基于共形几何代数的6-DOF机器人运动学逆解
|
摘要
机器人运动学模型的建立普遍利用Denavit-Hartenberg(D-H)参数法,但是该代数方法的计算复杂度高。共形几何代数作为一种新的运算工具,具有几何直观性、简洁性,已经应用于机器人运动学。针对广泛应用的6自由度工业机器人,利用共形几何代数建立点、直线、圆周、平面和球体等几何对象,通过各对象之间的几何约束解决机器人运动学逆解。首先,以工业机器人典型的肩部、肘部和腕部结构为基础,定义3种结构形式;然后,利用已知的点以及相交约束关系建立直线、平面、圆周和球体等几何对象,通过它们的几何约束关系计算得到各个关节点并构造连杆直线;最后,构造旋转直线对象以及旋转平面并利用平行和垂直的几何约束关系计算各关节的旋转角,完成机器人逆解的计算。以常用的后3个关节轴线相交于1点和Universal Robot UR3的6自由度关节机器人为例,利用该算法进行运动学逆解的验证,计算结果表明该算法的正确性。
Denavit-Hartenberg( D-H) notation method is usually used to set up the kinematics model of a robot,but the method has high computational complexity. Conformal Geometric Algebra( CGA) is a new computation tool. It has properties of geometric intuitiveness,simplicity,and has been used to robot kinematics. For a wide range of applications of 6-DOF industrial robot,the paper demonstrates that the solution of the inverse kinematics in CGA relies on the constrain relationship of geometric objects like lines,circles,planes and spheres. First three kinds of robot configurations are defined based on the classical frame of industrial robot for shoulder,elbow and wrist style. Then the geometric objects such as lines,circles,planes and spheres are set up by the points and intersection relationship between these objects,by which the joint points and the link lines could be obtained. Finally,the rotation angles are computed by the rotation line objects and rotation planes and the parallel and perpendicular constrain relationship,so the inverse kinematics of robot was completed. The correctness of the algorithm is verified by the robots with 6-DOF and with the last three joint axes intersecting to one point and the Universal Robot UR3,whose kinematics modes are set up by the proposed algorithm.
Denavit-Hartenberg( D-H) notation method is usually used to set up the kinematics model of a robot,but the method has high computational complexity. Conformal Geometric Algebra( CGA) is a new computation tool. It has properties of geometric intuitiveness,simplicity,and has been used to robot kinematics. For a wide range of applications of 6-DOF industrial robot,the paper demonstrates that the solution of the inverse kinematics in CGA relies on the constrain relationship of geometric objects like lines,circles,planes and spheres. First three kinds of robot configurations are defined based on the classical frame of industrial robot for shoulder,elbow and wrist style. Then the geometric objects such as lines,circles,planes and spheres are set up by the points and intersection relationship between these objects,by which the joint points and the link lines could be obtained. Finally,the rotation angles are computed by the rotation line objects and rotation planes and the parallel and perpendicular constrain relationship,so the inverse kinematics of robot was completed. The correctness of the algorithm is verified by the robots with 6-DOF and with the last three joint axes intersecting to one point and the Universal Robot UR3,whose kinematics modes are set up by the proposed algorithm.
引文
[1]CHITTA S,JONES E G,CIOCARLIE M,et al.Mobile manipulation in unstructured environments:perception,planning,and execution[J].IEEE Robotics and Automation Magazine,2012,19(2):58-71.
[2]JIA Y H,HU QUAN,XU S J.Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters[J].Acta Mechanica Sinica,2014,30(1):112-124.
[3]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(7):1083-1092.
[4]HILDENBRAND D.Foundations of geometric algebra computing[M].Springer Berlin Heidelberg,Berlin,Heidelberg,2013.
[5]KUCUK S,BINGUL Z.Inverse kinematics solutions for industrial robot manipulators with offset wrists[J].Applied Mathematical Modelling,2014,38(7-8):1983-1999.
[6]KOFINAS N,ORFANOUDAKIS E,LAGOUDAKIS M G.Complete analytical forward and inverse kinematics for the NAO humanoid robot[J].Journal of Intelligent&Robotic Systems,2015,77(2):251-264.
[7]CUI Y D,TAKAHASHI K,HASHIMOTO M.Design of control systems using quaternion neural network and Its application to inverse kinematics of robot manipulator[C]//Proceedings of the2013 IEEE/SICE International Symposium on System Integration,Kobe International Conference Center,Kobe,Japan,2013,MP1-J2,527-532.
[8]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.
[9]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.
[10]KIM J S,JEONG J H,PARK J H.Inverse kinematics and geometric singularity analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra[J].Mechanism&Machine Theory,2015,90:23-36.
[11]倪振松,廖启征,魏世民,等.空间一般6R机械手位置反解的新方法[J].北京邮电大学学报,2009,32(2):29-33.
[12]张忠海,李端玲.空间并联机构运动学分析的共形几何代数方法[J].农业机械学报,2015,46(4):325-330.
[2]JIA Y H,HU QUAN,XU S J.Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters[J].Acta Mechanica Sinica,2014,30(1):112-124.
[3]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(7):1083-1092.
[4]HILDENBRAND D.Foundations of geometric algebra computing[M].Springer Berlin Heidelberg,Berlin,Heidelberg,2013.
[5]KUCUK S,BINGUL Z.Inverse kinematics solutions for industrial robot manipulators with offset wrists[J].Applied Mathematical Modelling,2014,38(7-8):1983-1999.
[6]KOFINAS N,ORFANOUDAKIS E,LAGOUDAKIS M G.Complete analytical forward and inverse kinematics for the NAO humanoid robot[J].Journal of Intelligent&Robotic Systems,2015,77(2):251-264.
[7]CUI Y D,TAKAHASHI K,HASHIMOTO M.Design of control systems using quaternion neural network and Its application to inverse kinematics of robot manipulator[C]//Proceedings of the2013 IEEE/SICE International Symposium on System Integration,Kobe International Conference Center,Kobe,Japan,2013,MP1-J2,527-532.
[8]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.
[9]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.
[10]KIM J S,JEONG J H,PARK J H.Inverse kinematics and geometric singularity analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra[J].Mechanism&Machine Theory,2015,90:23-36.
[11]倪振松,廖启征,魏世民,等.空间一般6R机械手位置反解的新方法[J].北京邮电大学学报,2009,32(2):29-33.
[12]张忠海,李端玲.空间并联机构运动学分析的共形几何代数方法[J].农业机械学报,2015,46(4):325-330.