1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2002 Assembly Planning

2. Problem

3. Levels of Problems  Parts are assumed free-flying (1 st paper)  Assembly sequence planning  Tools/fixtures are taken into account (2 nd paper + paper by Romney)  Entire manipulation system is taken into account (next class)  Manipulation planning (movable objects)

4. 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

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

6. Assembly Sequences as an AND/OR Graph

7. Planning Approaches  Generate-and-test Contact analysis

8. Planning Approaches  Generate-and-test Contact analysis

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

10. Various Cases Multi-hand: An assembly on n parts may require up to n hands for its (dis-)assembly Non-monotonic 2-handed assembly: No single part can be added or remove:

11. Complexity of Partitioning  Assembly partitioning problem: Given a collection of non-overlapping polygons, decide if there is a proper subcollection of them that can be removed as a rigid body without colliding with the other polygons.  This problem is NP-complete

12. Application of NDBG  -part Hughes AIM-9X air-to-air missile (SANDIA National Labs)