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

robot dans le vide/Robot.scad

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 2 / 14

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


mechanism for a piping inspection robot

leg module leg expansion module

Digital Mock-up (DMU).

Simplified Mock-up

actuator

3 / 14

cinematiqueRot90.avi

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

Exam

ple

of barr

iers



Uneven inner surface Variations of diameter

Variations of curvature Variations of inclination

4 / 14

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

3 2 1



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 kx

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 :



R. HENRY

Multi-objective design optimization 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 lx



min

max

x

3l1 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

: 0.5 mm ;

: 35mm ;

g

g

Constraints of slider

1 2 3

1 2

1

1

1

3

1

3

2

: , , 50 mm ;

: , 3 mm ;

: 0 mm ;

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

7 / 14

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



R. HENRY

Multi-objective design optimization 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



R. HENRY

Multi-objective design optimization 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




R. HENRY

Multi-objective design optimization Crank and slider mechanism with 6 bars


─ 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




R. HENRY

Conclusions


• 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



R. HENRY

Perspectives


• 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



R. HENRY

Thanks for your kind attention

[email protected]

17/08/2014 14 / 14 Multi-objective design optimization of the leg


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)


xx

suprinfr

supr

infr

x



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




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

xx

x

suprinfr

offr

supr

infr

offr

x



1 sup

2 inf

3

=26.7 mm

=11.7

: ;

: ;

:

mm

=7.7 to 11.7 mm;off

r

rh

h r

h

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 lx

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



R. HENRY

Study on the variations of constraints 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



R. HENRY

Crank and slider mechanism with 6 bars

• 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

Crank and slider mechanism with 4 bars

• Medium sensitive to the constraints

• Always a feasible solution with Δx >25 mm

• Maximum transmission force efficiency is between 85% and 90%


Slot-follower mechanism

• High sensitive to the constraints

• Low feasible solution

• Maximum transmission force efficiency is between 60% and 100%





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 NameConstraint

Variation of objectives

functions and design

variables

Value of objectives


variables

Slot-follower mechanism


min 25% 45% 0% 0%

max 70% 45% 70% 95%

threshold Nan Nan 35 mm 22,5 mm

% feasible solution




R. HENRY

Study on the variations of constraints Crank and slider mechanism with 4 bars


min 80% 80% 0% 30%

max 80% 80% 70% 100%

threshold Nan Nan 25 mm 35 mm


% 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





R. HENRY

Study on the variations of constraints Crank and slider mechanism with 6 bars


min 100% 100% 100% 100%

max 100% 100% 100% 100%

threshold Nan Nan Nan Nan


% 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





presentation asme idetc_2014

Science