Presentation asme idetc_2014

R. HENRY
Multi-objective design optimization
of the leg mechanism for a piping
inspection robot
R. HENRY
D. CHABLAT
M. POREZ
F. BOYER
D. KANAAN

R. HENRY
Outline
 Introduction;
 Problematic;
 Design of a leg mechanism;
 Multi-objective design optimization;
 Conclusions;
 Perspectives.
17/08/2014
Multi-objective design optimization of the leg
mechanism for a piping inspection robot
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R. HENRY
Introduction
 Objectives :
• study , design, built a robot piping inspection
 Structure of robot
• 1 expansion module
• 2 leg module
• 3 legs by leg module
• 1 actuator by module
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leg module leg
expansion module
Digital Mock-up (DMU).
Simplified Mock-up
actuator
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R. HENRY
Introduction
 Locomotion constraints:
• Piping of 30 m of length ;
• Small cross section;
• Vertical and horizontal pipe;
• Small radius of curvature;
• “natural” obstacles …
 Problem:
• to pass the variations of diameter;
• to adapt the contacts on the inner surface of a pipe.
Park 2011
Exampleofbarriers
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Uneven inner surface Variations of diameter
Variations of curvatureVariations of inclination
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R. HENRY
1. Slot-follower mechanism:
• 3 passive joints;
• Complex joint witch is a combination of a revolute and a prismatic joint.
2. Crank and slider mechanism with 4 bars:
• 3 passive revolute joints;
3. Crank and slider mechanism with 6 bars:
• 6 passive revolute joints;
• Complex architecture of 6 bars
• Symmetric architecture to limit the singularities.
Design of a leg mechanism
32
1
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R. HENRY
 Pareto Optimal :
• An optimal solution is a solution that
is not dominated by any other
solution in the feasible space. Such a
solution is said Pareto optimal
 Design Optimization
• Find the design variables values that minimize or maximize the
objective functions while satisfying the constraints.
 1min ( ) ( ), , ( ), , ( )m k
x
F x xfx xf f  
 
 
0
0
l u
r r r
k
j
x
x
x
g
h
x x


 
1,
1,
1,
k p
j q
r n
 
 
 
subject to :
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R. HENRY
 Problem statement
• Objectives functions :
• Constraints:
x
p
f
a
F
F
 
pF
aF
1
2
minimize ( ) ;
maximize ( ) .f
f x
f 
 


x
x
 1 2 3,with , ,
T
d l l lx
17/08/2014
min
max
x
3l
1 5
6
3
42
:, and
, :and
g g g
g g g
Design constraints
8
7 : 35 mm ;
: 30% ;f
g x
g 
 

Constraints of
objectives functions
9 min
10 max
: 0.5mm ;
: 35mm ;
g
g

 

Constraints of slider
1 2 3
1 2
1
1
1
3
1
3
2
: , , 50mm ;
: , 3mm ;
: 0mm ;
g l l
l
l
g l l
g



Constraints of Lengths
1 sup
2 inf
: ;=29 mm
=14 ;mm:
h
rh
r
Constraints of pipe
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R. HENRY
 Pareto front
• Crank and slider mechanism with 4 and 6 bars:
─ Same performance
─
• Slot-follower mechanism :
─
75%f 
100%f 
l1 (mm) l2 (mm) l3 (mm) d Δρ (mm) ηf (%)
S1a 29,0 14,0 1 32,3 125%
S1b 29,0 10,5 1 29,1 94%
S1c 29,2 3,9 1 25,7 35%
S2a 20,0 20,0 9,0 2 35,0 76%
S2b 17,3 17,3 11,7 2 30,3 66%
S2c 13,8 13,8 15,2 2 25,4 52%
S3a 19,8 4,5 4,7 3 34,9 75%
S3b 14,7 7,1 7,2 3 25,7 56%
S3c 8,7 8,7 11,6 3 16,4 30%
ObjectivesDesign VariablesDesign
ID
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R. HENRY
 Slot-follower mechanism
• Optimum efficiency solution (S1a)
─ Lever arm with large l2
• Optimum size solution (S1c)
─ Lever arm with small l2
S1a : optimum efficiency solution
S1b : intermediate solution
S1c : optimum size solution
S1a 29,0 14,0 1 32,3 125%
S1b 29,0 10,5 1 29,1 94%
S1c 29,2 3,9 1 25,7 35%
Design
ID
Design Variables Objectives
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R. HENRY
 Crank and slider mechanism with 4 bars
─ lever arm with large l1, l2 and small l3
─ lever arm with small l1, l2 and large l3
• Note:
─ l1=l2 for all solutions
S2a : optimum efficiency solution S2b : intermediate solution S2c : optimum size solution
S2a 20,0 20,0 9,0 2 35,0 76%
S2b 17,3 17,3 11,7 2 30,3 66%
S2c 13,8 13,8 15,2 2 25,4 52%
Design
ID
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R. HENRY
─ lever arm with large l1 and small l2,l3
─ l2=l3
─ lever arm with small l1, l2 and large l3
─ l1=l2
S3a : optimum efficiency solution S3b : intermediate solution S3c : optimum size solution
S3a 19,8 4,5 4,7 3 34,9 75%
S3b 14,7 7,1 7,2 3 25,7 56%
S3c 8,7 8,7 11,6 3 16,4 30%
Design
ID
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R. HENRY
Conclusions
 Multi-objective design optimization
• Slot-follower mechanism is the best solution for a transmission force
efficiency:
• Difficult to build because of the passive prismatic and friction can
reduce its efficiency:
• Matlab genetic algorithm inefficient if the constraints are too released
• Dynamic mechanisms is negligible compared to effort clamping;
 DMU Catia
• Complex design with small parts
• Actuator size is not negligible
17/08/2014
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R. HENRY
Perspectives
 Multi-objective design optimization
• Study the sensitivity of leg mechanism on the variations of constraints
• Simulation the variations of inclination
• Simulation the variations of curvature
 DMU Catia
• Making the prototype of a robot
• Evaluating the prototype
• Comparing between the prototype and simulations
17/08/2014
13 / 14

R. HENRY
Thanks for your kind attention
Renaud.Henry@mines-nantes.fr
17/08/201414 / 14

R. HENRY
 Parameters of pipe (paper):
• Straight pipe with no curve
• : Maximum radius of the pipe (29 mm)
• : Minimum radius of the pipe (14 mm)
• : Size of the mechanism (max 45 mm)
x
x
supr
infr
supr
infr
x
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R. HENRY
 Implementation
• Classic approach to optimization : 12 billion combinations
─ 250 values for l1,l2,l3,ρ and 3 values of d.
• Genetic algorithm (Matlab 2010)
• Settings :
─ Population size: 6000;
─ Pareto fraction: 50%;
─ Tolerance function: 10e-4;
─ Number of sessions per problem: 5.
• Computation time per mechanism : 2 hours
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R. HENRY
 Parameters of pipe:
• Straight pipe with curve
• : Maximum radius of the pipe (26,7 mm)
• : Minimum radius of the pipe (11,7 mm)
• : Radius of the pipe in a curvature (7,7 to 11,7 mm)
• : Size of the mechanism (20 to 60 mm)
Study on the variations of constraints
x
x
x
supr
infr
offr
supr
infr
offr
x
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R. HENRY
 Problem statement
• Objectives functions :
• Constraints:
1
2
minimize ( ) ;
maximize ( ) .f
f x
f 
 


x
x
 1 2 3,with , ,
T
d l l lx
8
9 min
10 max
1 2 3
1 2
13
7
11
1
3
2
: 20 to 60 mm ;
: 0.3 ;
: 0.5 mm ;
: 20 to 60 mm ;
: , , 50 mm ;
: , 6 mm ;
: 0 to 6 mm ;
f
g x
g
g
g
g l l l
g l l
g l



 






x
p
f
a
F
F
 
pF
aF
1 sup
2 inf
3
=26.7 mm
=11.7
: ;
: ;
:
mm
=7.7 to 11.7 mm;off
r
rh
h r
h
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R. HENRY
 Method:
• % feasible solution :
─ 100 % : all feasible solution
─ 0% : any feasible solution
• Correlation between constraints and indicators
─ 100% : constraints linked to indicators
─ 0% : constraints unlinked to indicators
 Indicators:
• Variation of objectives functions and design variables:
─ Small variation : variety of diverse possible solution
─ Big variation : operating point
• Value of objectives functions and design variables
─ Big value : efficient solutions
─ Small value : ineffective solutions
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R. HENRY
• Low sensitive to the constraints
• Always a feasible solution
• Transmission force efficiency constant at 50 %
• Size of the mechanism is between 20 and 30 mm
• Medium sensitive to the constraints
• Always a feasible solution with Δx >25 mm
• Maximum transmission force efficiency is between 85% and 90%
• High sensitive to the constraints
• Low feasible solution
• Maximum transmission force efficiency is between 60% and 100%
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R. HENRY
hoff l3min Δ x ρmax
ηf 50% 70% 10% 5%
Δ x 20% 40% 30% 25%
l1 10% 25% 30% 25%
l2 50% 70% 5% 0%
ηf 90% 40% 25% 20%
Δ x 80% 20% 40% 30%
l1 60% 40% 30% 25%
l2 90% 40% 25% 20%
Correlation between constraints and indicators
indicator Name
Constraint
Variation of objectives
functions and design
variables
Value of objectives
variables
min 25% 45% 0% 0%
max 70% 45% 70% 95%
threshold Nan Nan 35 mm 22,5 mm
% feasible solution
indicator Name
Constraint
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R. HENRY
min 80% 80% 0% 30%
max 80% 80% 70% 100%
threshold Nan Nan 25 mm 35 mm
indicator Name
Constraint
% feasible solution
ηf 5% 5% 45% 90%
Δ x 5% 5% 45% 90%
l1 5% 5% 45% 90%
l2 5% 5% 45% 90%
l3 5% 10% 45% 90%
ηf 5% 5% 30% 60%
Δ x 5% 5% 30% 60%
l1 5% 5% 30% 60%
l2 5% 5% 30% 60%
l3 5% 5% 30% 60%
variables
Value of objectives
variables
indicator Name
Constraint
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R. HENRY
min 100% 100% 100% 100%
max 100% 100% 100% 100%
threshold Nan Nan Nan Nan
indicator Name
Constraint
% feasible solution
ηf 5% 0% 40% 70%
Δ x 5% 0% 40% 70%
l1 10% 0% 40% 70%
l2 5% 0% 40% 70%
l3 10% 0% 40% 70%
ηf 0% 0% 15% 30%
Δ x 10% 0% 15% 30%
l1 0% 0% 15% 30%
l2 0% 0% 15% 30%
l3 5% 0% 15% 30%
variables
Value of objectives
variables
indicator Name
Constraint
17/08/201423 / 17

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