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Assembly Planning “A Framework for Geometric Reasoning About Tools in Assembly” Randall H. Wilson Presentation by Adit Koolwal & Julie Letchner.

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Presentation on theme: "Assembly Planning “A Framework for Geometric Reasoning About Tools in Assembly” Randall H. Wilson Presentation by Adit Koolwal & Julie Letchner."— Presentation transcript:

1 Assembly Planning “A Framework for Geometric Reasoning About Tools in Assembly” Randall H. Wilson Presentation by Adit Koolwal & Julie Letchner

2 Overview Formal categorization of tools to allow reasoning about their use Does: determine whether or not there is space to use a tool Does not: Consider space for approach/manipulation Determine what tools to use Determine order of assembly of parts

3 Canonical Tools Formal definition of a tool & its usage Three components: Relative time of application Use volume Placement constraints A single physical tool can map to multiple canonical tools

4 Relative Time of Application Assume each tool application mates subassemblies S 1 and S 2 into a single subassembly S Notation: S = S 1 U S 2 S 1 S 2 S

5 Relative Time of Application Pre-tools: applied to S 1 Example: glue gun Post-tools: applied to S = S 1 U S 2 Example: welder, inspection camera In-tools: applied to S 1 and S 2 under relative motion Example: wrench, hammer Can often be approximated as pre- or post-tools

6 Use Volume Volume of space required to apply a given tool Fixed with respect to canonical reference frame Doesn’t include space required for approach/manipulation x y Use volume & canonical reference frame for a 45 degree wrench rotation

7 Placement Constraints Restrictions on the placement of the use volume Robotics framework: Treat the tool as a robot and the assembly parts as obstacles Model placement options as an m- dimensional configuration space 0<= m <= 4

8 Example: Wrench Time of application: in-tool Approximate as: post-tool Use volume: angle swept while turning wrench Dimensionality: 1 (angle at which sweep begins)

9 Example: Screwdriver Time of application: in-tool Approximate as: post-tool Use volume: volume of screwdriver Dimensionality: 0 What happens if the screwdriver need not be absolutely vertical relative to the screw’s axis?

10 Tool Applications Target Operation for a tool is an assembly requiring the use of that tool Target Part Set of an operation is the list of parts involved in an operation Example wrench target part set: {bolt, partX} O is a target operation for a tool with target part set T iff: T  S ^ T  S 1 ^ T  S 2

11 Tool Feasibility A Tool can be applied when: Use volume U obeys placement constraints, and doesn’t intersect any other parts Use volumes can be represented in a C-space All configurations exist in a 6-dimensional configuration space The C-space obstacle O u (P i ) represents the set of configurations where U intersects part P i Configuration C is collision-free if and only if C satisfies all placement constraints and lies outside all C-obstacles

12 Tool Feasibility Searching for use volumes takes polynomial time Searching for collision-free use volumes is polynomial in..  the total number of surfaces describing the parts,  the use volume, and  all placement constraints

13 Tool Feasibility Searching for use volumes takes polynomial time This assumes surfaces are all algebraic of bounded degree For 0-DOF tools, only one configuration satisfies placement constraints, so we need only check for intersection between use volume and parts

14 Preprocessing Steps Preprocessing minimizes repeated computation In preprocessing we compute interference sets For each configuration, a tool will intersect a set of parts We compute all interference sets. The tool application in subassembly S is feasible if and only if S has no parts from at least one of the interference sets.

15 Preprocessing Steps {C} {0} {A} {A,B} {B} C B A Calculating Interference Sets P i is in the interference set for C if and only if C Є O u (P i ). The boundaries of C-obstacles sub-divide the C-space into cells. The number of cells is polynomial in the number of surfaces.

16 Non-Directional Blocking Graphs NDBGs model the trajectory space of an assembly Constructing an NDBG (part one):  For an assembly A = {P 1, P 2, … P n } we consider all trajectories t  Each node is a part P i Є A. Arcs between nodes P i and P j indicate that P i will collide into P j when moved along t P4 P2 P5 P1P3

17 Non-Directional Blocking Graphs NDBGs model the trajectory space of an assembly Constructing an NDBG (part two):  Look for a subassembly S 1 which can move along t without colliding into parts in S 2 = A/S 1  The NDBG of A subdivides the space of all trajectories into cells where, in a given cell, each t has the same blocking graph P4 P2 P5 P1P3P1P3 P2 P5P4

18 Non-Directional Blocking Graphs Inclusion of Target Part Sets for Post-tools Post-tool applications with target part set T impose constraints on subassemblies S 1 and S 2 of A:  If T is not a subset of S 1 or S 2, its volume must be in A  If T’s volume is not in A, then any subassembly of A must include ALL or NONE of the parts in T

19 Non-Directional Blocking Graphs Inclusion of Target Part Sets for Post-tools To include T in a blocking graph, add bidirectional arcs between every pair of parts in T We can search for removable subassemblies that satisfy post- tool constraints in polynomial time by looking for cells whose blocking graphs are weakly connected

20 Experimentation Tool Feasibility Only 0-DOF tool feasibility has been implemented to date Testing Geometric Tool Constraints Tool constraints were tested on three assemblies, including the “discriminator,” which requires 55 laser spot welds, 8 uses of a Phillips screwdriver, 4 uses of a hex L-wrench, 4 subassembly test, and one use of pliers Archimedes found a tool level assembly plan in 50 seconds on an SGI 100 MHz R4000 Indigo II Extreme Workstation

21 Conclusions Framework can ultimately represent many tools Framework can support multiple simultaneous tool applications Future Extensions Allow for parameterized placement constraints as opposed to assuming fixed placement constraints Allow for parameterized use volumes Handle tool collisions


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