Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter...
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![Page 1: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/1.jpg)
Introduction to Robotics
Tutorial 7
Technion, cs department, Introduction to Robotics 236927
Winter 2010-2011
1
![Page 2: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/2.jpg)
Potential Functions
2
1. Write the attraction and repulsion potential functions.
Destination
ObstacleCenter at (L,0)Radius = R
x
y
![Page 3: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/3.jpg)
Destination
3
• The destination is modeled as an attractive charge.
Destination
x
y 22, yxyxU
ddU
A
A
-10-5
05
10
-10
-5
0
5
100
5
10
15
-10 -5 0 5 10-10
-8
-6
-4
-2
0
2
4
6
8
10
![Page 4: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/4.jpg)
Obstacle
4
• The Obstacle is modeled as a single repulsive charge.
22/,
/
yLxyxU
ddU
R
R
ObstacleCenter at (L,0)Radius = R
x
y
-10
-5
0
5
10
-10
-5
0
5
100
5
10
15
-10 -5 0 5 10-10
-8
-6
-4
-2
0
2
4
6
8
10
![Page 5: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/5.jpg)
Obstacle and Destination
5
yxUyxUyxU RA ,,,
-10-5
05
10
-10
-5
0
5
100
5
10
15
20
25
30
![Page 6: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/6.jpg)
Obstacle and Destination
6
yxFyxFyxF RA ,,,
-10 -5 0 5 10-10
-8
-6
-4
-2
0
2
4
6
8
10
2 3 4 5 6 7 8-3
-2
-1
0
1
2
3
![Page 7: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/7.jpg)
Potential Functions
7
2. For which α and β the robot will never hit the obstacle?
yyxLx
yLxyyxx
yx
yxFyxFyxF RA
ˆˆˆˆ
,,,
2/32222
Destination
ObstacleCenter at (L,0)Radius = R
x
y
![Page 8: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/8.jpg)
Potential Functions
8
3. Will the robot always arrive at the destination?
4. From which starting positions the robot will not arrive the destination?
![Page 9: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/9.jpg)
Different Obstacle Modeling
9
• The Obstacle is modeled as a single repulsive charge.
22
0
/
yLxd
else
RdRddU R
![Page 10: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/10.jpg)
Potential Functions
10
5. For which α and β the robot will never hit the obstacle?
6. Will the robot always arrive at the destination?
7. From which starting positions the robot will not arrive the destination?
8. How does changing β effects the resulting path?
![Page 11: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/11.jpg)
Different Obstacle Modeling
11
• The Obstacle is modeled as a single repulsive charge:
• Alternately:
Where d* is the distance to the closest point of the obstacle.
22
0
/
yLxd
else
RdRddU R
else
dddU R
0
0/ ***
![Page 12: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/12.jpg)
Different Obstacle Modeling
12
else
dddU R
0
0/ ***
![Page 13: Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649d2c5503460f94a02335/html5/thumbnails/13.jpg)
Another Example
13
Destination
x
y