Mobile Robot Path Planning Utilizing Probability Recursive Function

In this work a software simulation model has been proposed for two driven wheels mobile robot path planning; that can navigate in dynamic environment with static distributed obstacles. The work involves utilizing Bezier curve method in a proposed N order matrix form; for engineering the mobile robot path. The Bezier curve drawbacks in this field have been diagnosed. Two directions: Up and Right function has been proposed; Probability Recursive Function (PRF) to overcome those drawbacks. PRF functionality has been developed through a proposed; obstacle detection function, optimization function which has the capability of prediction the optimum path without comparison between all feasible paths, and N order Bezier curve function that ensures the drawing of the obtained path. The simulation results that have been taken showed; the mobile robot travels successfully from starting point and reaching its goal point. All obstacles that are located in its way have been avoided. This navigation is being done successfully using the proposed PRF techniques.




References:
[1] Jan Willemson1 and Maarja Kruusmaa, "Algorithmic Generation of Path
Fragment Covers for Mobile Robot Path Planning". Tartu University,
Estonia, 3rd IEEE Conference On Intelligent Systems September 2006.
[2] Kristo Heero, "Path Planning and Learning Strategies for Mobile Robot
in Dynamic Partially known Environment". Ph.D. thesis, may 2006.
Tartu Universit Press.
[3] G. Dudek and M. Jenkin, "Computational Principles of Mobile
Robotics".Cambridge University Press, 2005.
[4] R. L. Haupt, S. E. Haupt, "Practical Genetic Algorithms", Published by
John Wiley & Sons, Inc., Hoboken, New Jersey, Second edition, 2004.
[5] R. K. Bock and W. Krischer. Data Analysis BriefBook. Springer, Berlin,
1998. URL: (version current as of May 02, 2003).
[6] D. Marsh. Applied Geometry for Computer Graphics and CAD.
Springer-Verlag, New York, NY, 1999.
[7] John H. Mathews and Kurtis K. Fink," Numerical Methods Using
Matlab", 4th Edition, 2004, ISBN: 0-13-065248-2, USA.
[8] Kenneth I. Joy, "BERNSTEIN POLYNOMIALS", On-Line Geometric
Modeling Notes of Computer Science Department , University of
California, Davis, 2000.
[9] B. Sturmfels. Solving Systems of Polynomial Equations. AMS,
Providence, R.I., 2002.
[10] Kuldeep Singh. "Engineering mathematics through applications".
University of Hertfordshire, Department of Mathematics. Industrial
press, New York, 2003.
[11] Bernard K., Robert C., and Sharon C. "Discrete Mathematical
Structures". Fifth edition, Pearson Prentice Hall press, U.S.A, 2004.
[12] R. Murphy, "AI Robotics ", MIT press, 2000.
[13] Loo C. K., and at el. "Mobile Robot Path Planning Using Genetic
Algorithm and Traversability Vector Method". Intelligent Automation
and Soft Computing, Vol.1, pp. 51-64, 2004.
[14] V. Lumelsky and A. Stepanov. "Path planning strategies for a point
Mobile automaton moving amidst unknown obstacles of arbitrary shape.
Algorithmica, pp. 462-472, 1990.