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Assembly Planning Levels of Problems Parts are assumed free-flying ÆAssembly sequence planning Tools/fixtures are taken into account Entire manipulation system is taken into account Æ Manipulation planning Applications Answers to 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 process be parallelized? Design for manufacturing and servicing Design of manufacturing systems Assembly Sequence Planning Very constrained goal state, but unconstrained initial state Æ Disassembly planning Large number of dofs, but simple paths Æ Motion space Set of Assembly Sequences as an AND/OR Graph 1 Contact Analysis Contact Analysis How would you compute a direction of motion for the T-shaped object? Planning Approaches Directional Blocking Graph (for infinitesimal translations) Generate-and-test Generate Generate-and-test and test plus caching Non-directional blocking graph Interference diagram Directional Blocking Graph (for infinitesimal translations) R.H. Wilson and J.C. Latombe. Geometric Reasoning about Mechanical Assembly. Artificial Intelligence, 71(2):371-396, 1995. Directional Blocking Graph (for infinitesimal translations) R.H. Wilson and J.C. Latombe. Geometric Reasoning about Mechanical Assembly. Artificial Intelligence, 71(2):371-396, 1995. 2 Directional Blocking Graph (for infinitesimal translations) How do you see that this is a potentially good direction? Motion Space (for infinitesimal translations) The motion space is the space of all directions of motion It does not say which objects are moving Directional Blocking Graph (for infinitesimal translations) How do you see that this is a potentially good direction? Non-Directional Blocking Graph (for infinitesimal translations) The NDBG is a partition of a motion space into cells (points and arcs) S1 What happens when one switches from one cell to the next? Non-Directional Blocking Graph (for infinitesimal translations) Æ Assembly sequencing in polynomial time Non-Directional Blocking Graph (for extended translations) How would you compute the NDBG? 3 Sketch of an Assembly Planner Plan a sequence that is valid for extended translations If one is found, return it 9El plan 9Else l a sequence that th t is i valid lid for f infinitesimal translations 9If none is found then return failure • Else use a general motion planner to validate each step of the sequence Extension to 3-D (for infinitesimal or extended translations) Extension to 3-D (for infinitesimal or extended translations) What is the motion space? More Extensions What would be the motion space if we allowed parts to both translate and rotate? What about multi-step motions, e.g., along d1 for distance l1, then d2 for distance l2, ...? How would you do for extended translations? Contact Analysis 4 More Extensions Interference Diagram What would be the motion space if we allowed parts to both translate and rotate? What about multi-step motions, e.g., along d1 for distance l1, then d2 for distance l2, ...? Interference Diagram Assembly Sequences Generated Using NDBGs Sandia National Labs (R. Wilson) Number of Hands Munich University (F. Schwarzer) Mononoticity of an Assembly An assembly that requires n hands 5 Mononoticity of an Assembly Example Assemblies With translations only With translations only • monotone • two-handed • non-monotone, 2-handed • monotone, 3-handed With general motions • monotone, 2-handed Example Assemblies Nonlinearalizable 1-Handed Assembly With translations only With translations only • monotone • two-handed • non-monotone, 2-handed • monotone, 3-handed With general motions • monotone, 2-handed 6
