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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/ firstname.lastname@example.org,
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Fusion of probabilistic A* algorithm and fuzzy inferencesystem 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/ email@example.com, firstname.lastname@example.org 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)
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
The two algorithms Advantages Advantages Disadvantages Disadvantages
Training Optimize FIS parameters by GA Generate initial FIS Trained FIS Testing For all points pi in the solution by A* (i≥2) P ← Path by A* algorithm Use FIS planner using pi as goal and add result to path Generate Uncertain Map Stop General Algorithm
Map Level 1 Level 2 The 2 level map
(xi,yi) (xi+a,yi) (xi+a/2,yi+b/2) (xi,yi+b) (xi+a,yi+b) Lower Resolution Map
FIS Planner Outputs Inputs
Goal α= θ- φ θ φ Angle to Goal (α)
Obstacle a b c Robot Turn to avoid obstacle (to)
Membership Functions Angle to goal. Distance to goal. Turn to avoid obstacle Distance from obstacle. Turn (Output) (e) Turn (Output)
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)
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))
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
Fitness Function Plots Modified Original
Genetic Optimizations Maximize Performance for small sized benchmark Maps Benchmark Maps Used
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
Test Maps A* planning proposed algorithm Only FIS algorithm Only A* algorithm
Test Maps - 2 A* planning proposed algorithm Only FIS algorithm Only A* algorithm
Test Maps - 3 A* planning proposed algorithm Only FIS algorithm Only A* algorithm
Change in Grid Size Experiments with α = 1000, 100, 20, 10, 5, 1
Change in Grayness Parameter Experiments with β = 0, 0.2, 0.3, 0.5, 0.6, 1
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.
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/p8w555x67k626273/?p=97dca40536484374929e0959d1ab4dc3&pi=1
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