University of Pennsylvania 1 GRASP A Hierarchical Design Methodology for Multibody Systems with Frictional Contacts Vijay Kumar GRASP Lab Mechanical Engineering and Applied Mechanics Computer and Information Science University of Pennsylvania Jong-Shi Pang Mathematical Sciences Rennselaer Polytechnic Institute Peng Song Mechanical Engineering Rutgers University Bharath Mukundakrishnan GRASP Laboratory University of Pennsylvania Jeffrey Trinkle Computer Science Rennselaer Polytechnic Institute Jonathan Fink GRASP Lab, Penn ECS, RPI Joint work with Steve Berard Computer Science Rennselaer Polytechnic Inst.
37
Embed
A Hierarchical Design Methodology for Multibody Systems ...siconos.inrialpes.fr/SiCoNosDaVinci/Friday/Slides/Kumar.pdf · A Hierarchical Design Methodology for Multibody Systems with
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
University of Pennsylvania 1GRASP
A Hierarchical Design Methodology forMultibody Systems with Frictional Contacts
Vijay Kumar
GRASP LabMechanical Engineering and Applied Mechanics
Computer and Information ScienceUniversity of Pennsylvania
Jong-Shi Pang
Mathematical SciencesRennselaer Polytechnic Institute
Peng Song
Mechanical Engineering Rutgers University
Bharath Mukundakrishnan
GRASP LaboratoryUniversity of Pennsylvania
Jeffrey Trinkle
Computer ScienceRennselaer Polytechnic Institute
Jonathan Fink
GRASP Lab, PennECS, RPI
Joint work with
Steve Berard
Computer ScienceRennselaer Polytechnic Inst.
University of Pennsylvania 2GRASP
1. Decentralized Multirobot Manipulation
Motion plans derived from geometric models
Can we generalize to dynamic models?
Pereira, Campos and Kumar, WAFR 02
University of Pennsylvania 3GRASP
2. Part Feeding, Assembly
Design with geometric and kinematic models is possible.
Dynamic models are necessary.
[Boothroyd, 1968]
[Kraus, 2001]
University of Pennsylvania 4GRASP
3. Micro Manipulation
100 µ dia probe attached to10g load cell
0.4mm x 0.8mm part assembly
Configuration AConfiguration B
Test Fixture
2 mm
1.5 mm
University of Pennsylvania 5GRASP
Design Process or Plan TaskDynamical System
Intermittent contacts Contact state transitions Multiple contacts
Fundamental difficulties Static indeterminacy with traditional models (jamming,
wedging) Whitney, Dupont
No consistent models for frictional impacts Goldsmith, Pfeiffer, Keller, Brach, Wang and Mason, Stronge, Chatterjee and Ruina
No unified treatment for design and planning
University of Pennsylvania 6GRASP
Outline1. Background
Contact models Normal and tangential compliance Frictional contacts Time-stepping methods
2. Hierarchical Approach Models at different levels of fidelity Abstraction and model reduction Example
3. Algorithms for design optimization Randomized algorithms Time-stepping algorithms
4. Case Study: Part Feeder Modeling Iterative design process
University of Pennsylvania 7GRASP
Systems with Frictional Contacts
Friction T
O
c
T
O
cT
cO
λF
λF
µλN
University of Pennsylvania 8GRASP
Compliant Contact Models
UndeformedShell
ViscoelasticLayer
RigidCore
RigidCore
DeformedShell
N N
T
TδNδNϕ
Tϕslip
SRiTiTiTiTiTiT
iNiNiNiNiNiN
nnigf
gf
+=+=+=
,,1),()(
),()(
,,,,,,
,,,,,,
L&
&
δδδλ
δδδλ
Gross motion
Fine deformation
University of Pennsylvania 9GRASP
More Generally… Elastic Bodies
Linear Elastic,
Counterformal
Contacts
nØ i
niδA
Bdeformed
undeformed
University of Pennsylvania 10GRASP
Advantages of Compliant Contact Model
Proof of uniqueness and existence Contact forces can always be determined More realistic friction model
Tangential compliance Gross slip is preceded by small local deformations Hysteresis
Disadvantages Identification of parameters Computational time