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

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

31. [1] J. M. Ahuactzin, E. G. Talbi, P. Bessière, E. Mazer, Using Genetic Algorithms for Robot Motion Planning, Lecture Notes In Computer Science 708(1991) 84 – 93. [2] A. Alvarez, A. Caiti, R. Onken, Evolutionary path planning for autonomous underwater vehicles in a variable ocean, IEEE J. Ocean. Eng. 29 (2) (2004) 418-429. [3] K. M. S. Badran, P. I. Rockett, The roles of diversity preservation and mutation in preventing population collapse in multiobjective genetic programming, In: Proc. 9th Annual Conf. Genetic and Evolutionary Computation, GECCO’07, 2007, pp 1551 – 1558. [4] S. Carpin, E. Pagello, An experimental study of distributed robot coordination, Robotics and Autonomous Systems 57(2) (2009) 129-133. [5] L. H. Chen, C. H. Chiang, New approach to intelligent control systems with self-exploring process, IEEE Trans. Systems, Man, and Cybernetics, Part B: Cybernetics 33 (1) (2003) 56-66. [6] J. Cortes, L. Jaillet, T. Simeon, Disassembly Path Planning for Complex Articulated Objects, IEEE Trans. Robotics, 24(2) (2008) 475-481. [7] P. Dittrich, A. Bürgel, W. Banzhaf, Learning to move a robot with random morphology, Lecture Notes in Computer Science 1468(1998) 165-178. [8] L. Doitsidis, N. C. Tsourveloudis, S. Piperidis, Evolution of Fuzzy Controllers for Robotic Vehicles: The role of Fitness Function Selection, J. Intelligent and Robotic Systems (2009). [9] S. Garrido, L. Moreno, D. Blanco, Exploration of 2D and 3D Environments using Voronoi Transform and Fast Marching Method, J. Intelligent and Robotic Systems 55(1) (2009) 55 – 80.  [10] W. Han, S. Baek, T. Kuc, GA Based On-Line Path Planning of Mobile Robots Playing Soccer Games, In: Proc. 40th Midwest Symposium Circuits and Systems, 1(1) (1997). [11] N. Hazon, G. A. Kaminka, On redundancy, efficiency, and robustness in coverage for multiple robots, Robotics and Autonomous Systems 56(12) (2008) pp 1102-1114. [12] N. B. Hui, D. K. Pratihar, A comparative study on some navigation schemes of a real robot tackling moving obstacles, Robotics and Computer-Integrated Manufacturing 25(4-5)(2009) 810-828. [13] G. E. Jan, Y. C. Ki, L. Parberry, Optimal Path Planning for Mobile Robot Navigation, IEEE/ASME Trans. Mechatronics, 13(4)(2008) 451-460. [14] K. G. Jolly, R. S. Kumar, R. Vijayakumar, A Bezier curve based path planning in a multi-agent robot soccer system without violating the acceleration limits, Robotics and Autonomous Systems 57(1)(2009) 23-33. [15] C. F. Juang, A hybrid of genetic algorithm and particle swarm optimization for recurrent network design, IEEE Trans. Systems, Man, and Cybernetics Part B: Cybernetics, 34(2) (2004) 997-1008. [16] R. Kala, A. Shukla, R. Tiwari, S. Rungta, R. R. Janghel, Mobile Robot Navigation Control in Moving Obstacle Environment using Genetic Algorithm, Artificial Neural Networks and A* Algorithm, In: IEEE Proc. World Congress Computer Science and Information Engineering, CSIE ‘09, 2009, pp 705-713. [17] S. Kambhampati, L. Davis, Multiresolution path planning for mobile robots 2(3)(1986) 135-145. [18] K. J. O' Hara, D. B. Walker, T. R. Balch, Physical Path Planning Using a Pervasive Embedded Network, IEEE Trans. Robotics 24(3)(2008) 741-746. [19] T. Peram, K. Veeramachaneni, C. K. Mohan, Fitness-distance-ratio based particle swarm optimization, In: Proc. 2003 IEEE Swarm Intelligence Symp., SIS '03, 2003, pp. 174-181. [20] S. Patnaik, L. C. Jain, S. G. Tzafestas, G. Resconi, A. Konar, Innovations in Robot Mobility and Control, Springer, 2005. [21] M. Peasgood, C. M. Clark, J. McPhee, A Complete and Scalable Strategy for Coordinating Multiple Robots Within Roadmaps, IEEE Trains. Robotics 24(2)(2008) 283-292.

32. [22] C. Pozna, F. Troester, R. E. Precup, J. K. Tar, S. Preitl, On the design of an obstacle avoiding trajectory: Method and simulation, Mathematics and Computers in Simulation 79(7)(2009) 2211-2226. [23] S. K. Pradhan, D. R. Parhi, A. K. Panda, Fuzzy logic techniques for navigation of several mobile robots, Applied Soft Computing 9(1) (2009) 290-304. [24] N. Sadati, J. Taheri, Genetic algorithm in robot path planning problem in crisp and fuzzified environments, In: Proc. 2002 IEEE Int. Conf. Industrial Technology, ICIT '02, 2002, vol.1, 2002, pp. 175-180. [25] K. H. Sedighi, K. Ashenayi, T. W. Manikas, R. L. Wainwright, H. M. Tai, Autonomous local path planning for a mobile robot using a genetic algorithm, Cong. Evolutionary Computation, CEC’04, 2004, vol. 2, 2004, pp. 1338-1345. [26] T. Shibata, T. Fukuda, K. Kosuge, F. Arai, Selfish and coordinative planning for multiple mobile robots by genetic algorithm, In: Proc. 31st IEEE Conf. Decision and Control, 1992, Vol. 3, 1992, pp.2686-2691. [27] A. Shukla, R. Tiwari, R. Kala, Mobile Robot Navigation Control in Moving Obstacle Environment using A* Algorithm, In: Proc. Intl. Conf. Artificial Neural Networks in Engg., ANNIE’08, ASME Publications, Vol. 18, 2008, pp 113-120. [28] S. Squillero, A. P. Tonda, A novel methodology for diversity preservation in evolutionary algorithms, In: Proc. 2008 Conf. companion on Genetic and Evolutionary Computation, GECCO’08, 2008, pp 2223-2226. [29] A. Sud, E. Andersen, S. Curtis, M. C. Lin, D. Manocha, Real-Time Path Planning in Dynamic Virtual Environments Using Multiagent Navigation Graphs, IEEE Trans. Visualization and Computer Graphics 14(3) (2008) 526-538. [30] K. Sugihara, J. Yuh, GA-Based Motion Planning For Underwater Robotic Vehicles, In: Proc. 10th International Symp. on Unmanned Untethered Submersible Technology, Autonomous Undersea Systems Institute, 1996, pp 406—415. [31] R. Toogood, H. Hong , W. Chi, Robot Path Planning Using Genetic Algorithms, In: Proc. IEEE Int. Conf. Systems, Man and Cybernetics, 1995. Intelligent Systems for the 21st Century, Vol. 1, 1995, pp 489-494. [32] C. H. Tsai, J. S. Lee, J. H. Chuang, Path planning of 3-D objects using a new workspace model, IEEE Trans. Systems, Man, and Cybernetics, Part C: Applications and Reviews 31(3)(2001) 405-410. [33] J. Tu, S. Yang, Genetic algorithm based path planning for a mobile robot, In: Proc. of IEEE Intl. Conf. Robotics and Automation, ICRS’03, Vol. 1, 2003, pp 1221-1226. [34] C. Urdiales, A. Bandera, F. Arrebola, F. Sandoval, Multi-level path planning algorithm for autonomous robots, IEEE Electronics Letters 34(2)(1998) 223-224. [35] K. Veeramachaneni, T. Peram, C. Mohan, L. A. Osadciw, Optimization Using Particle Swarms with Near Neighbor Interactions, In: Proc. Genetic and Evolutionary Computation, GECCO ‘03, vol 2723, 2003, pp 110-121. [36] C. Wang, Y. C. Soh, H. Wang, H. Wang, A hierarchical genetic algorithm for path planning in a static environment with obstacles, In: Proc. IEEE Canadian Conf. Electrical and Computer Engineering, CCECE ’02, 2002, vol. 3, pp. 1652-1657. [37] J. Xiao, Z. Michalewicz, Z. Lixin, K. Trojanowski, Adaptive evolutionary planner/navigator for mobile robots, IEEE Trans. Evolutionary Computation 1(1) (1997)18-28. [38] S. X. Yang, M. Meng, An efficient neural network approach to dynamic robot motion planning, Neural Networks 13(2)(2000) 143-148. [39] D. J. Zhu, J. C. Latombe, New heuristic algorithms for efficient hierarchical path planning , IEEE Trans. Robotics and Automation 7(1)(1991) 9-20. [40] S. X. Yang, M. Meng, An efficient neural network approach to dynamic robot motion planning, Neural Networks 13 (2000) 143–148 [41] AR Willms, S X Yang, An Efficient Dynamic System for Real-Time Robot-Path Planning, IEEE Trans on Systems Man and Cybernetics – Part B Cybernetics, 36(4) (2006) 755-766 [42] S. Grossberg, “Contour enhancement, short term memory, and constancies in reverberating neural networks,” Studies in Applied Mathematics, 52 (3)(1973) 217–257 [43] A. Zelinsky, “Using path transforms to guide the search for findpath in 2d,” Int. J. of Robotic Research, 13(4)(1994) 315–325

33. Reference Analysis

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