Putting the Turing into Manufacturing: Algorithmic Automation and Recent Developments in Feeding and Fixturing Ken Goldberg, UC Berkeley.

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Presentation transcript:

Putting the Turing into Manufacturing: Algorithmic Automation and Recent Developments in Feeding and Fixturing Ken Goldberg, UC Berkeley

The Turing Machine, 1936 Precise vocabulary: 0, 1 Class of primitive operations: Read, Write, Shift Left, Shift Right Well Formed Sequences Correctness, Completeness Equivalence, Complexity

Algorithmic Automation: Define Admissible Inputs Define Admissible Operations Output: all solutions or negative report Complexity as function of input size

Two Examples Part Feeding Part Fixturing and Holding

Putting the Turing into Manufacturing Automation Algorithmic Part Feeding –2D Polygonal Parts –3D Polyhedral Parts –Traps –Blades Algorithmic Fixturing –Modular Fixtures –Unilateral Fixtures –D-Space and Deform Closure Related Work and Open Problems

Solution: Kinematically Yielding Gripper ( US Patent 5,098,145)

Example: resulting 3-step plan

Theorem (Completeness): A sensorless plan exists for any polygonal part. Theorem (Correctness): The algorithm will always find the shortest plan. Theorem (Complexity): For a polygon of n sides, the algorithm runs in time O(n 2 ) and finds plans of length O(n). Extensions: Stochastically Optimal Plans Extension to Non-Zero Friction Geometric Eccentricity and constant time result (van der Stappen) Pulling with point jaws inside concavities, Sorting with wedges

1770: Interchangeable Parts 1910: Assembly Lines 2030: Algorithmic Automation