1 Contact Analysis Contact Analysis How would you compute a - PDF document

Assembly Planning 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 Assembly Sequence Planning Applications � Answers to questions such as: � Very constrained goal state, but • How many parts need to be removed to unconstrained initial state extract a given part P? � Disassembly planning � Disassembly planning • Can the product be assembled by adding a Can the product be assembled by adding a single part at a time? • How much can the assembly process be parallelized? � Large number of dofs, but simple paths � Design for manufacturing and servicing � Design of manufacturing systems � 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? Directional Blocking Graph Planning Approaches (for infinitesimal translations) � Generate-and-test � Generate and test plus caching � Generate-and-test plus caching � Non-directional blocking graph � Interference diagram R.H. Wilson and J.C. Latombe. Geometric Reasoning about Mechanical Assembly. Artificial Intelligence, 71(2):371-396, 1995. Directional Blocking Graph Directional Blocking Graph (for infinitesimal translations) (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 Directional Blocking Graph (for infinitesimal translations) (for infinitesimal translations) How do you see that this is a How do you see that this is a potentially good direction? potentially good direction? Motion Space Non-Directional Blocking Graph (for infinitesimal translations) (for infinitesimal translations) The motion space is the space The NDBG is a partition of a of all directions of motion motion space into cells (points and arcs) It does not say which objects are moving S 1 What happens when one switches from one cell to the next? Non-Directional Blocking Graph Non-Directional Blocking Graph (for infinitesimal translations) (for extended translations) How would you compute the NDBG? � Assembly sequencing in polynomial time 3

Extension to 3-D Sketch of an Assembly Planner (for infinitesimal or extended translations) � Plan a sequence that is valid for extended translations � If one is found, return it � Else plan a sequence that is valid for � El l th t i lid f infinitesimal translations What is the motion space? � If none is found then return failure • Else use a general motion planner to validate each step of the sequence Extension to 3-D More Extensions (for infinitesimal or extended translations) � 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) Munich University (F. Schwarzer) Number of Hands Mononoticity of an Assembly An assembly that requires n hands 5

Mononoticity of an Assembly Example Assemblies � With translations only � With translations only • monotone • non-monotone, 2-handed • two-handed • monotone, 3-handed � With general motions • monotone, 2-handed Nonlinearalizable 1-Handed Example Assemblies Assembly � With translations only � With translations only • monotone • non-monotone, 2-handed • two-handed • monotone, 3-handed � With general motions • monotone, 2-handed 6