ABB工业机器人运动学研究报告

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ABBIRB6600争论报告机器人构造简介ABB工业机器人可以用于实现喷雾、涂胶、物料搬运、点焊等多种功能，是典型的机械臂，在网络上可以查找到较多的相关资料。本次作业就选取ABBIRB6600机器人作为争论对象，首先对其构造进展简洁简介。12ABBIRB6600是六自由度机器人，具有六个旋转关节，底座固定，通过各关节的旋转可以完成三维空间内的运动。图1ABBIRB6600机器人的照片及工作范围图，图2是其构造简图和各轴的转动的参数。机器人的运动学ABBIRB6600D-H建模并求出对应的转换JacobianJacobian变换矩阵。、机器人正运动学为了计算便利把机器人各关节前后两连杆共线作为初始状态，画出构造简图如图3图337实际上是末端执行机构。运用学过的D-H建模方法建立模型，建模过程中为了便利画出各关节坐标系，将局部连杆进展了拉长，且由于局部关节坐目标Z轴垂直于纸面，所以用XY轴画出坐标系，用右手定则既得到对应的Z轴。最终建立::1:..4：图44D-H参数表：i变量范围100[-180,180]2900[-65，80]300[-180，60]40-90[-300，300]5-900[-120，120]60-90[-300，300]7〔末端〕00——由此算出各关节变换矩阵：将这些关节坐标变换矩阵连乘就得到了由基坐标系到末端的坐标变换矩阵：但是由于矩阵规模较大，不便用矩阵形式写出，所以把malab计算得出的矩阵用分项的形式写出：sin(θ1)*sin(θ6)+cos(θ6)*(cos(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))+sin(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2)))cos(θ6)*sin(θ1)-sin(θ6)*(cos(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))+sin(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2)))sin(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))-cos(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2)),h5’*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))-h6*(cos(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3)))-h7*(cos(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3)))+h2’*cos(θ1)-(h4+h5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))+h7’*(sin(θ1)*sin(θ6)+cos(θ6)*(cos(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))+sin(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))))-h3*cos(θ1)*sin(θ2)cos(θ6)*(cos(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))+sin(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2)))-cos(θ1)*sin(θ6),-cos(θ1)*cos(θ6)-sin(θ6)*(cos(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))+sin(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2)))sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))-cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2)),sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))-cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2)),h5’*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))-h7’*(cos(θ1)*sin(θ6)-cos(θ6)*(cos(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))+sin(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))))-h6*(cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1)))-h7*(cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1)))+h2’*sin(θ1)-(h4+h5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-h3*sin(θ1)*sin(θ2)-cos(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))),sin(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))),cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)),h1+h2+(h4+h5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-h5’*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+h3*cos(θ2)+h6*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)))+h7*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)))-h7’*cos(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))用各关节转角的初值来检查变换矩阵内的正确性：设：代入各关节变换矩阵可以求出各矩阵初值，由于中没有关节变量，所以保持不变记为矩阵g图5将图5中的初值矩阵连乘可以得到基坐标系到末端坐标系的变换矩阵：6：图6观看图6中的矩阵，检查初始状态末端坐标系在基坐标系的位姿，很简洁看出：在中的坐标为，并且与反向，与反向，与同向，这与D-H建模图〔图4〕中所得到的结果一样，可以确定计算过程是正确的。、机器人逆运动学Jacobian法进展机器人逆运动学的求解。首先已经列出的，可以依次求出matlab计算过程中：把依次记作a，b，c，d，e，f把记作〔sitai〕计算结果如下:6T由于2 矩阵元素表达式较简洁，不便列出整个矩阵，所以逐列写出：第一列：其次列：第三列：第四列：6T 6T由于1 比2 的矩阵元素表达式更为简洁，所以逐项列出：-cos(θ6)*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))),sin(θ6)*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))),-cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)),h2’-(h4+h5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))-h5’*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-h3*sin(θ2)-h6*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))21a -sin(θ6),2122a -cos(θ6),22-cos(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))sin(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))),cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)),(h4+h5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-h5’*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+h3*cos(θ2)+h6*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)))066T与正运动学计算00时求得的7T除了最终一列之外完全一样，下面写出最终一列的元素：0h5’*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))-h6*(cos(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3)))+h2’*cos(θ1)-(h4+h5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))-h3*cos(θ1)*sin(θ2)h5’*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))-h6*(cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1)))+h2’*sin(θ1)-(h4+h5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-h3*sin(θ1)*sin(θ2)H1+h2+(h4+h5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-h5’*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+h3*cos(θ2)+h6*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)))利用求出各关节到末端的坐标变换矩阵，可以求出Jacobian矩阵各列。Jacobian矩阵第iJ的计算方法如下：in o ax x

px pn

pnn o a pyyyy

z x

y x6T y yi1 n o a

p,并且

poz

po x y

poy xz z z z

pa pa pa0 0 0 1

z x y y xpnpoz zpa 那么:Ji n z z o az z z依据此公式可以算出Jacobian矩阵的各列:sin(θ6)*(cos(θ3)*sin(θ5)+cos(θ5)*sin(θ3))*(h3+h6*(cos(θ3)*cos(θ5)-sin(θ3)*sin(θ5))+cos(θ3)*(h4+h5)-h5’*sin(θ3))+cos(θ6)*(cos(θ3)*sin(θ5)+cos(θ5)*sin(θ3))*(h6*(cos(θ3)*sin(θ5)+cos(θ5)*sin(θ3))+sin(θ3)*(h4+h5)+h5’*cos(θ3))-sin(θ6)*(cos(θ3)*cos(θ5)-sin(θ3)*sin(θ5))*(h3+h6*(cos(θ3)*cos(θ5)-sin(θ3)*sin(θ5))+cos(θ3)*(h4+h5)-h5’*sin(θ3))-cos(θ6)*(cos(θ3)*cos(θ5)-sin(θ3)*sin(θ5))*(h6*(cos(θ3)*sin(θ5)+cos(θ5)*sin(θ3))+sin(θ3)*(h4+h5)+h5’*cos(θ3)),cos(θ6)*(h3+h6*(cos(θ3)*cos(θ5)-sin(θ3)*sin(θ5))+cos(θ3)*(h4+h5)-h5’*sin(θ3))-sin(θ6)*(h6*(cos(θ3)*sin(θ5)+cos(θ5)*sin(θ3))+sin(θ3)*(h4+h5)+h5’*cos(θ3))]cos(θ3)*cos(θ5)-sin(θ3)*sin(θ5)cos(θ3)*sin(θ5)+cos(θ5)*sin(θ3),0,-sin(θ6)*(cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)))*((h4+h5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))-h2’+h5’*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))+h3*sin(θ2)+h6*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))),cos(θ6)*((h4+h5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))-h2’+h5’*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))+h3*sin(θ2)+h6*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))),-sin(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))*((h4+h5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))-h2’+h5’*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))+h3*sin(θ2)+h6*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))))-cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)),0,cos(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3))-sin(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2)),(sin(θ1)*sin(θ6)+cos(θ6)*(cos(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))+sin(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))))*(h6*(cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1)))-h5’*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))-h2’*sin(θ1)+(h4+h5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))+h3*sin(θ1)*sin(θ2))-(cos(θ6)*sin(θ1)-sin(θ6)*(cos(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))+sin(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))))*(h6*(cos(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3)))-h5’*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))-h2’*cos(θ1)+(h4+h5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))+h3*cos(θ1)*sin(θ2)),(cos(θ1)*cos(θ6)+sin(θ6)*(cos(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))+sin(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))))*(h6*(cos(θ5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))-sin(θ5)*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3)))-h5’*(cos(θ1)*sin(θ2)*sin(θ3)-cos(θ1)*cos(θ2)*cos(θ3))-h2’*cos(θ1)+(h4+h5)*(cos(θ1)*cos(θ2)*sin(θ3)+cos(θ1)*cos(θ3)*sin(θ2))+h3*cos(θ1)*sin(θ2))-(cos(θ1)*sin(θ6)-cos(θ6)*(cos(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))+sin(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))))*(h6*(cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1)))-h5’*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ3)*sin(θ1))-h2’*sin(θ1)+(h4+h5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))+h3*sin(θ1)*sin(θ2)),-cos(θ6)*(cos(θ5)*(cos(θ2)*sin(θ3)+cos(θ3)*sin(θ2))+sin(θ5)*(cos(θ2)*cos(θ3)-sin(θ2)*sin(θ3)))*(h6*(cos(θ5)*(cos(θ2)*sin(θ1)*sin(θ3)+cos(θ3)*sin(θ1)*sin(θ2))-sin(θ5)*(sin(θ1)*sin(θ2)*sin(θ3)-cos(θ2)*cos(θ