modal, the motionbetween branches and the trunk is somewhat independent, and the first-order resonancefrequency of tree decreases with increasing branches. Further, the dynamics of fruit tree wasmodeled by3D beam with Euler-Bernoulli beam theory. Finite element software (ANSYS) wasutilized to do modal analysis and harmonic analysis of a whole fruit tree. Both two results showthat the movements under vibration are obvious different between different branches. Thus, it isdifficult to find a simple vibratory way in which all branches can be moved effectively. On thebasis of harmonic analysis, further analysis showed that as long as the excitation directionperpendicular to the tangent of branch, the influence of rest two directions on accelerationresponse is small. It was found that the combined excitation with multiple directions is superiorto a single excitation, because it can stimulate most of branches in movement. The influence ofgeometry model within5%relative error of radius is small on natural frequencies, and is limitedon acceleration response. Thus, the accuracy of reconstructed3D tree model is sufficient fordynamic analysis.
6) Acceleration responses of test points in different branches could be obtained by twoexperiments both on partial branches indoor and on living tree in the field respectively, and werecompared with which calculated by dynamic simulation. Result shows that the dynamicsimulation by the proposed method can obtain a more accurate natural frequency of fruit tree,and determine the optimal rang of excitation frequency for harvesting.
引文
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