ISAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the
International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A.
APPLICATION OF MCDM METHODS FOR A GROUP OF
NONHOLONOMIC MOBILE ROBOTS TO DETERMINE
THE BEST ROUTE AND THE MOST SUITABLE ROBOT
TO THE GIVEN TASK
Alpaslan Yufka
Department of Electrical and Electronics Engineering
Anadolu University
Eskişehir, TURKEY
E-mail: ayufka@gmail.com
Müjgan Sağır Özdemir
Department of Industrial Engineering
Eskişehir Osmangazi University
Eskişehir, TURKEY
E-mail: msagir@ogu.edu.tr
ABSTRACT
In this study, a fire-fighting scenario in an office environment wherein three different
nonholonomic differential-drive mobile robots are used is considered as a case study. The
2D configuration space of the office environment is divided into grid cells by using the
method of “Occupancy Grid Map” such that each grid cell is associated with each
interrelated node. Each robot constructs a reachability three by using these nodes and
Breadth-First Search (BFS) algorithm. The back-tracking algorithm is used to obtain the
finite solution set of paths from the motion planning. The set of alternatives is
constructed by randomly selecting routes from the finite solution set of paths. Each robot
determines its own best route by applying Multi-Criteria Decision Making (MCDM)
methods such that “Elimination et Choix Traduisant la Realite (ELECTRE I)” and
“Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)”. Criteria
for the path selection is weighted by applying the method of “Analytic Hierarchy Process
(AHP)”. Then, each robot except the leader robot sends its best path-info to the leader so
that the leader robot determines the most suitable robot that conforms to the fire-fighting
task by using AHP. To analyze the effect of criteria’s weights on the alternatives and
perform sensitivity-graphs, Expert Choice 11 software is used. The robot determined by
the leader executes the task by tracking its own best path.
Keywords: Mobile robots, motion planning, Occupancy Grid Map, Breadth-First Search,
node, back-tracking, leader, Multi-Criteria Decision Making, ELECTRE I, TOPSIS,
AHP, Expert Choice, sensitivity-graphs.
International Journal of the
Analytic Hierarchy Process
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Washington, D.C.
June 29 – July 2, 2014
IJAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the
International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A.
1. Introduction
A mobile robot (MR) constructs its route from its start point to a specific point by using
motion planning techniques in order to execute the given task. In motion planning, the
total length of the path is generally considered as a main criteria (Ramos, 2010) and A*
algorithm is used to construct a minimal total-length path (Murphy, 2000). This criterion
is not only the one, but criteria such as “changes in direction”, “length in reverse gear”,
“index of smoothness”, “average distance” are also considered (Ramos, 2010). MR is
able to generate more than one path from its goal point to the specific point since the
configuration space is applicable. This occurs the finite-set of alternative paths such that
the best path is determined by MR according to previously defined criteria.
In (Ramos, 2010), nonholonomic car-like single MR is considered, and the best path is
chosen by using the methods of ELECTRE I, II and PROMETHEE I, II. It is also that
there is no info how the weights of criteria are specified. These Multi-Criteria Decision
Making (MCDM) methods are generally applied in the field of economics, environmental
issues, logictic, etc. and not commonly in the field of MR.
In this study, a fire-fighting scenario in an office environment wherein three different
nonholonomic differential drive multi-MR are used is considered as a case study. Each
MR determines its own best route by applying MCDM methods such that ELECTRE I
and TOPSIS. Criteria for the path selection which are “total length”, “number of
rotations”, “the amount of open space”, and “the floor-roughness” is weighted by
applying the method of “Analytic Hierarchy Process (AHP)” (Saaty, 1989). Then, each
robot except the leader robot sends its best path-info to the leader so that the leader robot
determines the most suitable robot that conforms to the fire-fighting task by using AHP.
To analyze the effect of criteria’s weights on the alternatives and perform sensitivitygraphs, Expert Choice 11 software is used. The robot determined by the leader executes
the task by tracking its own best path.
2. Literature Review
In general, navigation is the problem of finding a collision-free motion for the robot
system such a MR from a named place to another in configuration space that is known,
unknown or partially known environment (Choset, 2005). In practically, MR cannot
generate a direct motion path from a start (home) point to a goal (destination) point in
configuration space so that path planning techniques for MRs must be used in this
situation. Occupancy Grid Map (Moravec, 1985) method is used to divide 2D
configuration space into grid cells. Each cell is associated with interrelated nodes by
using offline planning. Breadth-First Search (BFS) algorithm (Murphy, 2000) which is
based on visiting all neighbor-nodes, is used for obtaining reachability tree from the start
point to the goal point. Back-tracking method is applied on this reachability tree to obtain
the set of paths.
International Symposium of
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Process
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Washington, D. C.
June 29 – July 2, 2014
IJAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the
International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A.
3. Hypotheses/Objectives
A two-phased decision methodology is used. Required data is mostly obtained from the
motion planning by using nodes and environment info. Each MR determines its own best
route and the leader robot chooses the most suitable robot that conforms to the task by
using AHP. Then, the robot determined by the leader executes the task by tracking its
own best path.
4. Research Design/Methodology
The mixed method which has 2 steps is used in this study. Data is mostly obtained from
the motion planning by using nodes and environment info.
1. Firstly, each robot determines its best route by using ELECTRE I and TOPSIS.
The result is the same in respect of both methods. The weights of criteria is
assigned by the AHP where data and author’s expert view are used for pairwise
comparisons. Criteria for the path selection are “total length”, “number of
rotations”, “the amount of open space”, and “the floor-roughness”.
2. Secondly, the leader robot determines the most suitable robot that conforms to
the task by using AHP. The weights of criteria is assigned by the AHP where
data and author’s expert view are used for pairwise comparisons. Criteria for the
robot selection are “velocity (linear/angular)”, “the capacity of the battery”, “the
capacity of the fire extinguisher”, and “criteria for the path previously determined
by each MR”.
5. Data/Model Analysis
TOPSIS, ELECTRE and AHP methods are used for different phases of this study. Figure
1 represents one of the paired comparison matrix for criteria - changes in direction”,
“length in reverse gear”, “index of smoothness”, and “average distance” related to the
path with the inconsistency index as 0.06. Figure 2 shows that if the weight for criterion
Speed increases, Robot 1 becomes the best alternative.
Figure 1. Paired comparison matrix for path criteria
Figure 2. An example view for sensitivity analysis
International Symposium of
the Analytic Hierarchy
Process
3
Washington, D. C.
June 29 – July 2, 2014
IJAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the
International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A.
6. Limitations
Assumptions are:
Grid cells, nodes and relations of nodes are offline planned.
Configuration space and objects are known by MR.
The goal/destination point is reachable.
MR has a perfect localization.
7. Conclusions
In this study, MCDM techniques which are ELECTRE I, TOPSIS and AHP are applied
on the field of robot motion planning. We have not come across a study uses MCDM
techniques to define the best route and/or the best robot in related topics. This could
motivate researchers on the area of Electric/Electronic Engineering and the Computer
Science for a multidisciplinary work. This study already is an example for that.
8. Key References
Choset, H. & et al (2005). Principles of Robot Motion: Theory, Algorithms, and
Implementations. MIT Press.
Moravec, H.P. & Elfes, A. (1985). High resolution maps from wide angle sonar. Robotics
and Automation, IEEE International Conference, (2), 116-121.
Murphy, R.R. (2000). Introduction to AI Robotics. MIT Press.
Ramos, J.M.M & et all (2010). Application of MCDM Techniques to Maneuver Planning
in Nonholonomic Robots. Expert Systems with Applications, 37, 3962–3976.
Saaty, T., & Alexander, J. (1989). Conflict Resolution: The Analytic Hierarchy Process.
New York, New York: Praeger.
9. Appendices
The configuration space is shown as in Figure 3. Figure 4 represents accessibility tree for
Robot 1, as an example.
International Symposium of
the Analytic Hierarchy
Process
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Washington, D. C.
June 29 – July 2, 2014
IJAHP Article: Mu, Saaty/A Style Guide for Paper Proposals To Be Submitted to the
International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A.
K
H
D
F
G
M
E
A
B
L
I
J
C
(a)
(b)
Figure 3. (a) 2D Configuration Space and (b) Offline Planning
Figure 4. Accessibility tree for Robot 1
International Symposium of
the Analytic Hierarchy
Process
5
Washington, D. C.
June 29 – July 2, 2014
APPLICATION OF MCDM METHODS FOR A GROUP OF NONHOLONOMIC
MOBILE ROBOTS TO DETERMINE THE BEST ROUTE AND THE MOST SUITABLE
ROBOT TO THE GIVEN TASK
Müjgan Sağır Özdemir
Alpaslan Yufka
Eskişehir Osmangazi University
Outline
OUTLINE
Motivation
Robot Motion Planning
• Mobile Robots and the Configuration Space
• Motion Planning
• Paths
Multi-Criteria Decision Making
•
•
•
•
•
Criteria and Weights
Application of TOPSIS
Application of ELECTRE I
Application of AHP
Sensitivity Analysis
Conclusion
1. Introduction
Motivation
• A mobile robot (MR) constructs its route from its start point to a
specific point by using motion planning techniques in order to
execute the given task. In motion planning, the total length of
the path is generally considered as a main criteria.
• This criterion is not only the one, but criteria such as “number
of rotations”, “the amount of open space”, and “the floorroughness” may be also considered.
3
Motivation (cont’d)
1. Introduction
• MR is able to generate more than one path from its
goal point to the specific point since the
configuration space is applicable. This occurs the
finite-set of alternative paths such that the best
path is determined by MR according to previously
defined criteria.
4
Robot motion planning
1. Introduction
• A fire-fighting scenario in an office environment
wherein three different non-holonomic differentialdrive mobile robots are used is considered.
• Each MR determines its own best route by ELECTRE I
and TOPSIS. Criteria for the path selection are weighted
by applying AHP.
5
Robot motion planning
1. Introduction
• Each MR except the leader one sends its best pathinfo to the leader so that the leader MR
determines the most suitable robot that conforms
to the fire-fighting task by using AHP.
6
Mobile Robots and the Configuration Space
7
Robot alternatives
• 1st Robot
• 2nd Robot
• 3rd Robot
Environment
Motion Planning
• The 2D configuration space of
the office environment is
divided into grid cells by using
the method of “Occupancy
Grid Map” such that each grid
cell is associated with each
interrelated node.
8
Motion
2.2Planning
Motion
Planning
• Each robot constructs a reachability three by using
these nodes and Breadth-First Search (BFS)
algorithm. The back-tracking algorithm is used to
obtain the finite solution set of paths from the
motion planning. The set of alternatives is
constructed by randomly selecting routes from the
finite solution set of paths.
• The path for the first robot is given in the following
slide as an example. Paths for other two robots are
obtained as similar as in the first robot.
9
2.3 Paths
For the 1st Robot
Paths
10
Total Number of The amount The floorLength rotations of open space roughness
Paths
1st Path
2nd Path
3rd Path
4th Path
5th Path
Goal Point
L
F
E
B
4
4
6
7
8
89/20
145/27
45/13
76/17
43/13
I
G
H
D
A
Start (Home) Point
13
16
12
13
12
K
Dead Node
J
C
Paths found randomly
1st Path : A B C J I L
2nd Path : A B D H G I L
3rd Path : A B E J I L
4th Path : A B E F G I L
5th Path : A B E F L
6,5
0
0
0
0
Criteria and weighing
Step 1- Criteria and their weights for the path selection
• Total length (0.538)
• Number of rotations (0.274)
• The amount of open space (0.128)
• The floor-roughness (0.060)
11
Criteria
weighing
3.1and
Criteria
and
Weights
Step 2- Criteria for the robot selection (AHP Model)
12
3.2 Application of TOPSIS
TOPSIS
13
1st Step) Path selection (using TOPSIS)
Ranking the alternatives
Path #
1
2
3
4
5
C* Rank
0,7072
1
0,5768
2
0,5666
3
0,4456
5
0,4619
4
1st Robot
Ranking the alternatives
Path #
1
2
3
4
5
C*
Rank
0,4323
2
1,0000
1
0,3284
5
0,3442
4
0,4025
3
2nd Robot
Ranking the alternatives
Path #
1
2
3
4
5
C*
Rank
1,0000
1
0,1306
4
0,1250
5
0,1413
3
0,1555
2
3rd Robot
1st step- Path selection (ELECTRE I)
C* :
D* :
Outranking
Average
Average
Cpq
0,50 Dpq
0,50
C(1,2)
Yes
D(1,2)
Yes
C(1,3)
No
D(1,3)
Yes
1st Path --> 2nd Path
1st Path --> 3rd Path
1st Path --> 4th Path
1st Path --> 5th Path
C(1,4)
Yes
D(1,4)
Yes
C(1,5)
No
D(1,5)
Yes
C(2,1)
No
D(2,1)
No
C(2,3)
No
D(2,3)
Yes
C(2,4)
No
D(2,4)
Yes
2nd Path --> 3rd Path
2nd Path --> 4th Path
C(2,5)
No
D(2,5)
Yes
2nd Path --> 5th Path
C(3,1)
Yes
D(3,1)
No
C(3,2)
Yes
D(3,2)
No
C(3,4)
Yes
D(3,4)
Yes
3rd Path --> 4th Path
3rd Path --> 5th Path
C* :
D* :
Outranking
Average
Average
Cpq
0,50 Dpq
0,50
C(1,2)
No
D(1,2)
No
C(1,3)
No
D(1,3)
Yes
C(1,4)
No
D(1,4)
Yes
C(1,5)
No
D(1,5)
No
C(2,1)
Yes
D(2,1)
Yes
C(2,3)
Yes
D(2,3)
Yes
C(2,4)
Yes
D(2,4)
Yes
C(2,5)
Yes
D(2,5)
Yes
C(3,1)
Yes
D(3,1)
C(3,2)
No
C(3,4)
Yes
C(3,5)
2nd Path --> 1st Path
2nd Path --> 3rd Path
2nd Path --> 4th Path
2nd Path --> 5th Path
No
D(2,1)
No
C(2,3)
No
D(2,3)
Yes
C(2,4)
No
D(2,4)
No
C(2,5)
Yes
D(2,5)
Yes
No
C(3,1)
No
D(3,1)
No
D(3,2)
No
C(3,2)
Yes
D(3,2)
No
D(3,4)
No
C(3,4)
Yes
D(3,4)
No
Yes
D(3,5)
No
C(3,5)
Yes
D(3,5)
No
C(4,1)
Yes
D(4,1)
No
C(4,1)
No
D(4,1)
No
C(4,2)
Yes
D(4,2)
Yes
C(4,3)
No
D(4,3)
Yes
C(4,5)
Yes
D(4,5)
Yes
C(5,1)
No
D(5,1)
No
C(5,2)
No
D(5,2)
No
C(5,3)
No
D(5,3)
Yes
C(5,4)
No
D(5,4)
No
Yes
D(3,5)
Yes
C(4,1)
No
D(4,1)
No
C(4,2)
No
D(4,2)
No
No
D(4,3)
Yes
C(4,2)
Yes
D(4,2)
No
C(4,3)
C(4,3)
No
D(4,3)
No
C(4,5)
No
D(4,5)
No
C(4,5)
No
D(4,5)
Yes
C(5,1)
Yes
D(5,1)
Yes
C(5,1)
Yes
D(5,1)
No
C(5,2)
No
D(5,2)
No
C(5,2)
Yes
D(5,2)
No
C(5,3)
No
D(5,3)
Yes
C(5,3)
No
D(5,3)
No
C(5,4)
Yes
D(5,4)
Yes
C(5,4)
Yes
D(5,4)
No
R1
1st Path --> 3rd Path
1st Path --> 4th Path
C* :
D* :
Outranking
Average
Average
Cpq
0,50 Dpq
0,50
C(1,2)
Yes D(1,2)
Yes 1st Path --> 2nd Path
C(1,3)
Yes D(1,3)
Yes 1st Path --> 3rd Path
C(1,4)
Yes D(1,4)
Yes 1st Path --> 4th Path
C(1,5)
Yes D(1,5)
Yes 1st Path --> 5th Path
C(2,1)
C(3,5)
4th Path --> 5th Path
14
R2
4th Path --> 3rd Path
5th Path --> 1st Path
5th Path --> 3rd Path
5th Path --> 4th Path
R3
2nd Path --> 3rd Path
2nd Path --> 5th Path
4th Path --> 2nd Path
4th Path --> 3rd Path
4th Path --> 5th Path
5th Path --> 3rd Path
2nd step- Robot selection (AHP Model)
15
Sensitivity analysis
16
Conclusion
17
• By using AHP, the first robot is determined as the most
suitable MR that conforms to the fire-fighting task.
• In the sensitivity analysis, the first robot is still the
most one as a result of changes in the weight of each
criterion except the path selection criterion.
• Each mobile robot generates its alternative paths to
the fire point such that the best path is determined
by using methods of ELECTRE I and TOPSIS. Criteria
for the path selection are weighted by using AHP. Both
methods result the same outcome.