CS 326 A: Motion PlanningCS 326 A: Motion Planning

http://robotics.stanford.edu/~latombe/cs326/2003

Assembly PlanningAssembly Planning

ProblemProblemDiscriminator (42 parts): mechanical safety device designed to prevent accidental operation of a system.

Levels of ProblemsLevels of Problems Parts are assumed free-flying (1st paper)

Assembly sequence planning Tools/fixtures are taken into

account (2nd paper)

Entire manipulation system is taken into account Manipulation planning(Laumond’s paper)

ApplicationsApplications

Answer questions such as:o How many parts need to be removed to

extract a given part P?o Can the product be assembled by adding

a single part at a time?o How much can the assembly processed

by parallelized?

Design for manufacturing and servicing

Design of manufacturing systems

Assembly Sequence Assembly Sequence PlanningPlanning

Example of a multi-robot coordination problem, but …

1.Very constrained goal state, but unconstrained initial state Disassembly planning

2.Many dofs, but simple paths Motion space

Set of Assembly Sequences as Set of Assembly Sequences as an AND/OR Graphan AND/OR Graph

[L. Homem de Mello and Sanderson]

Various “Interesting” CasesVarious “Interesting” CasesMulti-hand:

An assembly on n parts may require up to n hands for its(dis-)assembly [Natarajan]

Non-monotonic 2-handed assembly:

No single part can beadded or remove:

Planning ApproachesPlanning Approaches Generate-and-test: Hypothesize a subassembly

and test if it can separated from the rest using contact analysis …

But … exponential number of subassemblies: O(2n) subassemblies, but only two pairs can be separated

Planning ApproachesPlanning Approaches Generate-and-test

Generate-and-test plus caching

Non-directional blocking graph(limited to single-step motions)

Interference diagram

Non-Directional Blocking Non-Directional Blocking GraphsGraphs

NDBG for infinitesimal (local) translations

No assembly sequence no solution NDBG for extended translations

Assembly sequence solution

Incremental construction of NDBG

Criticality-Based Motion Criticality-Based Motion PlanningPlanning

• C-space, Motion space, …• Define property P• Find where P changes geometric arrangement: - critical curves/surfaces, - regular regions (cells)

Approach is practical only in low-dimensional spaces:- Complexity of the arrangement- Sensitivity to floating point errors

Assembly Sequences Assembly Sequences Generated Using NBBGsGenerated Using NBBGs

Sandia National Labs (R. Wilson) Munich University (F. Schwarzer)

Complexity of PartitioningComplexity of Partitioning

Assembly partitioning problem:

- Given a set of non-overlapping polygons,

- Decide if a proper subset of them can be

removed as a rigid body without colliding

with the other polygons.

This problem is NP-complete

OR Gate for uOR Gate for uiiuujjuukk