Post on 19-Dec-2015
Introduction to Robotics
Tutorial 7
Technion, cs department, Introduction to Robotics 236927
Winter 2010-2011
1
Potential Functions
2
1. Write the attraction and repulsion potential functions.
Destination
ObstacleCenter at (L,0)Radius = R
x
y
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
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
Obstacle and Destination
5
yxUyxUyxU RA ,,,
-10-5
05
10
-10
-5
0
5
100
5
10
15
20
25
30
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
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
Potential Functions
8
3. Will the robot always arrive at the destination?
4. From which starting positions the robot will not arrive the destination?
Different Obstacle Modeling
9
• The Obstacle is modeled as a single repulsive charge.
22
0
/
yLxd
else
RdRddU R
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?
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/ ***
Different Obstacle Modeling
12
else
dddU R
0
0/ ***
Another Example
13
Destination
x
y