Inverse kinematics of a heavy duty manipulator with 6-DOF based on dual quaternion
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摘要
An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.
An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.
An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.
引文
[1]HO C Y,YAO J C.Computer-controlled automated jumbo drilling robot manipulator[J].International Journal of Mining and Geological Engineering,1986,4:303-318.
[2]MANFRED L,HUSTY,MARTIN P,HANSPETER S.A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator[J].Mechanism and Machine Theory,2007,42:66-88.
[3]BRUYNINCKX H,SCHUTTER J D.Introduction to intelligent robotics[R].Leuven:Katholieke Universiteit de Leuven,2001.
[4]HUANG Liang-song,JIANG Ru-kang.A new method of inverse kinematics solution for industrial 7DOF robot[C]//Proceedings of the 32nd Chinese Control Conference.Xi’an,China:Chinese Control Conference,2013,7:26-28.
[5]KIM J H,KUMAR V R.Kinematics of robot manipulators via line transformations[J].Journal of Robotic Systems,1990,7:649-674.
[6]MANOCHA D,CANNY J F.Efficient inverse kinematics for general6R manipulators[J].IEEE Transaction on Robotics and Automation,1994,5(9):648-657.
[7]XIONG You-lun.Fundamentals of robotics[M].Wuhan:Huazhong University of Science and Technology Press,1996.(in Chinese)
[8]ANGELES J.On the numerical solution of the inverse kinematic problem[J].Robotics Research,1985,4(2):21-37.
[9]MITESH S,PATEL R V.Inverse Jacobian based hybrid impedance control of redundant manipulators[C]//IEEE International Conference on Mechatronics and Automation.Niagara:IEEE,2005:55-60.
[10]CHIDDARWAR S S,BABU N R.Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach[J].Engineering Applications of Artificial Intelligence,2010,23:1083-1092.
[11]ZHOU You-hang,HE Qing-hua,DENG Bo-lu.Trial mountain climbing algorithm for solving the inverse kinematics of redundant manipulator[J].Journal of Central South University of Technology,2002,9(4):285-288.
[12]LALO W,BRANDT T,SCHRAMM D,HILLER M.A linear optimization approach to inverse kinematics of redundant robots with respect to manipulability[C]//The 25th International Symposium on Automation and Robotics in Construction.Vilnius,Lithuania:ISARC,2008:175-180.
[13]ZHONG G G.Development of a hydraulic robot for tunnel drillingmanipulator kinematics and tracking control[D].Saskatoon:University of Saskatchewan,1995.
[14]HAMILTON W R.Elements of quaternion[M].New York:Chelsea,1869.
[15]YANG A T,FREUDENSTEIN F.Application of dual-number quaternion algebra to the analysis of spatial mechanisms[J].ASME Journal of Applied Mechanics,1964,31(2):300-308.
[16]SARIYILDIZ E,CAKIRAY E,TEMELTAS H.A comparative study of three inverse kinematic methods of serial industrial robot manipulators in the screw theory framework[J].International Journal of Advanced Robotic Systems,2011,8(5):9-24.
[17]GOUASMI M,OUALI M,BRAHIM F.Robot kinematics using dual quaternions[J].International Journal of Robotics and Automation,2012,1(1):13-30.
[18]SARIYILDIZ E,TEMELTAS H.Solution of inverse kinematic problem for serial robot using dual quaternions and Plücker coordinates[C]//Advanced Intelligent Mechatronics.Piscataway,NJ,USA:IEEE,2009:338-343.
[19]AYDIN Y,KUCUK S.Quaternion based inverse kinematics for industrial robot manipulators with Euler wrist[C]//International Conference on Mechatronics.Piscataway,NJ,USA:IEEE,2006:581-586.
[20]SYLVESTER J J.On a theory of syzegetic relations of two rational integral functions,comprising an application to the theory of Sturm’s functions,and that of the greatest algebraic common measure[J].Philosophical Transactions of the Royal Society,1853,143:407-548.
[2]MANFRED L,HUSTY,MARTIN P,HANSPETER S.A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator[J].Mechanism and Machine Theory,2007,42:66-88.
[3]BRUYNINCKX H,SCHUTTER J D.Introduction to intelligent robotics[R].Leuven:Katholieke Universiteit de Leuven,2001.
[4]HUANG Liang-song,JIANG Ru-kang.A new method of inverse kinematics solution for industrial 7DOF robot[C]//Proceedings of the 32nd Chinese Control Conference.Xi’an,China:Chinese Control Conference,2013,7:26-28.
[5]KIM J H,KUMAR V R.Kinematics of robot manipulators via line transformations[J].Journal of Robotic Systems,1990,7:649-674.
[6]MANOCHA D,CANNY J F.Efficient inverse kinematics for general6R manipulators[J].IEEE Transaction on Robotics and Automation,1994,5(9):648-657.
[7]XIONG You-lun.Fundamentals of robotics[M].Wuhan:Huazhong University of Science and Technology Press,1996.(in Chinese)
[8]ANGELES J.On the numerical solution of the inverse kinematic problem[J].Robotics Research,1985,4(2):21-37.
[9]MITESH S,PATEL R V.Inverse Jacobian based hybrid impedance control of redundant manipulators[C]//IEEE International Conference on Mechatronics and Automation.Niagara:IEEE,2005:55-60.
[10]CHIDDARWAR S S,BABU N R.Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach[J].Engineering Applications of Artificial Intelligence,2010,23:1083-1092.
[11]ZHOU You-hang,HE Qing-hua,DENG Bo-lu.Trial mountain climbing algorithm for solving the inverse kinematics of redundant manipulator[J].Journal of Central South University of Technology,2002,9(4):285-288.
[12]LALO W,BRANDT T,SCHRAMM D,HILLER M.A linear optimization approach to inverse kinematics of redundant robots with respect to manipulability[C]//The 25th International Symposium on Automation and Robotics in Construction.Vilnius,Lithuania:ISARC,2008:175-180.
[13]ZHONG G G.Development of a hydraulic robot for tunnel drillingmanipulator kinematics and tracking control[D].Saskatoon:University of Saskatchewan,1995.
[14]HAMILTON W R.Elements of quaternion[M].New York:Chelsea,1869.
[15]YANG A T,FREUDENSTEIN F.Application of dual-number quaternion algebra to the analysis of spatial mechanisms[J].ASME Journal of Applied Mechanics,1964,31(2):300-308.
[16]SARIYILDIZ E,CAKIRAY E,TEMELTAS H.A comparative study of three inverse kinematic methods of serial industrial robot manipulators in the screw theory framework[J].International Journal of Advanced Robotic Systems,2011,8(5):9-24.
[17]GOUASMI M,OUALI M,BRAHIM F.Robot kinematics using dual quaternions[J].International Journal of Robotics and Automation,2012,1(1):13-30.
[18]SARIYILDIZ E,TEMELTAS H.Solution of inverse kinematic problem for serial robot using dual quaternions and Plücker coordinates[C]//Advanced Intelligent Mechatronics.Piscataway,NJ,USA:IEEE,2009:338-343.
[19]AYDIN Y,KUCUK S.Quaternion based inverse kinematics for industrial robot manipulators with Euler wrist[C]//International Conference on Mechatronics.Piscataway,NJ,USA:IEEE,2006:581-586.
[20]SYLVESTER J J.On a theory of syzegetic relations of two rational integral functions,comprising an application to the theory of Sturm’s functions,and that of the greatest algebraic common measure[J].Philosophical Transactions of the Royal Society,1853,143:407-548.