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
Approach
Path
Planning
A* Algorithm
(Coarser Level)
FIS
(Finer Level)
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
Thesis Mid-Term Evaluation 3
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The two algorithms
Path Optimality
Non-holonomic
Constraints
Deadlocks
Time Complexity
Non-holonomic
Constraints
Input Size
Time Complexity
Path Optimality
Input Size
Deadlocks
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
Disadvantages
Disadvantages
FIS
Advantages
Advantages
A* Algorithm
Thesis Mid-Term Evaluation 3
April 1, ‘10
General Algorithm
Training
Generate initial
FIS
Optimize FIS
parameters by GA
Trained
Testing
FIS
Generate
Uncertain Map
P ← Path by
A* algorithm
For all
points pi in
the solution
by A* (i≥2)
Use FIS planner
using pi as goal and
add result to path
Stop
Soft Computing and Expert System Laboratory
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The 2 level map
Map
Level 1
Level 2
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Lower Resolution Map
(xi,yi)
(xi+a,yi)
(xi+a/2,yi+b/2)
(xi,yi+b)
(xi+a,yi+b)
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A* Guidance
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FIS Planner
Angle to goal (α)
Distance from goal (dg )
Outputs
Turn
Angle (β)
Distance from obstacle (do)
Turn to avoid obstacle (to)
Inputs
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
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Angle to Goal (α)
Goal
α= θ- φ
θ
φ
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Turn to avoid obstacle (to)
Obstacle
a
b
c
Robot
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
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Membership Functions
Angle to goal.
Distance to goal.
Turn to avoid
obstacle
Distance from obstacle.
Turn (Output)
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
Thesis Mid-Term Evaluation 3
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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
f(n) = h(n) + g(n)
C(n) = f(n)* Grey(P) +(1-Grey(P))



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
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
Thesis Mid-Term Evaluation 3
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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
Modified
Original
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
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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
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Fitness Function
Fi = Li * (1-Oi) * Ti
Li : Total path length
 Ti : Maximum turn taken any time in the path
 Oi : Distance from the closest obstacle anytime
in the run.

F = F1 + F2 + F3
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
Thesis Mid-Term Evaluation 3
April 1, ‘10
RESULTS
Genetic Optimization
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
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Performance on Benchmark Maps
Soft Computing and Expert System Laboratory
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Path traced by A* algorithm
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
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Test Maps
A* planning
proposed
algorithm
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
A* planning
proposed
algorithm
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
A* planning
proposed
algorithm
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
Experiments with
α = 1000, 100, 20, 10, 5, 1
Change in Grid Size
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Experiments with
β = 0, 0.2, 0.3, 0.5, 0.6, 1
Change in Grayness Parameter
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
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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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
Soft Computing and Expert System Laboratory
Indian Institute of Information Technology and Management Gwalior
Thesis Mid-Term Evaluation 3
April 1, ‘10