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 processed by 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

10. Number of Hands An assembly that requires n hands

11. Mononoticity of an Assembly

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

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

15. Nonlinearalizable 1-Handed Assembly

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

17. 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.

18. Directional Blocking Graph (for infinitesimal translations)

19. Non-Directional Blocking Graph (for infinitesimal translations) The NDBG is a partition of a motion space into cells

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

21. Non-Directional Blocking Graph (for extended translations)

22. Extension to 3-D

23. to 3-D Extension to 3-D

24. Interference Diagram

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