Putting the Turing into Manufacturing:

Algorithmic Automation and Recent Developments in Feeding and FixturingKen Goldberg, UC Berkeley

The Turing Machine, 1936

Precise vocabulary: 0, 1Class of primitive operations:

Read, Write, Shift Left, Shift RightWell Formed SequencesCorrectness, CompletenessEquivalence, Complexity

Algorithmic Automation:

Define Admissible Inputs Define Admissible OperationsOutput: all solutions or negative reportComplexity 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:

KinematicallyYielding 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(n2) 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