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ABB机器人|带连杆的机器人正运动学计算
发布时间：2020-06-24        浏览次数：621        返回列表
 

ABB机器人|带连杆的机器人正运动学计算

 

1. IRB1410 机器人为典型的带连杆的ABB机器人，J3电机如图所示。J3电机置于底部，可以减轻上部的机构重量

 

ABB机器人
 

2. 运动时，J3电机带动J3连杆。3轴，J3连杆，上臂和后端连杆构成如图的平行四边形结构。

3. 所以，若2轴电机转动，但3轴电机不转动，此时3轴和大臂的夹角会变化（没有连杆的机器人，2轴电机转动，3轴电机不转动，3轴和大臂夹角不会变化）

 

ABB机器人

ABB机器人


 

以上两幅图片，3轴均为0度，但由于2轴转动，3轴与大臂夹角不一样

4. 对于不带连杆的机器人正运动学，可以通过dh参数转化为各个轴的位姿矩阵，将6个位姿矩阵右乘即可得到当前机器人末端的笛卡尔坐标，具体参见  linktype="2" hasload="1" style="margin: 0px; padding: 0px; text-decoration-line: none; -webkit-tap-highlight-color: rgba(0, 0, 0, 0); cursor: pointer; max-width: 100%; box-sizing: border-box !important; overflow-wrap: break-word !important;">机器人如何从各轴角度算出当前XYZ

5. 但对于带连杆机器人，2轴的变化会导致3轴与大臂夹角发生变化。由于平行四边形结构的缘故，实质3轴与大臂夹角变化刚好等于2轴变化角度的负数。

6. 故在位姿矩阵右乘时，只需在右乘到轴3 矩阵后，再右乘一个旋转矩阵，将夹角补偿回来即可。

7. 1410机器人DH参数如下

ABB机器人

 

 

αi   (twist)

ai(mm)  length

Θi  Rotation

di(mm) offset

1

0

0

0

475

2

-π/2

150

-π/2

0

3

0

600

0

0

4

-π/2

120

0

720

5

π/2

0

-π

0

6

π/2

0

0

85

 

8. 针对1410类似带连杆机器人，机器人正运动学RAPID实现方法如下

 

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important; overflow-wrap: break-word !important;"> LOCALVAR num alpha{6}:=[0,-90,0,-90,90,90];important; overflow-wrap: break-word !important;">   LOCALVAR num a{6}:=[0,150,600,120,0,0];important; overflow-wrap: break-word !important;">   LOCALVAR num theta{6}:=[0,-90,0,0,-180,0];important; overflow-wrap: break-word !important;">LOCALVAR num d{6}:=[475,0,0,720,0,85];important; overflow-wrap: break-word !important;">!1410 机器人DH参数important; overflow-wrap: break-word !important;">
important; overflow-wrap: break-word !important;">VAR num no_dependent;important; overflow-wrap: break-word !important;">!3轴与大臂夹角important; overflow-wrap: break-word !important;">   PROC test_dh_pose()important; overflow-wrap: break-word !important;">       VAR num curr_angle{6}:=[0,0,0,0,0,0];important; overflow-wrap: break-word !important;">       VAR pose pose10{6};important; overflow-wrap: break-word !important;">       VAR pose pose_cal:=[[0,0,0],[1,0,0,0]];important; overflow-wrap: break-word !important;">       VAR jointtarget jtmp;important; overflow-wrap: break-word !important;">       jtmp:=CJointT();important; overflow-wrap: break-word !important;">       curr_angle{1}:=jtmp.robax.rax_1;important; overflow-wrap: break-word !important;">       curr_angle{2}:=jtmp.robax.rax_2;important; overflow-wrap: break-word !important;">       curr_angle{3}:=jtmp.robax.rax_3;important; overflow-wrap: break-word !important;">       curr_angle{4}:=jtmp.robax.rax_4;important; overflow-wrap: break-word !important;">       curr_angle{5}:=jtmp.robax.rax_5;important; overflow-wrap: break-word !important;">       curr_angle{6}:=jtmp.robax.rax_6;important; overflow-wrap: break-word !important;">       FOR i FROM 1 TO 6 DOimportant; overflow-wrap: break-word !important;">           IF i=3 THENimportant; overflow-wrap: break-word !important;">               no_dependent:=-curr_angle{2};important; overflow-wrap: break-word !important;">             !夹角等于2轴运动的负数important; overflow-wrap: break-word !important;">           endifimportant; overflow-wrap: break-word !important;">           pose10{i}:=f_dh2pose(i,alpha{i},a{i},theta{i}+curr_angle{i},d{i});important; overflow-wrap: break-word !important;">       ENDFORimportant; overflow-wrap: break-word !important;">       FOR i FROM 1 TO 6 DOimportant; overflow-wrap: break-word !important;">           pose_cal:=PoseMult(pose_cal,pose10{i});important; overflow-wrap: break-word !important;">       ENDFORimportant; overflow-wrap: break-word !important;">ENDPROCimportant; overflow-wrap: break-word !important;">
important; overflow-wrap: break-word !important;">   FUNC pose f_dh2pose(num i,num alpha,num a,num theta,num d)important; overflow-wrap: break-word !important;">       VAR pose pose1:=[[0,0,0],[1,0,0,0]];important; overflow-wrap: break-word !important;">       pose1:=PoseMult(pose1,[[0,0,0],orientzyx(0,0,alpha)]);important; overflow-wrap: break-word !important;">       pose1:=PoseMult(pose1,[[a,0,0],orientzyx(0,0,0)]);important; overflow-wrap: break-word !important;">       pose1:=PoseMult(pose1,[[0,0,0],orientzyx(theta,0,0)]);important; overflow-wrap: break-word !important;">       pose1:=PoseMult(pose1,[[0,0,d],orientzyx(0,0,0)]);important; overflow-wrap: break-word !important;">      IF i=3 THENimportant; overflow-wrap: break-word !important;">           pose1:=PoseMult(pose1,[[0,0,0],orientzyx(no_dependent,0,0)]);important; overflow-wrap: break-word !important;">       endifimportant; overflow-wrap: break-word !important;">       !针对轴3坐标系，需要再多乘一次旋转，将夹角补偿回来important; overflow-wrap: break-word !important;">       RETURN pose1;important; overflow-wrap: break-word !important;">   ENDFUNC



 

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