1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2003 Assembly Planning

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

3. Levels of Problems  Parts are assumed free-flying (1 st paper)  Assembly sequence planning  Tools/fixtures are taken into account (2 nd paper)  Entire manipulation system is taken into account  Manipulation planning (Laumond’s paper)

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, but unconstrained initial state  Disassembly planning 2. Many dofs, but simple paths  Motion space

6. Set of Assembly Sequences as an AND/OR Graph [L. Homem de Mello and Sanderson]

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 remove:

8. 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

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

10. Non-Directional Blocking Graphs  NDBG for infinitesimal (local) translations No assembly sequence  no solution  NDBG for extended translations Assembly sequence  solution Incremental construction of NDBG

11. Criticality-Based Motion Planning C-space, Motion space, … Define property P Find where P changes  geometric arrangement: - critical curves/surfaces, - regular regions (cells) Approach is practical only in low-dimensional spaces: - Complexity of the arrangement - Sensitivity to floating point errors

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

13. 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

15. OR Gate for u i  u j  u k