6自由度关节机器人运动学反解的共形几何代数方法

摘要

机器人运动学模型的建立普遍利用Denavit-Hartenberg (D-H)参数法和旋量法,但是D-H参数法的几何意义不够明确,旋量法则有低自由度、关节轴线相交于1点的结构限制.针对6自由度关节机器人反解问题提出一种利用共形几何代数求解的新方法.首先以旋转关节轴线和旋转平面为基础建立无坐标系机器人模型,并定义肩部、肘部和腕部3种机器人结构设计形式.然后在上述模型和机器人结构下利用已知共形点建立直线、平面、圆周和球体等共形几何对象,通过几何对象的约束关系进行简单的代数运算完成各关节轴的旋转角计算.另外,该方法在进一步简化代数运算的基础上,利用2直线对象和旋转平面法矢量的约束关系唯一确定旋转角,从而完成运动学反解计算.最后,以常用的人机协作的UNIVERSAL ROBOT UR5 6自由度关节机器人为例,利用该算法进行运动学反解的验证,计算结果表明该算法的正确性.%Denavit-Hartenberg (D-H) notation method and screw theory method are usually used to set up the kinematics model of a robot,but the D-H method doesn't have definite geometric meaning and the screw theory method has the structural constrain just as low DOF and the joint axes interesting to one point.A novel method for solving the 6-DOF robot inverse kinematics using conformal geometric algebra (CGA) is proposed in this paper.First the no coordinate robot model was set up based on the rotating joint axes and rotational planes,and three kinds of robot structural design frames were defined for shoulder,elbow and wrist.Then the conformal geometric objects just as lines,planes,circles and spheres were constructed by the conformal points based on the above model and the robot configure style,and the rotation angles were computed through the constrain relationship within the geometric objects based on the simple algebra computation.Furthermore,this method uniquely determined the rotation angles by using the constraint relationship between the constructed two lines objects and the normal vector of rotation plane based on the simplified algebra computation,thus the inverse kinematics was completed.Finally,the correctness of the algorithm was verified by the UR5 collaborative articulated robot with 6-DOF,whose kinematics model was set up by the proposed algorithm.