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
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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。
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, 2 P4 R. 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.
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, 2 P4 R. 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.
引文
[1]Singh A,Singla A.Kinematic modeling of robotic manipulators[J].Proceedings of the National Academy of Sciences India Section A:Physical Sciences,2016,87(3):303-319.
[2]An H S,Lee J H,Lee C,et al.Geometrical kinematic solution of serial spatial manipulators using screw theory[J].Mechanism and Machine Theory,2017,116:404-418.
[3]Pena C A,Guzman M A,Cardenas P F.Inverse kinematics of a 6 DOF industrial robot manipulator based on bio-inspired multi-objective optimization techniques[C]//2016 IEEEColombian Conference on Robotics and Automation(CCRA).IEEE,2016.
[4]Xu J,Liu Z,Cheng Q,et al.Models for three new screw-based IK sub-problems using geometric descriptions and their applications[J].Applied Mathematical Modelling,2018,67:399-412.
[5]Man C,Xun F,Li C R,et al.Kinematics analysis based on screw theory of a humanoid robot[J].Journal of China University of Mining and Technology,2007,17(1):49-52.
[6]孙恒辉,赵爱武,李达,等.基于新旋量子问题改进一类6R串联机器人逆解算法[J].机械工程学报,2016,52(1):79-86.Sun Henghui,Zhao Aiwu,Li Da,et al.Improvement of the algorithm of the inverse kinematics calculation for 6R series robots based on one novel Paden-Kahan sub-problem[J].Chinese Journal of Mechanical Engineering,2016,52(1):79-86.(in Chinese with English abstract)
[7]Wang H,Lu X,Sheng C,et al.General frame for arbitrary3R subproblems based on the POE model[J].Robotics and Autonomous Systems,2018,105:138-145.
[8]Dong Y,Phan H N,Rahmani A.Modeling and kinematics study of hand[J].International Journal of Computer Science and Applications,2015,12(1):66-79.
[9]赵杰,刘玉斌,蔡鹤皋.一种运动旋量逆解子问题的求解及其应用[J].机器人,2005,27(2):163-167.Zhao Jie,Liu Yubin,Cai Hegao.Solution for one type of inverse kinematics sub-problems in screw theory and its application[J].Robot,2005,27(2):163-167.(in Chinese with English abstract)
[10]Murray R M,Li Z,Sastry S S.A Mathematical Introduction to Robotic Manipulation[M].Florida:CRC Press,1994:19-81.
[11]钱东海,王新峰,赵伟,等.基于旋量理论和Paden-Kahan子问题的6自由度机器人逆解算法[J].机械工程学报,2009,45(9):72-76.Qian Donghai,Wang Xinfeng,Zhao Wei,et al.Algorithm for the inverse kinematics calculation of 6-DOF robots Based on Screw throry and Paden-Kahan sub-problems[J].Chinese Journal of Mechanical Engineering,2009,45(9):72-76.(in Chinese with English abstract)
[12]吕世增,张大卫,刘海年.基于吴方法的6R机器人逆运动学旋量方程求解[J].机械工程学报,2010,46(17):35-41.LüShizeng,Zhang Dawei,Liu Hainian.Solution of screw equation for inverse kinematics of 6R robot based on Wu’s method[J].Chinese Journal of Mechanical Engineering,2010,46(17):35-41.(in Chinese with English abstract)
[13]李盛前,谢小鹏.基于旋量理论和Sylvester结式法的6自由度机器人逆运动学求解分析[J].农业工程学报,2015,31(20):48-54.Li Shengqian,Xie Xiaopeng.Anlysis of inverse kinematic solution for 6R robot based on screw theory and Sylvester resultant[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(20):48-54.(in Chinese with English abstract)
[14]Sariyildiz E,Temeltas H.Solution of inverse kinematic problem for serial robot using quaterninons[C]//Proceedings of the IEEE International Conference on Mechatronics and Automation.Changchun:IEEE,2009:26-31.
[15]Gao Y,Chen W,Lu Z.Kinematics analysis and experiment of a cockroach-like robot[J].Journal of Shanghai Jiaotong University(Science),2011,16(1):71-77.
[16]陈庆诚,朱世强,王宣银,等.基于旋量理论的串联机器人逆解子问题求解算法[J].浙江大学学报:工学版,2014,48(1):8-14.Chen Qingcheng,Zhu Shiqiang,Wang Xuanyin,et al.Inverse kinematics sub-problem solution algorithm for serial robot based on screw theory[J].Journal of Zhejiang University:Engineering Science,2014,48(1):8-14.(in Chinese with English abstract)
[17]Wang H,Lu X,Zhang Z,et al.A novel second subproblem for two arbitrary axes of robots[J].International Journal of Advanced Robotic Systems,2018,15(2):1-7.
[18]Rocha C R,Tonetto C P,Dias A.A comparison between the Denavit-Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators[J].Robotics&Computer Integrated Manufacturing,2011,27(4):723-728.
[19]Li Y,Zhu S,Wang Z,et al.The kinematics analysis of a novel self-reconfigurable modular robot based on screw theory[J].DEStech Transactions on Engineering and Technol ogy Research,2016:23-30.
[20]Dai J S.Screw algebra and kinematic approaches for mechanisms and robotics[M].London:Springer,2014:49-80.
[21]Kevin M L,Frank C P.Modern robotics mechanics,planning,and control[M].Cambridge:Cambridge University Press,2017:59-114.
[22]Gallardo-Alvarado J.Kinematic analysis of parallel manipulators by algebraic screw theory[M].Switzerland:Springer International Publishing,2016:31-63.
[23]阳涵疆,李立君,高自成.基于旋量理论的混联采摘机器人正运动学分析与试验[J].农业工程学报,2016,32(9):53-59.Yang Hanjiang,Li Lijun,Gao Zicheng.Forward kinematics analysis and experiment of hybrid harvesting robot based on screw theory[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(9):53-59.(in Chinese with English abstract)
[24]王朋辉,李立君,高自成,等.摆动式林果采摘头设计与分析[J].西北林学院学报,2015,30(5):288-291.Wang Penghui,Li Lijun,Gao Zicheng,et al.The design and analysis of oscillating fruit picking head[J].Journal of Northwest Forestry University,2015,30(5):288-291.(in Chinese with English abstract)
[25]黄真,赵永生,赵铁石.高等空间机构学[M].北京:高等教育出版社,2014:2-26.
[26]李国利,姬长英,顾宝兴,等.多末端苹果采摘机器人机械手运动学分析与试验[J].农业机械学报,2016,47(12):14-21.Li Guoli,Ji Changying,Gu Baoxing,et al.Kinematics analysis and experiment of apple harvesting robot manipulator with multiple end-effectors[J].Transactions of the Chinese Society for Agricultural Machinery,2016,47(12):14-21.(in Chinese with English abstract)
[27]梅东棋.六自由度工业机器人全姿态精度补偿方法[D].南京:南京航空航天大学,2015.Mei Dongqi.Compensation Method of 6R Industrial Robot positioning Accuracy[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2015.(in Chinese with English abstract)
[28]Cho Y,Do H M,Cheong J.Screw based kinematic calibration method for robot manipulators with joint compliance using circular point analysis[J].Robotics and Computer-Integrated Manufacturing,2018,https://doi.org/10.1016/j.rcim.2018.08.001.
[29]Tabandeh S,Melek W W,Clark C M.An adaptive niching genetic algorithm approach for generating multiple solutions ofserial manipulator inverse kinematics with applications to modular robots[J].Robotica,2010,28(4):493-507.
[30]Liu Y,Wan M,Xing W J,et al.Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools[J].International Journal of Mechanical Sciences,2018,145:299-317.
[31]王先奎.机械制造工艺学[M].北京:机械工业出版社,2013:199-226.
[2]An H S,Lee J H,Lee C,et al.Geometrical kinematic solution of serial spatial manipulators using screw theory[J].Mechanism and Machine Theory,2017,116:404-418.
[3]Pena C A,Guzman M A,Cardenas P F.Inverse kinematics of a 6 DOF industrial robot manipulator based on bio-inspired multi-objective optimization techniques[C]//2016 IEEEColombian Conference on Robotics and Automation(CCRA).IEEE,2016.
[4]Xu J,Liu Z,Cheng Q,et al.Models for three new screw-based IK sub-problems using geometric descriptions and their applications[J].Applied Mathematical Modelling,2018,67:399-412.
[5]Man C,Xun F,Li C R,et al.Kinematics analysis based on screw theory of a humanoid robot[J].Journal of China University of Mining and Technology,2007,17(1):49-52.
[6]孙恒辉,赵爱武,李达,等.基于新旋量子问题改进一类6R串联机器人逆解算法[J].机械工程学报,2016,52(1):79-86.Sun Henghui,Zhao Aiwu,Li Da,et al.Improvement of the algorithm of the inverse kinematics calculation for 6R series robots based on one novel Paden-Kahan sub-problem[J].Chinese Journal of Mechanical Engineering,2016,52(1):79-86.(in Chinese with English abstract)
[7]Wang H,Lu X,Sheng C,et al.General frame for arbitrary3R subproblems based on the POE model[J].Robotics and Autonomous Systems,2018,105:138-145.
[8]Dong Y,Phan H N,Rahmani A.Modeling and kinematics study of hand[J].International Journal of Computer Science and Applications,2015,12(1):66-79.
[9]赵杰,刘玉斌,蔡鹤皋.一种运动旋量逆解子问题的求解及其应用[J].机器人,2005,27(2):163-167.Zhao Jie,Liu Yubin,Cai Hegao.Solution for one type of inverse kinematics sub-problems in screw theory and its application[J].Robot,2005,27(2):163-167.(in Chinese with English abstract)
[10]Murray R M,Li Z,Sastry S S.A Mathematical Introduction to Robotic Manipulation[M].Florida:CRC Press,1994:19-81.
[11]钱东海,王新峰,赵伟,等.基于旋量理论和Paden-Kahan子问题的6自由度机器人逆解算法[J].机械工程学报,2009,45(9):72-76.Qian Donghai,Wang Xinfeng,Zhao Wei,et al.Algorithm for the inverse kinematics calculation of 6-DOF robots Based on Screw throry and Paden-Kahan sub-problems[J].Chinese Journal of Mechanical Engineering,2009,45(9):72-76.(in Chinese with English abstract)
[12]吕世增,张大卫,刘海年.基于吴方法的6R机器人逆运动学旋量方程求解[J].机械工程学报,2010,46(17):35-41.LüShizeng,Zhang Dawei,Liu Hainian.Solution of screw equation for inverse kinematics of 6R robot based on Wu’s method[J].Chinese Journal of Mechanical Engineering,2010,46(17):35-41.(in Chinese with English abstract)
[13]李盛前,谢小鹏.基于旋量理论和Sylvester结式法的6自由度机器人逆运动学求解分析[J].农业工程学报,2015,31(20):48-54.Li Shengqian,Xie Xiaopeng.Anlysis of inverse kinematic solution for 6R robot based on screw theory and Sylvester resultant[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(20):48-54.(in Chinese with English abstract)
[14]Sariyildiz E,Temeltas H.Solution of inverse kinematic problem for serial robot using quaterninons[C]//Proceedings of the IEEE International Conference on Mechatronics and Automation.Changchun:IEEE,2009:26-31.
[15]Gao Y,Chen W,Lu Z.Kinematics analysis and experiment of a cockroach-like robot[J].Journal of Shanghai Jiaotong University(Science),2011,16(1):71-77.
[16]陈庆诚,朱世强,王宣银,等.基于旋量理论的串联机器人逆解子问题求解算法[J].浙江大学学报:工学版,2014,48(1):8-14.Chen Qingcheng,Zhu Shiqiang,Wang Xuanyin,et al.Inverse kinematics sub-problem solution algorithm for serial robot based on screw theory[J].Journal of Zhejiang University:Engineering Science,2014,48(1):8-14.(in Chinese with English abstract)
[17]Wang H,Lu X,Zhang Z,et al.A novel second subproblem for two arbitrary axes of robots[J].International Journal of Advanced Robotic Systems,2018,15(2):1-7.
[18]Rocha C R,Tonetto C P,Dias A.A comparison between the Denavit-Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators[J].Robotics&Computer Integrated Manufacturing,2011,27(4):723-728.
[19]Li Y,Zhu S,Wang Z,et al.The kinematics analysis of a novel self-reconfigurable modular robot based on screw theory[J].DEStech Transactions on Engineering and Technol ogy Research,2016:23-30.
[20]Dai J S.Screw algebra and kinematic approaches for mechanisms and robotics[M].London:Springer,2014:49-80.
[21]Kevin M L,Frank C P.Modern robotics mechanics,planning,and control[M].Cambridge:Cambridge University Press,2017:59-114.
[22]Gallardo-Alvarado J.Kinematic analysis of parallel manipulators by algebraic screw theory[M].Switzerland:Springer International Publishing,2016:31-63.
[23]阳涵疆,李立君,高自成.基于旋量理论的混联采摘机器人正运动学分析与试验[J].农业工程学报,2016,32(9):53-59.Yang Hanjiang,Li Lijun,Gao Zicheng.Forward kinematics analysis and experiment of hybrid harvesting robot based on screw theory[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(9):53-59.(in Chinese with English abstract)
[24]王朋辉,李立君,高自成,等.摆动式林果采摘头设计与分析[J].西北林学院学报,2015,30(5):288-291.Wang Penghui,Li Lijun,Gao Zicheng,et al.The design and analysis of oscillating fruit picking head[J].Journal of Northwest Forestry University,2015,30(5):288-291.(in Chinese with English abstract)
[25]黄真,赵永生,赵铁石.高等空间机构学[M].北京:高等教育出版社,2014:2-26.
[26]李国利,姬长英,顾宝兴,等.多末端苹果采摘机器人机械手运动学分析与试验[J].农业机械学报,2016,47(12):14-21.Li Guoli,Ji Changying,Gu Baoxing,et al.Kinematics analysis and experiment of apple harvesting robot manipulator with multiple end-effectors[J].Transactions of the Chinese Society for Agricultural Machinery,2016,47(12):14-21.(in Chinese with English abstract)
[27]梅东棋.六自由度工业机器人全姿态精度补偿方法[D].南京:南京航空航天大学,2015.Mei Dongqi.Compensation Method of 6R Industrial Robot positioning Accuracy[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2015.(in Chinese with English abstract)
[28]Cho Y,Do H M,Cheong J.Screw based kinematic calibration method for robot manipulators with joint compliance using circular point analysis[J].Robotics and Computer-Integrated Manufacturing,2018,https://doi.org/10.1016/j.rcim.2018.08.001.
[29]Tabandeh S,Melek W W,Clark C M.An adaptive niching genetic algorithm approach for generating multiple solutions ofserial manipulator inverse kinematics with applications to modular robots[J].Robotica,2010,28(4):493-507.
[30]Liu Y,Wan M,Xing W J,et al.Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools[J].International Journal of Mechanical Sciences,2018,145:299-317.
[31]王先奎.机械制造工艺学[M].北京:机械工业出版社,2013:199-226.