李立君, 刘涛, 高自成, 廖凯, 李禹卓, 许世斌. 基于旋量理论的六自由度林果采摘混联机械臂运动学逆解[J]. 农业工程学报, 2019, 35(8): 75-82. DOI: 10.11975/j.issn.1002-6819.2019.08.009
    引用本文: 李立君, 刘涛, 高自成, 廖凯, 李禹卓, 许世斌. 基于旋量理论的六自由度林果采摘混联机械臂运动学逆解[J]. 农业工程学报, 2019, 35(8): 75-82. DOI: 10.11975/j.issn.1002-6819.2019.08.009
    Li Lijun, Liu Tao, Gao Zicheng, Liao Kai, Li Yuzhuo, Xu Shibin. Inverse kinematics of 6-DOF hybrid manipulator for forest-fruit harvest based on screw theory[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2019, 35(8): 75-82. DOI: 10.11975/j.issn.1002-6819.2019.08.009
    Citation: Li Lijun, Liu Tao, Gao Zicheng, Liao Kai, Li Yuzhuo, Xu Shibin. Inverse kinematics of 6-DOF hybrid manipulator for forest-fruit harvest based on screw theory[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2019, 35(8): 75-82. DOI: 10.11975/j.issn.1002-6819.2019.08.009

    基于旋量理论的六自由度林果采摘混联机械臂运动学逆解

    Inverse kinematics of 6-DOF hybrid manipulator for forest-fruit harvest based on screw theory

    • 摘要: 针对传统Paden-Kahan子问题求解机械臂运动学逆解时需确定关节轴线交点坐标的问题,对该子问题进行改进。利用末端执行器位姿信息获取轴线交点坐标,建立物体坐标与末端执行器期望位姿的映射关系,结合子问题求解6自由度林果采摘机械臂运动学逆解;根据主动关节变量取值范围分析所求逆解的可行性,得到可行封闭解,提高机械臂控制速度、稳定性和准确性。在实验室环境下利用所提出的算法求解10组工作目标位置信息对应的关节值,结果表明,所求逆解能使林果采摘机械臂到达正确位姿,末端执行器最大位置误差不超过夹持器最大开度的3.30%,最大姿态误差不超过1(,满足采摘要求。该算法为机械臂快速、稳定及精确地控制提供技术依据。

       

      Abstract: Abstract: A method for inverse kinematics analysis based on screw theory was presented in this paper, which can directly map the position and orientation of the working object to the joint variables of the manipulator with its application to a full inverse kinematics analysis of forest-fruit harvesting manipulator characterized by a hybrid kinematic structure, 2P4R. The solution of inverse kinematics modeling derived by screw theory was commonly realized by Paden-Kahan sub-problem method, which decomposes a full kinematics problem into sub-problem with obviously geometrical meaning through choosing appropriate point, usually, intersection of adjacent joint, such as wrist joint, to reduce the number of the variable quantity, and then close-form solution can be easily obtained. However, in practice, it is hard to gain the position of those points through measure because of their absence before end-effector actually moving to the desired position. And few researchers mentioned this issue in the relevant literature. In order to discuss this problem, firstly, a geometrical method was proposed for this issue to obtain the position of the required point, wrist joint, according to the orientation of end-effector and its geometric properties and geometric relationships through using the vector algebra method. Furthermore, a mapping between driving and driven join was gained in order to simplify the solving process of the equation set at a later, according to the solution of the structural equation of the manipulator derived by the product-of-exponentials (POEs) formula and structural character of manipulator. Meanwhile, the closed-form solution for each driving joint variables was derived by employing the proposed method with Paden-Kahan sub-problem method. A mapping relationship between the plücker coordinates of the object and the location information of end-effector was derived through an algebraic method according to the principle of minimum displacement and its operating mode in which the gripper of end-effector should reach the position of the trunk with two labels detected by the robot vision system and be perpendicular to the orientation of the trunk. In addition, the problem of multiple solutions in the inverse kinematics analysis for the harvesting manipulator was solved according to the range of joint variables. Finally, the real-world experiment was performed under laboratory environment. In order to vertify the correctness and obtain the accuracy of the method proposed in this paper. A wooden stick with two markers was placed in the kinematics test platform as the object, which consisted of a laser tracker and a harvesting manipulator. Then, the values of each joint variable could be calculated via the proposed method according to the plücker coordinate data of the markers measured in the object. The results showed that the forest-fruit harvesting manipulator was driven by the solution of inverse kinematics to the position on the stick that its end-effect reached and normal to the stick, which meant this method could meet the requirements of the operating mode. Then ten sets of joint variable values were randomly generated where the positions were measured and the manipulator was sequentially driven by that. The joint variable values were calculated according to the positions through the method proposed in this paper. At last, the calculated results were re-inputted into the controller to drive the manipulator to the new positions. The two measure results on different positions driven by joint variable values generated and calculated were used to obtain the error. The results showed that the maximum position error of end-effector was 6.597 mm, far less than the open size of its gripper, 200 mm, and no more than 3.30%, with the maximum orientation error of 0.975°. The method in this paper was not limited by the specific structure, therefore it is versatile.

       

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