1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2002 Collision Detection and Distance Computation

2. C-Space Sampling  Need for efficient collision-checking algorithms

3. Collision Checking vs. Distance Computation Distance is in the workspace between the two closest points distance = 0  collision

4. It may be easier to check collision than to compute distance

5. Pure collision checking does not allow us to rigorously test segments C-space

6. Pure collision checking does not allow us to rigorously test segments C-space

7. Articulated Robot

8. High-Level Algorithm 1.Set d to  2.For every pair (L,O) of robot link and workspace obstacle do a.Compute the distance  between L and O b.If  = 0 then return collision c.If  < d then reset d to  3.Return d

9. Basic problem Given two objects A and B: - either compute the distance between them - or determine whether they collide, or not

10. Two Approaches  Hierarchical bounding approximation of objects (different types of primitive volumes)  Tracking of closest features

11. Two Approaches  Hierarchical bounding approximation of objects  Tracking of closest features