1. Introduction to Robotics Tutorial 7 Technion, cs department, Introduction to Robotics 236927 Winter 2010-2011 1

2. Potential Functions 2 1.Write the attraction and repulsion potential functions. Destination Obstacle Center at (L,0) Radius = R

3. Destination 3 The destination is modeled as an attractive charge. Destination

4. Obstacle 4 The Obstacle is modeled as a single repulsive charge. Obstacle Center at (L,0) Radius = R

5. Obstacle and Destination 5

6. 6

7. Potential Functions 7 2.For which α and β the robot will never hit the obstacle? Destination Obstacle Center at (L,0) Radius = R

8. Potential Functions 8 3.Will the robot always arrive at the destination? 4.From which starting positions the robot will not arrive the destination?

9. Different Obstacle Modeling 9 The Obstacle is modeled as a single repulsive charge.

10. 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?

11. 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.

12. Different Obstacle Modeling 12

13. Another Example 13 Destination