Methodology for the Optimal Design of Metamorphic Manipulators - PhD Dissertation

Methodology For The Optimal Design Of
Metamoprhic Manipulators
Charalampos Valsamos

Aims of the Dissertation
1. The proposal and of Modular Metamorphic
Manipulators as a new robotic manipulator class.
2. The proposal and development of a methodology and
the development of optimal kinematic design tools for
open chain modular metamorphic manipulators.
3. The development of an experimental prototype
metamorphic manipulator and the design and
execution of relative experiments.
2
Methodology for the optimal design of Metamorphic
Manipulators

Dissertation Structure
3
Determination of Gaps
Design/development of
basic elements
Basic definitions
Structure representation
Metamorphic links
Analytical parametric
solution to the inverse
kinematics
Optimal Kinematic Synthesis
of Metamorphic Topologies
Methodology
Task based
methodology for the
determinaltion of the
optimal anatomy
Methodology for the
determination of the
global optimal
anatomy
Expremental set-up
Manipulators

PART 1
Open Chain
Modular
Metamorphic
Manipulators

Existing Classes of Open Chain Manipulators
5
Fixed Anatomy Manipulators
+
• Multitude of methods and indices for
design
• In use for decades with increasing
numbers tendency
-
• Fixed anatomy for “good”
performance based on global
criteria
• Fixed anatomy limits task types to
be performed
Reconfigurable Manipulators1,2
+
• Structuring from basic parts allows
anatomy to task mapping
• Greater flexibility and adaptability
-
• Lack of homogeneity in basic parts
• Require resourses for
reconfiguration
• New class – Tools and methods
under development
1. Chen I-M, Rapid Response Manufacturing through a Rapidly Reconfigurable Robotic Workcell. Robotics and Computer Integrated Manufacturing 17, pp.
199-213, 2001
2. Paredis C., Brown B., Khosla P., A rapidly deployable manipulator system , Proceedings of the International Conference on Robotics and Automation,
1996, pp. 1434-1439
Manipulators

Pseudo - Joint
6
• Manual rotating connector
• At each setting can be considered fixed to a
given value of the pseudo joint parameter θp
• Constructed using composites and aluminium
alloy
• 2 connection surfaces
• 2 prototypes
Manipulators

Basic definitions
1. Metamorphic parameters – anatomy: A metamorphic anatomy
is depicted by the vector θp of the pseudo joint parameters.
2. Metamorphic Topology: An open kinematic chain formed by a
combination of the three basic elements and their
interconnections.
3. Metamorpgic structure: The physical materialization of a
metamoprhic topology.
4. Reference anatomy: where θp=0
5. Reference Configuration: where joint variables are zero
7
1 2
... ... , , 1,2,..., ,
: 0,1,2,...,12, 1,2,...
12
T
p p p pj pm
m
pj
L U
pj pjL
pj pj
j m
k k j m
    
 
 
 

   
  
     
  
θ V
V
V
Manipulators

Metamorphic Structure Representation (MSR)
• Enumeration of Basic Elements and Connection types
8
Basic Element Type
Active Joint (AJ) Pseudo Joint (P)
Digit 0 1
Relative position of consecutive joint twists (Connection
type) (Ci)
Perpendicular Parallel Skew
Digit 1 2 3
(a): 0-1-1-#
(b): 0-3-1-#
(c): 0-2-1-#
Manipulators

Metamorphic Structure
• A proper mathematical representation of a metamorphic
structure composed of n+m basic elements (n being the
active joints number and m the pseudo joints number)
is:
9
     

1 1 2 1
1 2 2 1
... : 0,1 1,2,3 ,3 0 6,
0, 2, 0 0, 1,2,...,
i i i i i i
i i i i i n m n m n m
S M C M C M C M C M
M M M M M M M M i n m

      
     
          
Manipulators

Determination of possible relative position of
consecutive active joint twists within a metamorphic link
10
     
 
 
2 1 1 2
1 2
1 2
0
( )
( )
p p
p
p
a
b
c
    


 


ω θ t ω t θ
ω ω θ 0
t t θ
            2 2 2 2 2 2
TT
p p p p p p           
θ t θ ω θ q θ ω θ ω θ
Manipulators

Enumeration process results
11
Metamorphic links with one pseudo joint
Metamorphic links with two pseudo joints (partial)
MSR Relative position of consecutive active joint twists as a function of θpi i=1,2
Intersecting Parallel Skew Sngular
01 11 11 0#    0
1 2 0p p    0
1 2 90p p
   0
1 2 0p pand NA
01 11 12 0# NA   0
1 0p   0
1 0p NA
01 11 13 0# NA    0
1 90p
και
  0
2 0p
   0
1 90p
NA
01 12 11 0#    0
1 2 0p p    0
1 2 0p p
and
1 2
0 0
0 0p pand  
NA    0
1 2 0p p
01 12 12 0#    0
1 2 0p p
NA    0
1 2 0p p
NA
01 12 13 0#     0
1 2 90p p    0
1 2 90p p
NA NA
01 13 11 0#   0 0
1 20 0p pand or
  0 0
2 10 0p pand
NA   0
1 0p
and
  0
2 0p
   0
1 2 0p p
MSR Relative position of consecutive active joint twists as a function of θp1
Intersecting Parallel Skew Singular
01 11 0#   0
1 0p
NA NA   0
1 0p
01 12 0#   0
1 0p
NA   0
1 0p
NA
01 13 0#    0
1 90p    0
1 90p
NA NA
02 11 0#   0
1 0p
NA   0
1 0p
NA
02 12 0# NA  1p
NA NA
02 13 0# NA NA  1p
NA
03 11 0#    0
1 90p    0
1 90p
NA NA
03 12 0# NA NA  1p NA
03 13 0#   0
1 0p   0
1 0p
NA NA
Manipulators

Dissertation contribution
1. The proposal of the new class of modular metamorphic
open chain manipulators.
i. The new class modular structure allows the rapid
modification of a metamorphic structure to a new one.
ii. The use of the pseudo joint allows the metamorphosis
of a structure to different anatomies without any need
for disassembly/reassembly of the existing
components.
iii. The proposed class presents high homogeneity
regarding basic components.
2. New basic definition were introduced (structure, anatomy,
metamorphic parameters etc.).
3. The Metamorphic Structure Representation was
presented (MSR).
12
Manipulators

Analytical Parametric Solution Of The Inverse
Kinematics Problem
• For reconfigurable manipulators a numerical solution is
usually preferred3
• The metamorphic parameters of a structure are
defined as parameters.
• The Product of Exponential Formula was used to
determine the kinematic equations
• The Paden Kahan sub problems method was used to
decompose the kinematic equations for the inverse
kinematics solution
13
3. Chen I-M., Gao Y., Inverse Kinematics for Modular Robots, Proc. Of the 1998 IEEE Int. Conference on Robotics and Automation,
Leuven, Belgium
Manipulators

Dissertation Contribution
14
• Rapid solution of the kinematic equations
• Capability of obtaining analytical solutions for all
anatomies of 3 and 4 degrees of freedom. Capability of
obtaining solutions for different anatomies of 5 d.o.f.
structures under perquisites. Capability of obtaining
solution for all 6 d.o.f. structures anatomies provided a
spherical wrist is used.
• Multiple solutions to the inverse kinematics
• No new algebraic calculations are need once the final set
of equations for a structure is determined
• Solution to the inverse kinematics for non-typical
anatomies
Manipulators

PART 2
Optimal
Kinematic Design
of Modular
Metamorphic
Manipulators
Methodology

Optimal Kinematic Synthesis of Metamorphic
Topologies
State of the Art:
• Fixed anatomy manipulators5,6
• Synthesis takes place using global indices and
optimal anatomy searching methods.
• Reconfigurable manipulators7,8
• Synthesis takes place with respect to task
specifications to ensure best performance
16
5. Gonzalez Palacios, M.A., Angeles, J., Ranjbaran, F.,1993, “Kinematics Synthesis of Serial Manipulators With a Prescribed Jacobian”, Proceedings of
the IEEE International Conference on Robotics and Automation, 1, pp. 450-455, Atlanta, GA, USA
6. Ting-Li Yang, An-Xin Liu, Qiong Jin, 2009, “Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms”, Journal
of Mechanical Design. 131, (2), pp. 0210011-02100117
7.O. Chocron, 2008, “Evolutionary Design of Modular Robotic Arms”, Robotica,26 (3), pp 323-330
8. Yang G., Chen I-M., 2000, “Task-based Optimization of Modular Robot Configurations: Minimized Degree of Freedom Approach”, Mechanism and
Machine Theory, 35, pp. 517-540
Manipulators

Introduced Criteria for the Evaluation of
Metamorphic Topologies
I. Structure Simplicity
II. Structure Anatomical Wealth
III. Structure Kinematic Solvability
17
Manipulators

Metamorphic Link Categories
18
Category MSR Relative position of consecutive active joint twists
Intersecting I1 Parallel I2 Skew I3 Singular I4
1 01 11 11 0# 0.0059 0.0237 0.9704 0
01 13 12 0# 0.0651 0.0118 0.9231 0
01 13 13 0# 0.0651 0.0118 0.9231 0
02 13 11 0# 0.0651 0.1538 0.7811 0
02 13 13 0# 0.0710 0.0769 0.8521 0
03 13 11 0# 0.0651 0.0118 0.9231 0
03 13 12 0# 0.0710 0.0769 0.8521 0
2 01 13 0# 0.8462 0.1538 0 0
03 11 0# 0.8462 0.1538 0 0
03 13 0# 0.9231 0.0769 0 0
01 12 11 0# 0.9231 0.0710 0 0.0059
01 12 13 0# 0.9172 0.0828 0 0
03 12 11 0# 0.9172 0.0828 0 0
03 12 13 0# 0.9231 0.0769 0 0
3 01 11 12 0# 0 0.0769 0.9231 0
01 11 13 0# 0 0.0118 0.9882 0
02 11 11 0# 0 0.0769 0.9231 0
02 11 13 0# 0 0.1538 0.8462 0
03 11 11 0# 0 0.1538 0.8462 0
03 11 12 0# 0 0.1538 0.8462 0
03 11 13 0# 0 0.0059 0.9941 0
03 13 13 0# 0 0.0237 0.9763 0
4 01 12 0# 0.0769 0 0.9231 0
02 11 0# 0.0769 0 0.9231 0
01 12 12 0# 0.0769 0 0.9231 0
01 13 11 0# 0.1479 0 0.8462 0.0059
02 11 12 0# 0.0769 0 0.9231 0
02 12 11 0# 0.0769 0 0.9231 0
5 01 11 0# 0.9231 0 0 0.0769
6 02 12 0# 0 1 0 0
02 12 12 0# 0 1 0 0
7 02 13 0# 0 0 1 0
03 12 0# 0 0 1 0
02 12 13 0# 0 0 1 0
02 13 12 0# 0 0 1 0
03 12 12 0# 0 0 1 0
• Category 1: Links that may present all
three types of relative active joint twists
positions.
• Categories 2,3 και 4: Links that may
present two out of three types of
relative active joint twists positions.
• Categories 5,6 και 7: Links that may
only present one of the three types of
relative active joint twists positions.
Manipulators

Simplicity – Anatomical Wealth
• Simplicity Index:
• Index for the grading of metamorphic links based on
anatomical wealth
• Anatomical wealth index
19
  . . .
1 1
A
,0 1
(n+m)
d o f
z S z  
3
1
1 1,0 1
0.037
b
b
I
B B
  

 
2
1
2 2,0 1
0.211369
l
r
r
B
z S z
l

  


Manipulators

Solvability
• Enumeration process results for solvability of possible
structures
• Solvability index
20
D.o.f. Total structures Fully
solvable
Solvable Non - solvable
3 50653 50653 0 0
4 1874161 1874161 0 0
5 69343957 1462055 55521497 12360405
 3 3,0 1
13m
numberof solvableanatomies
z S z  
Manipulators

Optimal kinematic synthesis methodology for
metamorphic topologies
• Objective function (multicriteria evaluation index for
metamorphic topologies)
• Where w1+w2+w3=1 weights set by the designer with
respect to specifications.
• The optimal kinematic synthesis problem solution is:
21
       1 1 2 2 3 3z S w z S w z S w z S  
  *
arg maxS z S
 
  
 
Manipulators

Optimal topology search method
• Genetic Algorithm
• Encoding: The structure’s MSR was used (variable
size chromosome)
• Crossover:
• Mutation (2 types):
• Mutating a single gene corresponding to a connection type
• Mutating a string corresponding to a link
22
Manipulators

Indicative Results
• Results for w1=0.35, w2=0.4, w3=0.25
• Individual criteria values
23
Number of GA run Objective
function value
Structure MSR
1 0.663816 0311011311011303131103
2 0.663816 02110211110311031103
3 0.663816 02121303130213031101
4 0.663816 0311130113031302111303
5 0.663816 0312120311031303111103
Number of GA run z1 z2 z3
1 0.8824 0.2625 1
2 0.8824 0.2625 1
3 0.8824 0.2625 1
4 0.8824 0.2625 1
5 0.8824 0.2625 1
Manipulators

Graphic illustration of selected best determined
topologies
24
GA run Number 1
GA run Number 5
Manipulators

• Quantification of qualitative aspects not commonly used
for topology synthesis.
• The proposal of the methodology for the optimal
kinematic synthesis of metamorphic manipulators.
• The application of the proposed method provides a
number of different structures meeting the
specifications accordingly.
• This is a definite advantage as it allows the designer
to select the optimal amongst a large number of
equally suitable structures.
25
Manipulators

Task Based Optimal Anatomy Determination
State of the Art:
• Fixed anatomy manipulators
• Performance increase via optimal positioning of the
task in the robot’s workspace or the robot’s base for
a given task position9,10
• Reconfigurable manipulators
• Determination of optimal anatomy/structure for given
task position for maximum performance11,12
26
9 A. Nektarios, N. Aspragathos, “Optimizing Velocity Performance of a Position and Orientation Path Following Task”, Robotics and Computer
Integrated Manufacturing, 26(2), (2010), 162-1736.
10. Feng X., Holmgren B., Olvander J., Evaluation and optimization of industrial robot families using different kinematic measures, 2009 ASME
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009; San Diego, CA; 30
August 2009 through 2 September 2009
11. Kim, J.; Khosla, P.K., "A formulation for task based design of robot manipulators," Intelligent Robots and Systems '93, IROS '93. Proceedings of the
1993 IEEE/RSJ International Conference on , vol.3, no., pp.2310,2317 vol.3, 26-30 Jul 1993
12. A. K. Dash, I. -M. Chen, S. H. Yeo & G. Yang, Task oriented configuration design for reconfigurable parallel manipulator systems, Int. Journal of
Computer Integrated Manufacturing, 18(7), 615-634, 2005
Manipulators

Optimal Anatomy Determination Process
27
Optimal task
location for in
the reference
anatomy’s
workspace
determination
Optimal
anatomy for
the given task
location
determination
Task
Reference
anatomy
Optimal task
position
Anatomies
Task
based
optimal
anatomy
Manipulators

Point to point task
28
Manipulators

Optimal task position for point to point task
29
Point p1
given as BTS
BTi=BTS
STi ,
i=2…k
Inverse Kinematics
θi,j(BTS), j=1…8
Determine Ji,j(BTS)
Solution?
wi,j=0
Determine
wi,j(BTS)
Determine min wi,j(BTS)
Other points position and orientation relative to p1
Yes
No
W(BTS)
Manipulators

Introduced index for he determination of the
optimal position of point to point task
• Yoshikawa’s manipulability index at each point:
• Introduced task based index:
30
         , , , ,det , 1,..., , 1,...,8B B B
S S S
T
i j i j i j i jT T Tw i k j   θ θ θJ J
     B B
S Si,j
i j
T TW min min w i 1,...,k j 1,...,8  
Manipulators

Trajectory following application
31
Manipulators

Introduced index for optimal anatomy
determination for trajectory following application
• MVR (Manipulator Velocity Ratio)
• is given as:
• MVR index value for each segment:
32
( ) ( ) ( ) ( )( )min , , , 1,..., 2, 1...B B B B
vi S vn S vs S vf S
n
r T r T r T r T n N i m= = - =
( ) ( )( )minB B
v S vi S
i
R T r T=
 
1
1 T T
v v v v vr

 
V
u J J u
q&
Manipulators

Optimal anatomy determination –
point to point task
• Yoshikawa’s manipulability index at each point:
• Proposed task based index:
• Solution to the optimal anatomy determination problem:
33
         , , , ,det , 1,..., , 1,...,8i j
T
p i j p i j p i j pw i k j   θ θ θ θ θ θJ J
     i,jp p p
i j
W min min i 1,...,k j 1,...,8pw  θθ
  *
p p p
p
arg max W
 
  
 θ
θ θ
Manipulators

Optimal anatomy determination –
trajectory following task
• MVR value for each segment:
• Solution to the optimal anatomy determination problem:
34
        min , , , 1,..., 2, 1...vpi p vn p vs p vf p
n
r r r r n N i m   θ θ θ θ
    minvp p vpi p
i
R rθ θ
  *
arg max
p
p vp pR   
 θ
θ θ
Manipulators

Method application
35
• The illustrated
pointstrajectories are
considered
• A G.A. was used to determine the optimal task(s) location, its fitness
function identical to the problem’s objective function
• A brute force algorithm was used to determine the optimal anatomy to
provide comparison data for all of the structures the considered anatomy
could be metamorphosed to
Manipulators

Results – Point to Point Task
36
Reference anatomy Optimal anatomy
Wp θa θb θc θd θe θf
2.1930 75 90 90 0 15 0
2.1927 75 90 0 -90 30 0
2.1405 75 90 90 0 30 0
2.1320 75 75 90 0 15 0
2.1235 75 75 90 0 15 15
2.0479 75 90 90 0 15 15
2.1927 75 90 0 -90 30 0
2.1405 75 90 90 0 30 0
0.411088 0 0 0 0 0 0
Manipulators

Results – Trajectory Following Task
37
Reference anatomy Optimal anatomy
RVp
θa θb θc θd θe θf
1.2516 15 0 15 -90 45 60
1.2309 0 0 0 -75 45 60
1.2174 0 0 15 -90 30 45
1.2147 15 0 15 -90 60 75
1.2055 15 0 0 -75 45 45
1.2046 15 0 0 -75 45 60
0.769798 0 0 0 0 0 0
Manipulators

Considered metamorphic structure’s possible
anatomies comparison
38
Point to point task Trajectory following task
Manipulators

• The proposed method allows the determination of the
optimal anatomy of a metamorphic structure for best
possible performance during task execution.
• The performance comparison between the fixed
anatomy manipulator (reference anatomy, PUMA type
manipulator) and the possible anatomies of the
metamorphic structure leads to the conclusion that the
latter surpasses the former.
• The full extend of the presented method allows both for
the optimal task placement and optimal anatomy
determination to maximize performance.
39
Manipulators

Introduction of global kinematic and dynamic
anatomies evaluation indices
40
• In joint space an index values form a
hypersurface
• The following values are determined:
• The mean index value in joint
space
• The mean value of a number g of
maximum index values
• The distance of the two means
• The distance of the overall
maximum value from 𝑦max, δy
y
max
1
max
g
i
i
g
y
y 


max max
y y y  
Manipulators

Introduced kinematic and dynamic index
• The multicriteria index is composed of 𝑦, 𝛿 𝑦max και δy
• A “good” anatomy should present high values for the
first two criteria and small values for the third
• The method was extended to use Yoshikawa’s dynamic
manipulability measure to create a global dynamic
index.
41
Manipulators

Proposed method for the rapid determination
of the introduced global index
• The Choquet integral is used to determine the index
value
• An ANFIS was trained to rapidly calculate the index
value
42
       1
1
:
n
i
u p j j j
j
C x u A C u A C 

  
 θ
Manipulators
Set of random
configurations θ
Set of random
anatomies p
θ
Index
calculation
  ,puC y θ θ
ANFIS
Training Data
set  ,p puC  θ θ
New anatomy
p
new
θ
New Index
 p
new
uC θ

Method application – Results
43
Θp1 Θp2 Θp3 Θp4 Θp5 Θp6 Τιμή
Δείκτ
η
90 90 90 30 30 90 1.4880
0 5 10 15 20 25 30
0
0.5
1
1.5
2
2.5
3
Samples
EvaluationScore
Trained Results
Calculated Results
Considered anatomy
Global kinematic index Global dynamic index
Θp1 Θp2 Θp3 Θp4 Θp5 Θp6 Τιμή
Δείκτ
η
90 0 0 0 0 0 177.79
92
Manipulators

• Introduction and development of multicriteria anatomy
evaluation indices, based on local kinematic and
dynamic performance measures.
• The procedure for the development of the global
kinematic indices can be applied to all local kinematic
performance measures.
• The proposed global indices can help rapidly evaluate
the possible anatomies of a metamorphic structure in
terms of overall performance.
44
Manipulators

Anatomies Evaluation Method Based On The Connected
High Performance Area For 3 D.O.F. Metamorphic Structures
State of the Art:
• The high manipulability area of the workspace has
been used as a global performance index in
manipulator design.
• Examples: 12, 13
45
12. D. Chablat, P. Wenger, F. Majou, J-P.Merlet, An interval analysis based study for the design and the comparison of three-degrees-of-freedom
parallel kinematic machines, The Int. Journal of Robotic Research 23 (2004) 615–624.
13. Z. Li, D. Glozman, D. Milutinovic, J. Rosen, Maximizing dexterous workspace and optimal port placement of a multi-arm surgical robot,
in: IEEE International Conference on Robotics and Automation, pp. 3394–3399.
Manipulators

Proposed global index
46
Manipulators

Proposed global index calculation
47
Yoshikawa’s manipulability index
values w>1 mapping to cartesian
space from a given grid in joint
space
Rotated index values (aligned with x-z
plane)
Projection to the x-z plane
Manipulators

Proposed index calculation (cont.)
48
• New grid creation
• The proposed index value is the
approach of the area where w>1
Manipulators

Proposed method application
• Reference anatomy
• Optimal anatomies
49
N
o
Chromosome Anatomy Area (dm2 )
1 [1 14 30 25 6 0] [-85 -20 60 35 -60 0] 9.5213
2 [1 15 4 14 7 1] [-85 -15 -70 -20 -75 5] 9.0988
3 [2 15 34 21 27 0] [-80 -15 65 -15 45 0] 8.9847
4 [4 31 1 15 8 3] [-70 65 -85 15 -50 15] 8.3171
5 [3 14 25 31 31 2] [-75 -20 35 -65 65 10] 8.2168
6 [18 0 0 18 0 0] [0 0 0 -90 0 0] 3.2616
No Chromosome Anatomy Area (dm2 )
1 [4 14 35 23 33 0] [-70 -15 85 -25 75 0] 6.2850
2 [4 15 32 26 32 1] [-70 -10 70 -40 70 5] 5.9565
3 [36 23 1 14 5 0] [90 25 -85 20 -45 0] 5.8774
4 [13 3 9 4 5 4] [-25 -75 -45 70 -65 20] 5.8018
5 [5 14 26 31 3 4] [-65 -20 40 -65 -75 20] 5.5989
6 [18 0 0 18 0 0] [0 0 0 -90 0 0] 2.4007
Based on Yoshikawa’s index Based on KCI
w>1 KCI>0.25
Manipulators

Results
50
Manipulators

• The proposed index and optimal anatomy
determination method:
• Allows the evaluation of the anatomies with respect
to performance during kinematic task execution.
• May be easily modified to be applicable to other
classes of open chain manipulators.
51
Manipulators

Experimental Set-Up
• Prototype metamorphic 3 d.o.f. robot
53
Lengths (m)
L1 0.365
L2 0.3185
L3 0.3725
L4 0.1795
L5 0.0845
Active joints twists directions
𝜔1 0,0,1 T
𝜔2 0,1,0 T
𝜔3 0, −1,0 T
Pseudo joints twists directions
𝜔 𝑝1
−1,0,0 T
𝜔 𝑝2
0,0,1 T
Points on active joint axes of rotation
𝑃1 0,0,0 T
𝑃2 0,0,0.365 T
𝑃3 0.3725,0.2735,0.365 T
Points on pseudo joints axes of rotation
𝑃𝑝1
0,0,0.365 T
𝑃𝑝2
0.1665,0.3185,0.365 T
Metamorphic parameter values
𝜃 𝑝1
0o
𝜃 𝑝2
0o
Manipulators

Experimental Set-Up (Details)
54
Manipulators

Results – Point to point task
55
Initial points position
S𝐭𝐚𝐫𝐭𝐢𝐧𝐠 𝐩𝐨𝐢𝐧𝐭
𝑃𝑖𝑛𝑖𝑡
0.457, 0.139, 0.365 𝑇
E𝐧𝐝 𝐩𝐨𝐢𝐧𝐭
𝑃𝑓𝑖𝑛
−0.1390, 0.2494, 0.5090 𝑇
Optimal points location
S𝐭𝐚𝐫𝐭𝐢𝐧𝐠 𝐩𝐨𝐢𝐧𝐭
𝑃𝑖𝑛𝑖𝑡
−0.4650, −0.0386, 0.365 𝑇
E𝐧𝐝 𝐩𝐨𝐢𝐧𝐭
𝑃𝑓𝑖𝑛
−0.0904, −0.4380,0.5090 𝑇
Metamorphic
parameter value
Degrees
Θp1 60o
Θp2 0o
Manipulators

Results - Videos
56
Manipulators
Reference anatomy Optimal Anatomy

Conclusions
• Open chain modular metamorphic manipulators are a
step in the evolution of modular reconfigurable
manipulators.
• The extent of the possibilities that the new class
presents the designer with is increased compared to
other classes
• The proposed MSR allows for the rapid and effortless
automation of the development of metamorphic
structures
• The methodology for the optimal kinematic synthesis of
metamorphic topologies allows the determination of a
significant number of them fulfilling the set
specifications.
57
Manipulators

Conclusions (cont.)
• The proposed performance indices whether task based
or global can be easily modified to be applicable to
other classes.
• The presented methods application results show that
the proposed manipulator class presents extended
performance capabilities compared to the existing
classes.
58
Manipulators

Publications
Journals
Valsamos C. Moulianitis V. Aspragathos N. Index based optimal anatomy of a
metamorphic manipulator for a given task. In Robotics and Computer Integrated
Manufacturing, volume 28, pages 517 - 529, 2012.
Valsamos C. Moulianitis V. Aspragathos N. Kinematic Synthesis of Structures for
Metamorphic Serial Manipulators J. Mechanisms Robotics 6, 041005 (2014) (14
pages doi:10.1115/1.4027741
C Valsamos, V C Moulianitis, A I Synodinos and N A Aspragathos. Introduction
of the high performance area measure for the evaluation of metamorphic
manipulator anatomies. Mechanism and Machine Theory 86(0):88 - 107, 2015.
Moulianitis, V. C., Synodinos, A. I., Valsamos, C. D., & Aspragathos, N. A. Task-
based optimal design of metamorphic service manipulators. Journal of
Mechanisms and Robotics, 2016.
59
Manipulators

Publications
Conferences (Selected)
Valsamos H., Aspragathos N.A. (2007), “Design of a Versatile Passive Connector for Reconfigurable
Robotic Manipulators with Articulated Anatomies and their Kinematic Analysis”, I*PROMS 2007 Virtual
Conference.
Βάλσαμος Χ. Ασπραγκαθος Ν., Ταχεία Μεταμόρφωση της Ανατομίας Ρομποτικού Βραχίονα με Χρήση
Ψευδό-– Αρθρώσεων και Παραμετρική Επίλυση του Αντιστρόφου Κινηματικού Προβλήματος, 1ο
ΠΑΣΥΡΟ, 2009 (in Greek)
Valsamos H., Moulianitis V., Aspragathos N., A Generalized Method for Solving the Kinematics of 3
D.O.F. Reconfigurable Manipulators, I*PROMS 2009 Virtual Conference, (2009)
Valsamos H., Nektarios, A., Aspragathos N.A., 2005, Optimal Placement of Path Following Robot Task
using Genetic Algorithms, SYROCO 2006.
Valsamos H., Aspragathos N. (2009), “Determination of Anatomy and Configuration of a Reconfigurable
Manipulator for the Optimal Manipulability”, ASME/IFToMM International Conference on Reconfigurable
Mechanisms and Robots, London, pp. 497-503
Βάλσαμος Χ.,Μουλιανίτης Β., Ασπραγκαθος Ν., Διαμόρφωση ανατομίας μεταμορφικού βραχίονα –
Βέλτιστη τοποθέτηση εργασίας στο χώρο εργασίας αυτού., 2ο ΠΑΣΥΡΟ, 2010 (In Greek)
60
Manipulators

Publications
Valsamos H., Moulianitis V., Aspragathos N., Rapid evaluation of reconfigurable robots anatomies using computational
intelligence, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture
Notes in Bioinformatics), Volume 6277 LNAI, Issue PART 2, 2010, Pages 341-350
Βάλσαμος Χ.,Μουλιανίτης Β., Ασπραγκαθος Ν., Δείκτης αξιολόγησης ανατομιών μεταμορφικού ρομποτικού βραχίονα και
υπολογισμός αυτού μέσω συστήματος ANFIS, 2ο ΠΑΣΥΡΟ, 2010 (in Greek)
Valsamos H., Moulianitis V., Aspragathos N., Rapid Evaluation of Anatomies For Metamorphic Robots Based on Dynamic
Manipulability Using an ANFIS System, ECCOMAS Multibody Dynamics 4-7 July 2011, Brussels, Belgium
Valsamos C., Moulianitis V., Aspragathos N.,, Metamorphic Structure Representation: Designing and Evaluating Anatomies
of Metamorphic Manipulators, Advances in Reconfigurable Mechanisms and Robots I , 2012, pp 3-11
V.C. Moulianitis, N.A. Aspragathos, C Valsamos. Suboptimal anatomy of metamorphic manipulators based on the high
rotational dexterity Advances in Reconfigurable Mechanisms and Robots II, 509-519,2016. (Best Paper Award)
Vassilis C. Moulianitis, Nikos A Aspragathos, Aris I Synodinos and Charalampos D. Valsamos.Task-based optimal design of
serial metamorphic manipulators. Accepted for presentation in ICRA 2014 WS Task Based Optimal Design of Robots, 2014.
Charalampos Valsamos, Vassilis Moulianitis and Nikos Aspragathos. Experimental verification of the advantages of a
modular open chain metamorphic manipulator. In 47th International Symposium on Robotics (ISR2016), 2016, 215-221.
61
Manipulators

Other Publications
Περιοδικά
Papachristou, A., Valsamos, H., Dentsoras, A., Optimal initial positioning of
excavators in digging processes, Proceedings of the Institution of Mechanical
Engineers. Part I: Journal of Systems and Control Engineering 224 (7) , pp. 835-844
Συνέδρια
Papachristou, A., Valsamos, H., Dentsoras, A., Optimal positioning of excavators in
digging processes, Innovative Production Machines and Systems Conference 2009
Hoepf, M., Valsamos, H., Research Topics in Manufacturing - The I*PROMS Delphi
Study, IEEE INDIN 2008 Conference on Industrial Informatics (2008)
62
Manipulators

• Thank you very much for your attendance
63
Manipulators

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