Singla E., Performance Indices for Robotic Arms

7/28/2019 Singla E., Performance Indices for Robotic Arms

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IIT Ropar

Talk @ Thapar University, March 23rd, 2013

Performance Indices for Robotic arms

Ekta [email protected]
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Introduction: Robotic Arms

Robotics

Applied SciencesFiction

Elbow Legs

Fingers14th Century

Arms

Brain --- Controller

Human senses --- Sensers

Muscles --- actuators

Arm --- Manipulator


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Robotic arms: Series of segments connected together through

sliding or revolute joints --- Serial Manipulators.

TSL 2

TSL 1

TSL

3

TSL 4

Introduction: Robotic Arms

IIT Ropar


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Customized Manipulation

Given a work cell --- design a manipulator

- work efficiently at the desired locations

- while avoiding the obstacles


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Performance Indices

Manipulator design: Determination of design parameters satisfying certain

requirements.

Decision of design variables Expectations from the manipulator

to be designed

Performance Measures

Optimal robot design

Motion planning strategies

Measures for manipulator analysis

Efficiency comparison

Posture planning


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Kinematic characteristics: Usual performance criteria

Largest work volume

Minimum Singularities

Maximum collision avoidance

Highly dexterous

- - - - - - - -

-- - - - - - -


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Manipulator Work volume

Largest work volume



Highly dexterous

- - - - - - - -

-- - - - - - -

Challenge: Computingwork volume!


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Introducing Manipulator Jacobian

Largest work volume



Highly dexterous

- - - - - - - -

-- - - - - - -

The matrix representing the mapping between end-

effector velocity of a manipulator to its joint rates as:

Jx

x

x

)(

f

)f(

=

=

=

Joint variables

End-effector coordinates

End-effector

Jacobian


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Introducing Manipulator Jacobian

Largest work volume



Highly dexterous

- - - - - - - -

-- - - - - - -

Local Inversions

21

21 ,mm

RR rr

{ } .)(),(

1111

2,1

n

n

iii

R

f

+=

=

=

yyJJIrJ

r

Global inversions

Performance index of integral type:

dtt

t

t=1

0

),p(2 r--- Use of Variational Methods


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Manipulator Singularities

Largest work volume



Highly dexterous

- - - - - - - -

-- - - - - - -

--- Workspace Boundary Singularity

--- Workspace Interior Singularities

SignificanceJacobian Condition Number

min

max

=


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Collision detection and avoidance

Largest work volume



Highly dexterous

- - - - - - - -

-- - - - - - -

What if only the bounding boxes collide?


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Collision detection and avoidance

Largest work volume



Highly dexterous

- - - - - - - -

3D models

(triangulated mesh)

Work cell

Robot links

0)( = Dg x

Distance between two objects(Use of PQP, collide, bullet etc)

Quantitative measure, D

Positive (distance between the objects),

in case of no collision

Negative (penetration distance), in case

of collision.

Penetration Calculation


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Dexterity / Manipulability

Largest work volume



Highly dexterous

- - - - - - - -

-- - - - - - -

Measure of Manipulability (MOM)

{ })()(det JJ TM =

--- works for both non-redundant and

redundant robotic arms


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Redundancy in degrees of freedom

Kinematic r edundantindicates that the

number of degrees of freedom exceeds

the minimal number required to perform

in a particular task space.

Why to opt for Redundancy?

Obstacle avoidance

Increase in manipulability

Singularity avoidance

Improve fault tolerance

Local/global conversions


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Approaches based on Jacobian

Klein & Blaho

Comparison dexterity measures

Gosselin

Jacobian invariant to scaling

Angeles

Isotropic design conditions

Gonzales & AngelesKinematic synthesis,

prescribed Jacobian

Kircanski

Optimal design conditions,

Joint angles and link length

Ranjbaran

Formulating opti. problem

(90s 2000)

Stocco

GII (Global Isotropic Index)

We have given up the idea of finding a

globally optimal robot design, given a

number of degrees of freedom. - 1996

Jacobian

Condition Number

Jacobian Inverse

Minimum Singular Value

Jacobian rates

Extended Jacobian


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Usually used performance indices

Manipulability

Minimum Singular Value

Joint Range availability

Global Isotropy Index

Condition Number

Workspace based

Global torque minimization

Local Performance Indices

Global Performance Indices

Global velocity/acceleration index

Maximum workspace

Dexterity

Maximum safety

Well-connectedworkspace


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Usually used performance indices

Minimum Joint movement

Minimum collision avoidance

Design

Motion Planning

Minimum link-lengths

Maximum conditioning

Mayorga

Rate of change of isotropy condition

Kucuk and Bingul

Workspace volume 3D

Badescu et al

Three criteria:

Workspace volume (Monte Carlo

Condition number

Global conditioning)

Wunderlich

Minimum degrees of freedom

Carbone et alMultiple objective problem

(2000 --- 2010)

Oetomo et al

Collection of all achievable points


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RoboGin: Robot Margin

RoboGinP: The minimum RoboGinC of the manipulator, while traversing the path.

Focus: The capability of the manipulator to operate between the specified locations

in best sense.

RoboGin


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Compute: Robot Margin

Constraints Handling

Obstacles avoidanceLimits to design variables

Kinematic equations (Reaching all

TSLs)

Simulated Annealing

Objective : RoboGinPMaximizing the minimum margin between the robot and the obstacles

along the paths

For each new solution:

Compute the inverse

kinematics for each TSL..

Develop the paths between

the TSLs.

Compute the CRITICAL

DISTANCE.


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Acknowledgements

Thanks to the organizers

Thank you!

Singla E., Performance Indices for Robotic Arms

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