fusion of probabilistic a* algorithm and fuzzy inferencesystem for robotic path planning

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

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

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 Optimality

Deadlocks

Non-holonomicConstraints

Time Complexity

Input Size

FIS

Non-holonomicConstraints

Time Complexity

Input Size

Path Optimality

Deadlocks

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 pi as goal and

add result to path

Generate initial

FIS

For all

points pi in

the solution

by A* (i≥2)

Optimize FIS

parameters by GA

P ← Path by

A* algorithm

Stop

Training

TestingTrained

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

(xi,yi)

(xi,yi+b)

(xi+a,yi+b)

(xi+a,yi)

(xi+a/2,yi+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

θφ

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 (to)

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

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

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

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 SizeE

xp

erim

ents

wit

h

α =

10

00

, 1

00, 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 ParameterE

xp

erim

ents

wit

h

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): 275-327

Impact Factor: 0.119

Available at:

http://springerlink.com/content/p8w55

5x67k626273/?p=97dca405364843749

29e0959d1ab4dc3&pi=1

REFERENCES

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid-Term Evaluation 3

April 1, ‘10

[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.

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid-Term Evaluation 3

April 1, ‘10

[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 App lied 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

Soft Computing and Expert System Laboratory

Indian Institute of Information Technology and Management Gwalior

Thesis Mid-Term Evaluation 3

April 1, ‘10

Reference Analysis

Factor Value

No. of References 43

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