| 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. |
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