cs 326 a: motion planning
DESCRIPTION
CS 326 A: Motion Planning. http://robotics.stanford.edu/~latombe/cs326/2003 Assembly Planning. Problem. Discriminator (42 parts): mechanical safety device designed to prevent accidental operation of a system. Levels of Problems. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/1.jpg)
CS 326 A: Motion PlanningCS 326 A: Motion Planning
http://robotics.stanford.edu/~latombe/cs326/2003
Assembly PlanningAssembly Planning
![Page 2: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/2.jpg)
ProblemProblemDiscriminator (42 parts): mechanical safety device designed to prevent accidental operation of a system.
![Page 3: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/3.jpg)
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)
![Page 4: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/4.jpg)
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
![Page 5: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/5.jpg)
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
![Page 6: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/6.jpg)
Set of Assembly Sequences as Set of Assembly Sequences as an AND/OR Graphan AND/OR Graph
[L. Homem de Mello and Sanderson]
![Page 7: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/7.jpg)
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:
![Page 8: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/8.jpg)
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
![Page 9: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/9.jpg)
Planning ApproachesPlanning Approaches Generate-and-test
Generate-and-test plus caching
Non-directional blocking graph(limited to single-step motions)
Interference diagram
![Page 10: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/10.jpg)
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
![Page 11: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/11.jpg)
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
![Page 12: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/12.jpg)
Assembly Sequences Assembly Sequences Generated Using NBBGsGenerated Using NBBGs
Sandia National Labs (R. Wilson) Munich University (F. Schwarzer)
![Page 13: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/13.jpg)
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
![Page 14: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/14.jpg)
![Page 15: CS 326 A: Motion Planning](https://reader036.vdocument.in/reader036/viewer/2022062304/56813723550346895d9eb12c/html5/thumbnails/15.jpg)
OR Gate for uOR Gate for uiiuujjuukk