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

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management GwaliorThesis Mid-Term Evaluation 3 April 1, ‘10

Fusion of probabilistic A* Fusion of probabilistic A* algorithm and fuzzy algorithm and fuzzy inferenceinferencesystem for robotic path system for robotic path planningplanning

Rahul Kala,


Indian Institute of Information Technology and Management Gwalior

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

[email protected],

[email protected], 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)



The ProblemThe 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



ApproachApproach



The two algorithmsThe two algorithmsAdvantage

Advantage

ssDisadvanta

Disadvanta

ges

ges

Advantage

Advantage

ssDisa

dvanta

Disa

dvanta

ges

ges



General AlgorithmGeneral Algorithm

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

Stop

TrainingTraining

TestingTesting Trained

FIS

Trained

FIS



The 2 level map The 2 level map

Map

Level 1

Level 2



Lower Resolution Map Lower Resolution Map

(xi,yi)

(xi,yi+b)

(xi+a,yi+b)

(xi+a,yi)

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



A* GuidanceA* Guidance



FIS PlannerFIS Planner

InputsInputs

OutputsOutputs



Angle to Goal (Angle to Goal (α)α)

Goal

θ φ

α= θ- φ



Turn to avoid obstacle (tTurn to avoid obstacle (too))

c

a

Obstacle

Robot

b



Membership FunctionsMembership Functions

Angle to goal. Distance to goal.

Distance from obstacle. Turn to avoid obstacle

Turn (Output)



RulesRules 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)



A* Nodal CostA* 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))



A* Nodal Cost - 2A* 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



Fitness Function PlotsFitness Function Plots

Original

Modified



Genetic OptimizationsGenetic Optimizations

Maximize Performance for small sized benchmark Maps

Benchmark Maps Used



Fitness FunctionFitness 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

RESULTSRESULTS



Genetic OptimizationGenetic Optimization



Performance on Benchmark Performance on Benchmark MapsMaps



Path traced by A* Path traced by A* algorithmalgorithm



Test MapsTest Maps

proposed algorithm

A* planning

Only A* algorithm

Only FIS algorithm



Test Maps - 2Test Maps - 2

proposed algorithm

A* planning

Only A* algorithm

Only FIS algorithm



Test Maps - 3Test Maps - 3

proposed algorithm

A* planning

Only A* algorithm

Only FIS algorithm



Change in Grid SizeChange in Grid SizeE

xper

imen

ts w

ith

α

= 1

000,

100

, 20,

10,

5, 1



Change in Grayness Change in Grayness ParameterParameterE

xper

imen

ts w

ith

β

= 0

, 0.2

, 0.3

, 0.5

, 0.6

, 1



Parameter 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.



PublicationPublication 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/p8w555x67k626273/?p=97dca40536484374929e0959d1ab4dc3&pi=1

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Reference AnalysisReference Analysis

Factor Value

No. of References 43

Percent of Recent References (than 5 years old)

51.11% (22/43)



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

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