fusion of probabilistic a* algorithm and fuzzy inferencesystem for robotic path planning

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,



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

[email protected],

[email protected]

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)

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




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




April 1, ‘10

Path Planning

A* Algorithm

(Coarser Level)

FIS

(Finer Level)

Approach




April 1, ‘10

The two algorithms

A* Algorithm

Path Optimality

Deadlocks

Non-holonomicConstraints

Time Complexity

Input Size

FIS

Non-holonomicConstraints

Time Complexity

Input Size

Path Optimality

Deadlocks

Advantages

Disadvantages

Advantages

Disadvantages




April 1, ‘10

General Algorithm

Generate

Uncertain Map

Use FIS planner

using pi as goal and

add result to path

Generate initial

FIS

For all

points pi in

the solution

by A* (i≥2)

Optimize FIS

parameters by GA

P ← Path by

A* algorithm

Stop

Training

TestingTrained

FIS




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The 2 level map

Map

Level 1

Level 2




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Lower Resolution Map

(xi,yi)

(xi,yi+b)

(xi+a,yi+b)

(xi+a,yi)

(xi+a/2,yi+b/2)




April 1, ‘10

A* Guidance




April 1, ‘10

FIS Planner

Angle to goal (α)

Distance from goal (dg )

Distance from obstacle (do)

Turn to avoid obstacle (to)

Inputs

Outputs

Turn Angle (β)




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Angle to Goal (α)

Goal

θφ

α= θ- φ




April 1, ‘10

Turn to avoid obstacle (to)

c

a

Obstacle

Robot

b




April 1, ‘10

Membership Functions

Angle to goal. Distance to goal.

Distance from obstacle.Turn to avoid

obstacle

Turn (Output)




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)




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))




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




April 1, ‘10

Fitness Function Plots

Original

Modified




April 1, ‘10

Genetic Optimizations

Maximize Performance for small sized

benchmark Maps

Benchmark Maps Used




April 1, ‘10

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

RESULTS




April 1, ‘10

Genetic Optimization




April 1, ‘10

Performance on Benchmark Maps




April 1, ‘10

Path traced by A* algorithm




April 1, ‘10

Test Maps

proposed

algorithm

A* planning

Only A*

algorithm

Only FIS

algorithm




April 1, ‘10

Test Maps - 2

proposed

algorithm

A* planning

Only A*

algorithm

Only FIS

algorithm




April 1, ‘10

Test Maps - 3

proposed

algorithm

A* planning

Only A*

algorithm

Only FIS

algorithm




April 1, ‘10

Change in Grid SizeE

xp

erim

ents

wit

h

α =

10

00

, 1

00, 20

, 10

, 5,

1




April 1, ‘10

Change in Grayness ParameterE

xp

erim

ents

wit

h

β=

0,

0.2

, 0

.3, 0.5

, 0.6

, 1




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.




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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April 1, ‘10

Reference Analysis

Factor Value

No. of References 43

Percent of Recent References (than 5 years old) 51.11%

(22/43)




April 1, ‘10

Thank You

fusion of probabilistic a* algorithm and fuzzy inferencesystem for robotic path planning

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