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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/ rahulkalaiiitm@yahoo.co.in,

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Fusion of probabilistic A* algorithm and fuzzy inference system for robotic path planning


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    1. 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/ 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)

    2. 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

    3. Approach

    4. The two algorithms Advantages Advantages Disadvantages Disadvantages

    5. 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

    6. Map Level 1 Level 2 The 2 level map

    7. (xi,yi) (xi+a,yi) (xi+a/2,yi+b/2) (xi,yi+b) (xi+a,yi+b) Lower Resolution Map

    8. A* Guidance

    9. FIS Planner Outputs Inputs

    10. Goal α= θ- φ θ φ Angle to Goal (α)

    11. Obstacle a b c Robot Turn to avoid obstacle (to)

    12. Membership Functions Angle to goal. Distance to goal. Turn to avoid obstacle Distance from obstacle. Turn (Output) (e) Turn (Output)

    13. 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)

    14. 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))

    15. 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

    16. Fitness Function Plots Modified Original

    17. Genetic Optimizations Maximize Performance for small sized benchmark Maps Benchmark Maps Used

    18. 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

    19. RESULTS

    20. Genetic Optimization

    21. Performance on Benchmark Maps

    22. Path traced by A* algorithm

    23. Test Maps A* planning proposed algorithm Only FIS algorithm Only A* algorithm

    24. Test Maps - 2 A* planning proposed algorithm Only FIS algorithm Only A* algorithm

    25. Test Maps - 3 A* planning proposed algorithm Only FIS algorithm Only A* algorithm

    26. Change in Grid Size Experiments with α = 1000, 100, 20, 10, 5, 1

    27. Change in Grayness Parameter Experiments with β = 0, 0.2, 0.3, 0.5, 0.6, 1

    28. 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.

    29. 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

    30. References

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    33. Reference Analysis

    34. Thank You