algorithm and fuzzy inference

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Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Fusion of probabilistic A*
algorithm and fuzzy inference

system for robotic path planning

Rahul

Kala,

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior


http://students.iiitm.ac.in/~ipg_200545/


rahulkalaiiitm@yahoo.co.in,

rkala@students.iiitm.ac.in

Kala, Rahul, Shukla, Anupam, & Tiwari, Ritu (2010) Fusion of probabilistic A* algorithm and fuzzy inference system for
robotic path planning
, Artificial Intelligence Review, Springer Publishers, Vol. 33, No. 4, pp 275
-
306

(Impact Factor:
0.119)


Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

The Problem


Inputs


Robotic Map


Location of Obstacles


All Obstacles Static



Output


Path P such that no collision occurs



Constraints


Time Constraints


Dimensionality of Map


Non
-
holonomic constraints



Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Path
Planning

A
* Algorithm

(Coarser Level)

FIS

(Finer Level)

Approach

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

The two algorithms

A* Algorithm

Path Optimality

Deadlocks

Non
-
holonomic

Constraints

Time Complexity

Input Size

FIS

Non
-
holonomic

Constraints

Time Complexity

Input Size

Path Optimality

Deadlocks

Advantages

Disadvantages

Advantages

Disadvantages

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

General Algorithm

Generate
Uncertain Map

Use FIS planner
using p
i

as goal and
add result to path

Generate initial
FIS

For all
points p
i

in
the solution
by A* (i≥2)


Optimize FIS
parameters by GA

P ← Path by
A* algorithm

Stop

Training

Testing

Trained

FIS

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

The 2 level map


Map

Level 1

Level 2

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Lower Resolution Map

(x
i
,y
i
)

(x
i
,y
i
+b)

(x
i
+a,y
i
+b)

(x
i
+a,y
i
)

(x
i
+a/2,y
i
+b/2)

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

A* Guidance

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

FIS Planner

Angle to goal (
α)

Distance from goal (d
g

)

Distance from obstacle (d
o
)

Turn to avoid obstacle (t
o
)

Inputs

Outputs

Turn
Angle (
β
)

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Angle to Goal (
α)

Goal

θ

φ

α= θ
-

φ



Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Turn to avoid obstacle (t
o
)

c

a

Obstacle

Robot

b

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Membership Functions

(e) Turn (Output)

Angle to goal.

Distance to goal.

Distance from obstacle.

Turn to avoid
obstacle

Turn (Output)

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Rules


Rule1: If (
α

is less_positive) and (do is not near) then (
β

is less_right) (1)


Rule2: If (
α

is zero) and (do is not near) then (
β

is no_turn) (1)


Rule3: If (
α

is less_negative) and (do is not near) then (
β

is less_left) (1)


Rule4: If (
α

is more_positive) and (do is not near) then (
β

is more_right) (1)


Rule5: If (
α

is more_negative) and (do is not near) then (
β

is more_left) (1)


Rule6: If (do is near) and (to is left) then (
β

is more_right) (1)


Rule7: If (do is near) and (to is right) then (
β

is more_left) (1)


Rule8: If (do is far) and (to is left) then (
β

is less_right) (1)


Rule9: If (do is far) and (to is right) then (
β

is less_left) (1)


Rule10: If (
α

is more_positive) and (do is near) and (to is no_turn) then (
β

is
less_right) (0.5)


Rule11: If (
α

is more_negative) and (do is near) and (to is no_turn) then (
β

is
less_left) (0.5)


Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

A* Nodal Cost


If Grey(P) is 0, it means that the path is not feasible. The fitness in
this case must have the maximum possible value i.e. 1


If Grey(P) is 1, it means that the path is fully feasible. The fitness in
this case must generalize to the normal total cost value i.e. f(n)


All other cases are intermediate


f(n) = h(n) + g(n)


C(n) = f(n)* Grey(P) +(1
-
Grey(P))


Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

A* Nodal Cost
-

2

To control ‘grayness’ contribution


C(n) = f(n)* Grey’(P) +(1
-
Grey`(P))


Grey’(P) = 1, if Grey(P) > β



Grey(P) otherwise

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Fitness Function Plots

Original

Modified

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Genetic Optimizations

Maximize Performance for small sized
benchmark Maps

Benchmark Maps Used

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Fitness Function

F
i

= L
i

* (1
-
O
i
) * T
i



L
i
: Total path length


T
i
: Maximum turn taken any time in the path


O
i
: Distance from the closest obstacle anytime
in the run
.


F = F
1

+ F
2

+ F
3


RESULTS

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Genetic Optimization

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Performance on Benchmark Maps

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Path traced by A* algorithm



Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Test Maps











proposed

algorithm

A* planning

Only A*
algorithm

Only FIS
algorithm

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Test Maps
-

2











proposed

algorithm

A* planning

Only A*
algorithm

Only FIS
algorithm

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Test Maps
-

3











proposed

algorithm

A* planning

Only A*
algorithm

Only FIS
algorithm

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Change in Grid Size

Experiments with

α = 1000, 100, 20, 10, 5, 1

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Change in Grayness Parameter

Experiments with

β

= 0, 0.2, 0.3, 0.5, 0.6, 1

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Parameter


Contribution of the Fuzzy Planner makes path smooth,
reduces time. It however may result in a longer path or
the failure in finding path


Contribution of the A* algorithm reduces path length
(α), which can solve very complex maps with most
optimal path length at the cost of computational time


The contribution of the A* to maximize the probability
of the path (β), would usually increase the path length.

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Publication


R. Kala, A. Shukla, R. Tiwari (2010)
Fusion of probabilistic A* algorithm
and fuzzy inference system for robotic
path planning. Artificial Intelligence
Review. 33(4): 275
-
327



Impact Factor: 0.119



Available at:
http://springerlink.com/content/p8w55
5x67k626273/?p=97dca405364843749
29e0959d1ab4dc3&pi=1


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Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

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Term Evaluation 3
April 1, ‘10

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Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Reference Analysis

Factor

Value

No. of

References

43

Percent of Recent References

(than 5 years old)

51.11%

(22/43)

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid
-
Term Evaluation 3
April 1, ‘10

Thank You