1. Assembly Planning

2. Levels of Problems  Parts are assumed free-flying  Assembly sequence planning  Tools/fixtures are taken into account  Entire manipulation system is taken into account  Manipulation planning

3. Applications  Answers to questions such as: How many parts need to be removed to extract a given part P? Can the product be assembled by adding a single part at a time? How much can the assembly process be parallelized?  Design for manufacturing and servicing  Design of manufacturing systems

4. Assembly Sequence Planning  Very constrained goal state, but unconstrained initial state  Disassembly planning  Large number of dofs, but simple paths  Motion space

5. Set of Assembly Sequences as an AND/OR Graph

7. Contact Analysis How would you compute a direction of motion for the T-shaped object?

8. Contact Analysis

9. Planning Approaches  Generate-and-test  Generate-and-test plus caching  Non-directional blocking graph  Interference diagram

10. Directional Blocking Graph (for infinitesimal translations) R.H. Wilson and J.C. Latombe. Geometric Reasoning about Mechanical Assembly. Artificial Intelligence, 71(2):371-396, 1995.

11. Directional Blocking Graph (for infinitesimal translations) R.H. Wilson and J.C. Latombe. Geometric Reasoning about Mechanical Assembly. Artificial Intelligence, 71(2):371-396, 1995.

12. Directional Blocking Graph (for infinitesimal translations)

13. How do you see that this is a potentially good direction?

14. Directional Blocking Graph (for infinitesimal translations) How do you see that this is a potentially good direction?

15. Motion Space (for infinitesimal translations) The motion space is the space of all directions of motion It does not say which objects are moving S1S1

16. Non-Directional Blocking Graph (for infinitesimal translations) The NDBG is a partition of a motion space into cells (points and arcs) What happens when one switches from one cell to the next?

17. Non-Directional Blocking Graph (for infinitesimal translations)  Assembly sequencing in polynomial time

18. Non-Directional Blocking Graph (for extended translations) How would you compute the NDBG?

19. Sketch of an Assembly Planner  Plan a sequence that is valid for extended translations  If one is found, return it Else plan a sequence that is valid for infinitesimal translations If none is found then return failure Else use a general motion planner to validate each step of the sequence

20. Extension to 3-D (for infinitesimal or extended translations) What is the motion space?

21. Extension to 3-D (for infinitesimal or extended translations) How would you do for extended translations?

22. More Extensions  What would be the motion space if we allowed parts to both translate and rotate?  What about multi-step motions, e.g., along d1 for distance l1, then d2 for distance l2,...?

23. Contact Analysis

25. More Extensions  What would be the motion space if we allowed parts to both translate and rotate?  What about multi-step motions, e.g., along d1 for distance l1, then d2 for distance l2,...?

26. Interference Diagram

28. Assembly Sequences Generated Using NDBGs Sandia National Labs (R. Wilson) Munich University (F. Schwarzer)

29. Number of Hands An assembly that requires n hands

30. Mononoticity of an Assembly

32.  With translations only monotone two-handed  With translations only non-monotone, 2-handed monotone, 3-handed  With general motions monotone, 2-handed Example Assemblies

33.  With translations only monotone two-handed  With translations only non-monotone, 2-handed monotone, 3-handed  With general motions monotone, 2-handed Example Assemblies

34. Nonlinearalizable 1-Handed Assembly