1. A Geometric Approach to Error Detection and Recovery for Robot Motion Planning with Uncertainty Bruce R. Donald, 1988 Presented by Kristof Richmond

2. Error Detection  What is an error?

3. Error Detection  What is an error?

4. Error Detection  What is an error?

5. Error Detection  What is an error?

6. Error Detection  What is an error?  There exists no guaranteed plan.

7. Outline  Description of variable environments Extra degrees of freedom Different physics  EDR Error Detection and Recovery Single-step strategies Geomteric construction of EDR regions

8. R B ec Simple Example BA Goal Robot ( x,y ) vv 

9. R B ec Simple Example BA vv 

10. R B ec Simple Example BA vv 

11. Generalized configuration space G G B A x y J G R

12. Modes of motion  “Gross” In free space In constant-  slices  Pushing On surfaces Non-zero  -component  “Compliant” On surfaces In constant-  slices (Sliding)

13. Moving along J ff ff x y J B G

14. Error Detection and Recovery  Assume simple model  Motion strategy – “Go straight until you’re done” Single commanded velocity Termination predicate  This allows simple geometric constructions

15. EDR axioms  An EDR plan should: Attain the goal if reachable Signal failure if not reachable Allow attainment of the goal through luck Never prematurely signal failure

16. EDR region Goal B ec vqvq F H BA R

17. EDR construction R B ec G F P PwPw H H

18. Preimage with model uncertainty x y J A G G G B ec

19. EDR axioms  An EDR plan should: Attain the goal if reachable Signal failure if not reachable Allow attainment of the goal through luck Never prematurely signal failure

20. Conclusions  A method for representing environmental variability exists: G Unique physics Planning of pushing motions  Geometric EDR: H Forward projections Preimages