Introduction to Robotics Tutorial 10

1. Introduction to RoboticsTutorial 10 Technion, cs department, Introduction to Robotics 236927 Winter 2013-2014 1

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

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

4. Potential Functions 4

5. Gradient Descent • Gradient descent is a well-known approach to optimization problems. The idea is simple. Starting at the initial configuration, take a small step in the direction opposite the gradient. This gives a new configuration, and the process is repeated until the gradient is zero. More formally, we can define a gradient descent algorithm

6. Gradient Descent

7. Obstacle • The Obstacle is modeled as a single repulsive charge. Obstacle Center at (L,0) Radius = R 7

8. Obstacle and Destination 8

9. Obstacle and Destination 9

10. Potential Functions • For which α and β the robot will never hit the obstacle? Destination Obstacle Center at (L,0) Radius = R 10

11. Potential Functions • For which α and β the robot will never hit the obstacle? • Will the robot always arrive at the destination? • From which starting positions the robot will not arrive the destination? • How does changing β effects the resulting path? 11

12. Local Minima Problem

13. Different Obstacle Modeling • The Obstacle is modeled as a single repulsive charge. 13

14. Different Obstacle Modeling • The Obstacle is modeled as a single repulsive charge: • Alternately: • Where d* is the distance to the closest point of the obstacle. 14

15. Different Obstacle Modeling 15