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 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 (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 OptimalityDeadlocks Non-holonomic Constraints Time ComplexityInput Size FIS Non-holonomic Constraints Time ComplexityInput SizePath OptimalityDeadlocks 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 (dg )Distance from obstacle (do)Turn to avoid obstacle (to) 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): Impact Factor: Available at: 5x67k626273/?p=97dca e0959d1ab4dc3&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 Reference Analysis FactorValue No. of References43 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