CS 326 A: Motion PlanningProblemLevels of ProblemsApplicationsAssembly Sequence PlanningAssembly Sequences as an AND/OR GraphPlanning ApproachesSlide 8Slide 9Various CasesComplexity of PartitioningApplication of NDBGCS 326 A: Motion CS 326 A: Motion PlanningPlanninghttp://robotics.stanford.edu/~latombe/cs326/2002Assembly PlanningAssembly PlanningProblemProblemLevels of ProblemsLevels of ProblemsParts are assumed free-flying (1st paper)Assembly sequence planning Tools/fixtures are taken intoaccount (2nd paper + paper by Romney)Entire manipulation system is taken into account (next class) Manipulation planning (movable objects)ApplicationsApplicationsAnswer 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 servicingDesign of manufacturing systemsAssembly Sequence Assembly Sequence PlanningPlanningExample of a multi-robot coordination problem, but …1. Very constrained goal state and unconstrained initial state Disassembly planning 2. Large number of dofs, but simple paths Motion spaceAssembly Sequences as Assembly Sequences as an AND/OR Graphan AND/OR GraphPlanning ApproachesPlanning ApproachesGenerate-and-testContact analysisPlanning ApproachesPlanning ApproachesGenerate-and-testContact analysisPlanning ApproachesPlanning ApproachesGenerate-and-testGenerate-and-test plus cachingNon-directional blocking graph(limited to single-step motions)Interference diagramVarious CasesVarious CasesMulti-hand:An assembly on n parts may require up to n hands for its(dis-)assemblyNon-monotonic 2-handed assembly:No single part can beadded or remove:Complexity of PartitioningAssembly partitioning problem:Given a collection of non-overlapping polygons, decide if there is a proper subcollection of them that can be removed as a rigid body without colliding with the other polygons.This problem is NP-completeApplication of NDBGApplication of NDBG22-part Hughes AIM-9X -part Hughes AIM-9X air-to-air missile air-to-air missile (SANDIA National Labs) (SANDIA National
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