Fusion of probabilistic A algorithm and fuzzy inference

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, 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) 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

Approach Path Planning A* Algorithm (Coarser Level) Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior FIS (Finer Level) Thesis Mid-Term Evaluation 3 April 1, ‘ 10

A* Algorithm FIS Path Optimality Non-holonomic Constraints Deadlocks Time Complexity Non-holonomic Constraints Input Size Time Complexity Path Optimality Input Size Deadlocks Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Disadvantage Advantages s The two algorithms Thesis Mid-Term Evaluation 3 April 1, ‘ 10

General Algorithm Training Generate initial FIS Optimize FIS parameters by GA Trained Testing FIS Generate Uncertain Map P ← Path by A* algorithm For all points pi in the solution by A* (i≥ 2) Use FIS planner using pi as goal and add result to path Stop 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 (xi, yi) (xi, yi+b) (xi+a, yi) (xi+a/2, yi+b/2) (xi+a, yi+b) 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) Outputs Turn Angle (β) Turn to avoid obstacle (to) Inputs 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 α= θ- φ θ Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior φ Thesis Mid-Term Evaluation 3 April 1, ‘ 10

Turn to avoid obstacle (to) Obstacle a b c Robot Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Thesis Mid-Term Evaluation 3 April 1, ‘ 10

Membership Functions Angle to goal. Distance to goal. Turn to avoid obstacle Distance from 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 Rule 1: If (α is less_positive) and (do is not near) then (β is less_right) (1) Rule 2: If (α is zero) and (do is not near) then (β is no_turn) (1) Rule 3: If (α is less_negative) and (do is not near) then (β is less_left) (1) Rule 4: If (α is more_positive) and (do is not near) then (β is more_right) (1) Rule 5: If (α is more_negative) and (do is not near) then (β is more_left) (1) Rule 6: If (do is near) and (to is left) then (β is more_right) (1) Rule 7: If (do is near) and (to is right) then (β is more_left) (1) Rule 8: If (do is far) and (to is left) then (β is less_right) (1) Rule 9: If (do is far) and (to is right) then (β is less_left) (1) Rule 10: If (α is more_positive) and (do is near) and (to is no_turn) then (β is less_right) (0. 5) Rule 11: If (α is more_negative) and (do is near) and (to is no_turn) then Thesis Mid-Term Evaluation 3 April (β is less_left) (0. 5) Indian Institute of Information Technology and Management Gwalior 1, ‘ 10 Soft Computing and Expert System Laboratory

A* Nodal Cost f(n) = h(n) + g(n) C(n) = f(n)* Grey(P) +(1 -Grey(P)) 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) Soft Computing and Expert System Laboratory Thesis Mid-Term Evaluation 3 April Information All other cases are intermediate Indian Institute of Technology and Management Gwalior 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 Modified Original 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 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 = F 1 + F 2 + F 3 Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Thesis Mid-Term Evaluation 3 April 1, ‘ 10

RESULTS

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 A* planning proposed algorithm Only A* algorithm Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Only FIS algorithm Thesis Mid-Term Evaluation 3 April 1, ‘ 10

Test Maps - 2 A* planning proposed algorithm Only A* algorithm Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Only FIS algorithm Thesis Mid-Term Evaluation 3 April 1, ‘ 10

Test Maps - 3 A* planning proposed algorithm Only A* algorithm Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Only FIS algorithm Thesis Mid-Term Evaluation 3 April 1, ‘ 10

Experiments with α = 1000, 100, 20, 10, 5, 1 Change in Grid Size Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Thesis Mid-Term Evaluation 3 April 1, ‘ 10

Experiments with β = 0, 0. 2, 0. 3, 0. 5, 0. 6, 1 Change in Grayness Parameter 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): 275 -327 Impact Factor: 0. 119 Available at: http: //springerlink. com/content/p 8 w 555 x 67 k 626273/? p=97 dca 405364 84374929 e 0959 d 1 ab 4 dc 3&pi=1 Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Thesis Mid-Term Evaluation 3 April 1, ‘ 10

REFERENCES

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Reference Analysis Factor Value No. of References 43 Percent of Recent References (than 5 years 51. 11% old) (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 Soft Computing and Expert System Laboratory Indian Institute of Information Technology and Management Gwalior Thesis Mid-Term Evaluation 3 April 1, ‘ 10