1. CS 326A: Motion Planning ai.stanford.edu/~latombe/cs326/2007/index.htm Criticality-Based Motion Planning (2)

2. Topics  Target finding  Information (or belief) state/space  Part orientation  Sensorless reduction of uncertainty  Assembly planning  Path space  Stereotaxic radiosurgery

3. Assembly Planning 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. 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. 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:

7.  With translations only  monotone  two-handed  With translations only  non-monotone, 2-handed  monotone, 3-handed  With general motions  monotone, 2-handed Various “Interesting” Cases

8. 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

10. OR Gate for u i  u j  u k

11. 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

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