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CS 326 A: Motion Planning

CS 326 A: Motion Planning. http://robotics.stanford.edu/~latombe/cs326/2003 Assembly Planning. Problem. Discriminator (42 parts): mechanical safety device designed to prevent accidental operation of a system. Levels of Problems.

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CS 326 A: Motion Planning

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  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 (1st paper)Assembly sequence planning • Tools/fixtures are taken intoaccount (2nd paper) • Entire manipulation system is taken into account  Manipulation planning(Laumond’s paper)

  4. Applications • Answer 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

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

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

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

  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(2n) 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

  14. OR Gate for uiujuk

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