end effector
DESCRIPTION
End effector. End effector - the last coordinate system of figure Located in joint N . But usually, we want to specify it in base coordinates . 1. End effector. A transformation from the link N to the base : . 2. End effector. We can also express it as - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/1.jpg)
End effector•End effector - the last coordinate system of
figure•Located in joint N.•But usually, we want to specify it in base
coordinates.
1
![Page 2: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/2.jpg)
End effectorA transformation from the link N to the
base :
2
![Page 3: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/3.jpg)
End effector•We can also express it as •three rotations (around each of the
coordinate axes)• followed by a translation
•How can we establish a relation with the other expression ?
3
![Page 4: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/4.jpg)
End effector•The origin of a coordinate frame
relative to some base coordinate frame is specified by the translation :
4
![Page 5: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/5.jpg)
End effector•Any 3D orientation relative to some base coordinate frame can be specified by :three rotations, one around each of the coordinate axes.
We do them in this order : around x, y, z. 5
![Page 6: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/6.jpg)
End effector
6
![Page 7: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/7.jpg)
End effector•Orientation•The roll, pitch and yaw
transformation is then expressed :
7
![Page 8: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/8.jpg)
End effector•Finally, the transformation from a coordinate
frame to the base frame is expressed :
8
![Page 9: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/9.jpg)
End effector
We obtain directly the translation vector :
9
![Page 10: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/10.jpg)
End effector
We can obtain the yaw angle :Because :
arctan is π-periodic. Let’s use our function arctan2 to get the right angle.
10
![Page 11: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/11.jpg)
End effectorKnowing the yaw angle, we can obtain the pitch angle :
Because :
Again, let’s use our function arctan2 :
11
![Page 12: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/12.jpg)
End effector
We can obtain the roll angle :
Because :
Again, let’s use our function arctan2 :
12
21
11
sin cos sinarctan arctan arctancos cos cos
mm
2 21 11( , )arctan m m
![Page 13: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/13.jpg)
End effectorLet’s define the state vector
13
![Page 14: End effector](https://reader033.vdocuments.us/reader033/viewer/2022061608/5681615a550346895dd0e497/html5/thumbnails/14.jpg)
End effectorAs previously shown,
The state vector is composed of elements of this matrix. It’s also a function of joint parameters :
14