7/28/2019 Singla E., Performance Indices for Robotic Arms
1/20
IIT Ropar
Talk @ Thapar University, March 23rd, 2013
Performance Indices for Robotic arms
Ekta [email protected]
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2/20
IIT Ropar
Introduction: Robotic Arms
Robotics
Applied SciencesFiction
Elbow Legs
Fingers14th Century
Arms
Brain --- Controller
Human senses --- Sensers
Muscles --- actuators
Arm --- Manipulator
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3/20
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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4/20
IIT Ropar
Customized Manipulation
Given a work cell --- design a manipulator
- work efficiently at the desired locations
- while avoiding the obstacles
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5/20
IIT Ropar
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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6/20
IIT Ropar
Kinematic characteristics: Usual performance criteria
Largest work volume
Minimum Singularities
Maximum collision avoidance
Highly dexterous
- - - - - - - -
-- - - - - - -
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7/20
IIT Ropar
Manipulator Work volume
Largest work volume
Minimum Singularities
Maximum collision avoidance
Highly dexterous
- - - - - - - -
-- - - - - - -
Challenge: Computingwork volume!
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8/20
IIT Ropar
Introducing Manipulator Jacobian
Largest work volume
Minimum Singularities
Maximum collision avoidance
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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9/20
IIT Ropar
Introducing Manipulator Jacobian
Largest work volume
Minimum Singularities
Maximum collision avoidance
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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10/20
IIT Ropar
Manipulator Singularities
Largest work volume
Minimum Singularities
Maximum collision avoidance
Highly dexterous
- - - - - - - -
-- - - - - - -
--- Workspace Boundary Singularity
--- Workspace Interior Singularities
SignificanceJacobian Condition Number
min
max
=
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11/20
IIT Ropar
Collision detection and avoidance
Largest work volume
Minimum Singularities
Maximum collision avoidance
Highly dexterous
- - - - - - - -
-- - - - - - -
What if only the bounding boxes collide?
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12/20
IIT Ropar
Collision detection and avoidance
Largest work volume
Minimum Singularities
Maximum collision avoidance
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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13/20
IIT Ropar
Dexterity / Manipulability
Largest work volume
Minimum Singularities
Maximum collision avoidance
Highly dexterous
- - - - - - - -
-- - - - - - -
Measure of Manipulability (MOM)
{ })()(det JJ TM =
--- works for both non-redundant and
redundant robotic arms
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14/20
IIT Ropar
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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15/20
IIT Ropar
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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16/20
IIT Ropar
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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17/20
IIT Ropar
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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18/20
IIT Ropar
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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19/20
IIT Ropar
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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20/20
IIT Ropar
Acknowledgements
Thanks to the organizers
Thank you!
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