1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2004 Assembly Planning

2. Problem Discriminator (42 parts): mechanical safety device designed to prevent accidental operation of a system.

3. Another Example

4. 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

5. 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

6. Assembly Sequence Planning Example of a multi-robot coordination problem, but … 1. Very constrained goal state, but unconstrained initial state  Disassembly planning 2. Many dofs, but simple paths  Motion space

7. Various “Interesting” Cases Multi-hand: An assembly on n parts may require up to n hands for its (dis-)assembly [Natarajan] Non-monotonic 2-handed assembly: No single part can be added or removed:

8. Examples  With translations only  monotone  two-handed  With translations only  non-monotone, 2-handed  monotone, 3-handed  With general motions  monotone, 2-handed

9. Complexity of Partitioning  Assembly partitioning problem: - Given a set of non-overlapping polygons, - Decide if a proper subset of them can be removed as a rigid body without colliding with the other polygons.  This problem is NP-complete

11. OR Gate for u i  u j  u k

12. Planning Approaches  Generate-and-test: Hypothesize a subassembly and test if it can separated from the rest using contact analysis …  But … exponential number of subassemblies: O(2 n ) subassemblies, but only two pairs can be separated

13. Planning Approaches  Generate-and-test  Generate-and-test plus caching  Non-directional blocking graph (limited to single-step motions)  Interference diagram

14. Directional Blocking Graphs  Directional blocking graphs for infinitesimal (local) translations Property P: Blocking graph

15.  Assembly sequencing in polynomial time Non-Directional Blocking Graph The NDBG is a partition of a motion space into cells

16. Extension to 3-D

18. Other Extensions  Generalized infinitesimal motions in 2-D and 3-D  Extended translations  Multiple translations (interference diagram)

19. Applications  Answer questions such as: oHow many parts need to be removed to extract a given part P? oCan the product be assembled by adding a single part at a time? oHow much can the assembly processed by parallelized?  Design for manufacturing and servicing  Design of manufacturing systems