Manipulability-Based Analysis of
Download
1 / 53

Agenda - PowerPoint PPT Presentation


  • 289 Views
  • Updated On :

Manipulability-Based Analysis of Cooperative Payload Transport by Robot Collectives. Chin Pei Tang ([email protected]) Advisor : Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo. Part I. Part II. Agenda. Motivation & Our System

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Agenda' - Antony


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Slide1 l.jpg

Manipulability-Based Analysis of

Cooperative Payload Transport by

Robot Collectives

Chin Pei Tang ([email protected])

Advisor : Dr. Venkat Krovi

Mechanical and Aerospace Engineering

State University of New York at Buffalo


Agenda l.jpg

Part I

Part II

Agenda

  • Motivation & Our System

  • Literature Survey & Research Issues

  • Kinematic Model

  • Twist-Distribution Analysis

  • Manipulability

  • Cooperative Systems

  • Conclusion & Future Work


Motivation l.jpg
Motivation

  • Why Cooperation?

    • Tasks are too complex

    • Distinct benefits – “Two hands are better than one”

    • Instead of building a single all-powerful system, build multiple simpler systems

    • Motivated by the biological communities

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Our system l.jpg
Our System

  • Flexible, scalable and modular framework for cooperative payload transport

  • Autonomous wheeled mobile manipulator

    • Differentially-driven wheeled mobile robots (DD-WMR)

    • Multi-link manipulator mounted on the top

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Features l.jpg
Features

Accommodate changes in the relative configuration

Using the compliant

linkage

Detect relative configuration changes

Using sensed articulation

Compensate for external disturbances

Using redundant actuation of the bases

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Research issues l.jpg
Research Issues

  • Challenges

    • Nonholonomic (wheel) / holonomic (closed-loop) constraints

    • Mobility / workspace increased (but also increases redundancy)

    • Mixture of active/passive components

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Literature survey l.jpg
Literature Survey

  • Applications of Robot Collectives

    • Collective foraging, map-building and reconnaissance

  • Coordination & Control

    • Formation Paradigm

      • Leader-follower [Desai et. al., 2001]

      • Virtual structures [Lewis and Tan, 1997]

      • Mixture of approaches [Leonard and Fiorelli, 2001],

        [Lawton, Beard and Young, 2003]

No physical interaction

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Literature survey8 l.jpg
Literature Survey

  • Physical Interaction

    • Teams of simple robots

      • box pushing [Stilwell and Bay, 1993], [Donald et. al., 1997]

      • caging [Pereira et. al., 2002], [Wang & Kumar, 2002]

    • Teams of mobile manipulators [Khatib et. al., 1996]

    • Design modifications [Kosuge et. al., 1998],

      [Humberstone & Smith, 2000]

Upenn MARS

Univ. of Alberta CRIP

NASA Cooperative Rovers

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Literature survey9 l.jpg
Literature Survey

  • Performance Measures

    • Single agent

      • Service angle [Vinogradov et. al, 1971], conditioning [Yang and Lai, 1985], manipulability [Yoshikawa, 1985], singularity [Gosselin and Angeles, 1990], dexterity [Kumar and Waldron, 1981], etc.

    • Multiple agents (Robot teams)

      • Social entropy – Measuring diversity of robots in a team (Information-theoretic) [Balch, 2000]

      • Kinetic energy – Left-invariant Riemannian metrics

        [Bhatt et. al., 2004]

  • Manipulability

    • Serial chain – Yoshikawa’s measure [Yoshikawa, 1985], condition number [Craig and Salisbury, 1982], isotropy index [Zanganeh and Angeles, 1997]

    • Closed chain [Bicchi and Prattichizza, 2000], [Wen and Wilfinger, 1999]

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Research issues10 l.jpg
Research Issues

  • Part I – Physical Cooperation

    • System level constraints

    • Motion planning strategy

  • Part II – Performance Evaluation & Optimization

    • Performance measures

    • Formulation that takes holonomic/nonholonomic constraints and active/passive joints into account

    • Different actuation schemes

    • Optimal configuration

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Mathematical preliminaries l.jpg
Mathematical Preliminaries

Homogeneous Matrix Representation

Body-fixed Twist

Similarity Transformation

Twist Matrix  TwistVector

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model l.jpg

Mobile Platform

Kinematic Model

Reaching any point

in the plane

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model13 l.jpg

Nonholonomic

Constraints

Kinematic Model

Mobile Platform

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model14 l.jpg

Nonholonomic

Constraints

Kinematic Model

Mobile Platform

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model15 l.jpg
Kinematic Model

Mobile Platform

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model16 l.jpg
Kinematic Model

Manipulator

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model17 l.jpg
Kinematic Model

Manipulator

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model18 l.jpg

Assembled

Jacobian

Kinematic Model

Twist Vectors

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Mobility verification l.jpg
Mobility Verification

  • Verify that arbitrary end-effector motion is feasible.

  • Partitioning of feasible motion distribution:

    • Actively-realizable

      (using wheeled bases)

    • Passively-accommodating

      (using articulations)

  • Configuration dependent partitioning

  • Steer the actively-realizable vector-fields

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Twist distribution analysis l.jpg

Passive Distributions

Active Distributions

Twist-Distribution Analysis

Partition the Jacobian

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Twist distribution analysis21 l.jpg

Feasibility check

Alternate constructive approach

Reciprocal

Wrench

Twist-Distribution Analysis

Can any arbitrary twist be realized using only the active distribution?

Not constructive

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Twist distribution analysis22 l.jpg

0

Twist-Distribution Analysis

Given arbitrary twist

Condition:

To understand this condition better:

Transform an arbitrary twist from {Ek} to {M}:

Achieved by aligning the forward travel direction with the direction of the velocity

The Motion Planning Strategy

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Manipulability l.jpg
Manipulability

  • Jacobian Matrix

Joint manipulation rates space

Task velocity space

Manipulability is defined as the measure of the flexibility of the manipulator to transmit the

end-effector motion in response to a unit norm motion of the rates of the active joints in the system

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Manipulability svd l.jpg
Manipulability – SVD

  • Singular Value Decomposition

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Rr manipulator example l.jpg
RR Manipulator Example

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Manipulability indices l.jpg
Manipulability Indices

  • Yoshikawa’s Measure (Volume of Ellipsoid)

  • Condition Number

  • Isotropy Index

Not able to distinguish the ratio of major/minor axes of ellipsoid

Value goes out of bound at singular position

Better numerical behavior

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Rr manipulator example27 l.jpg
RR Manipulator Example

Yoshikawa’s Measure

Condition Number

Adopted measure

Isotropy Index

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Manipulability closed loop l.jpg
Manipulability (Closed-Loop)

Generalized Coordinates

Forward Kinematic

Closed-Loop Kinematic Constraints

Not easy to compute

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Manipulability closed loop29 l.jpg
Manipulability (Closed-Loop)

Partition according to active/passive manipulation variable rates

Exact Actuation

Redundant Actuation

Manipulability Jacobian

Solved explicitly

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Cooperative model l.jpg
Cooperative Model

Team up

End-effectors need to be

re-aligned

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic model with end effector offset angle l.jpg
Kinematic Model (with end-effector offset angle)

Similarity Transformation

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Simulation l.jpg
Simulation

  • Step 1: Identify

  • Step 2: Construct manipulability Jacobian

  • Step 3: Compute isotropy index

  • Case I – MB static, R1 actuated

  • Case II – MB static, R2 actuated

  • Case III – MB moves, R1 & R2 passive

  • Case IV – MB moves, R1 locked

  • Case V – MB moves, R2 locked

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Simulation parameters 3 rrr nomenclature l.jpg
Simulation Parameters (3-RRR Nomenclature)

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case i mb static r1 actuated l.jpg
Case I: MB static R1 actuated

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case study i a l.jpg
Case Study I-A

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case study i b l.jpg
Case Study I-B

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case ii mb static r2 actuated l.jpg
Case II: MB static, R2 actuated

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case ii mb static r2 actuated38 l.jpg
Case II: MB static, R2 actuated

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case iii mb moves r1 and r2 passive l.jpg
Case III: MB moves, R1 and R2 passive

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Self motion l.jpg
Self-Motion

Feasible motions of passive joints due to the actuations but

not violating constraints

Feasible self-motion when all the active joints locked

Underconstrained

Lock this number of joints

Dimension of self-motion manifold

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Self motion41 l.jpg
Self-Motion

Lock this number of joints

  • 2 Cases:

  • Locking R1

  • Locking R2

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case iv mb moves r1 locked l.jpg
Case IV: MB moves, R1 locked

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case iv mb moves r1 locked43 l.jpg
Case IV: MB moves, R1 locked

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case v mb moves r2 locked l.jpg
Case V: MB moves, R2 locked

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case v mb moves r2 locked45 l.jpg
Case V: MB moves, R2 locked

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case study configuration optimization l.jpg

Subject to: Closed-Kinematic Loop Constraints

Case Study – Configuration Optimization

Constrained

Optimization

Problem

Unconstrained

Optimization

Problem

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Configuration optimization case iv l.jpg
Configuration Optimization – Case IV

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Configuration optimization case v l.jpg
Configuration Optimization – Case V

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Conclusion l.jpg
Conclusion

  • Modular Formulation

  • Motion-Distribution Analysis

  • Evaluation of Performance Measures

  • Manipulability Jacobian Matrix Formulation

  • Effect of Different Actuation Schemes

  • Optimal Configuration Determination

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Future work l.jpg
Future Work

  • Global Manipulability

  • Force Manipulability

  • Singularity Analysis

  • Decentralized Control

  • Redundant Actuation

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Thank you l.jpg

Thank You!

Acknowledgments:

Dr. V. Krovi

Dr. T. Singh

Dr. J. L. Crassidis

& all the audience…




ad