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Chin Pei Tang (chintang@eng.buffalo) Advisor : Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo - PowerPoint PPT Presentation


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

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Manipulability-Based Analysis of

Cooperative Payload Transport by

Robot Collectives

Chin Pei Tang (chintang@eng.buffalo.edu)

Advisor : Dr. Venkat Krovi

Mechanical and Aerospace Engineering

State University of New York at Buffalo


Part I

Part II

Agenda

  • Motivation & Our System

  • Literature Survey & Research Issues

  • Kinematic Model

  • Twist-Distribution Analysis

  • Manipulability

  • Cooperative Systems

  • Conclusion & Future Work


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

  • 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

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

  • 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

  • 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 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 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 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

Homogeneous Matrix Representation

Body-fixed Twist

Similarity Transformation

Twist Matrix  TwistVector

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Mobile Platform

Kinematic Model

Reaching any point

in the plane

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Nonholonomic

Constraints

Kinematic Model

Mobile Platform

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Nonholonomic

Constraints

Kinematic Model

Mobile Platform

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic Model

Mobile Platform

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic Model

Manipulator

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic Model

Manipulator

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Assembled

Jacobian

Kinematic Model

Twist Vectors

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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


Passive Distributions

Active Distributions

Twist-Distribution Analysis

Partition the Jacobian

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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


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

  • 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

  • Singular Value Decomposition

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


RR Manipulator Example

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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 Example

Yoshikawa’s Measure

Condition Number

Adopted measure

Isotropy Index

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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-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

Team up

End-effectors need to be

re-aligned

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Kinematic Model (with end-effector offset angle)

Similarity Transformation

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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)

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case I: MB static R1 actuated

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case Study I-A

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case Study I-B

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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 actuated

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case III: MB moves, R1 and R2 passive

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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-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

Generalized Coordinates

Forward Kinematics

General Constraints

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Case IV: MB moves, R1 locked

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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 locked

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Configuration Optimization – Case V

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


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

  • Global Manipulability

  • Force Manipulability

  • Singularity Analysis

  • Decentralized Control

  • Redundant Actuation

Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion


Thank You!

Acknowledgments:

Dr. V. Krovi

Dr. T. Singh

Dr. J. L. Crassidis

& all the audience…


Twist Matrix as Velocity Operator


Single Module Payload Transport


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