**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30458

##### Autonomous Vehicle Navigation Using Harmonic Functions via Modified Arithmetic Mean Iterative Method

**Authors:**
Jumat Sulaiman,
Azali Saudi

**Abstract:**

**Keywords:**
Path Planning,
Laplace’s equation,
Modified Arithmetic Mean method,
Harmonic
functions

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.2643972

**References:**

[1] A. Saudi and J. Sulaiman. Block Iterative Method for Robot Path Planning. The 2nd Seminar on Engineering and Information Technology, Kota Kinabalu, July 7 8, 2009.

[2] A. Saudi and J. Sulaiman. Numerical Technique for Robot Path Planning using Four Point-EG Iterative Method. In proc. of the Int. Symposium on Information Technology, 2010, pp. 831 836.

[3] A. Saudi and J. Sulaiman. Indoor Path Planning for Mobile Robot using LBBC-EG. Int. J. of Imaging and Robotics, 11(3), 2013, pp. 37-45.

[4] A. Saudi and J. Sulaiman. Hybrid Path Planning for Indoor Robot with Laplacian Behaviour-Based Control via Four Point-Explicit Group. Int. J. of Imaging and Robotics, 12(1), 2014, pp. 12-21.

[5] C. I. Connolly, J. Burns, and R. Weiss. Path planning using Laplace’s equation. In Proceedings of the IEEE International Conference on Robotics and Automation, May 13-18, 1990, Cincinnati, USA, pp. 2102-2106.

[6] C. I. Connolly and R. A. Grupen. The applications of harmonic functions to robotics. Journal of Robotic Systems, 10(7), 1993, pp. 931-946.

[7] D. E. Koditschek. Exact robot navigation by means of potential functions: Some topological considerations. In Proceedings of the IEEE International Conference on Robotics and Automation, March 31 - April 3, 1987, Raleigh, USA, vol. 4, 1987, pp. 1-6.

[8] D. M. Young. Iterative Methods for Solving Partial Difference Equations of Elliptic Type. PhD Thesis. Harvard University, 1950.

[9] D. R. Kincaid and D. M. Young. The modified successive overrelaxation method with fixed parameters. Mathematics and Computations, 119, 1972, pp. 705-717.

[10] I. Galligani and V. Ruggiero. The Arithmetic Mean method for solving essentially positive systems on a vector computer. Int. J. Computer Math., 32, 1990. pp. 113121.

[11] J. Sulaiman, M. Othman and M. K. Hasan. A new Half-Sweep Arithmetic Mean (HSAM) algorithm for two-point boundary value problems. In Proceedings of the International Conference on Statistics and Mathematics and its Application in the Development of Science and Technology, 2004, pp. 169-173.

[12] J. Sulaiman, M. Othman and M. K. Hasan. A new Quarter Sweep Arithmetic Mean (QSAM) method to solve diffusion equations. Chamchuri Journal of Mathematics, 1(2), 2009, pp. 93-103.

[13] M. D. Pedersen and T. I. Fossen. Marine vessel path planning and guidance using potential flow. In Proceedings of the 9th IFAC Conference on Manoeuvring and Control of Marine Craft, Sep 19-21, 2012, Arenzano, Italy, pp. 188-193.

[14] M. S. Muthuvalu and J. Sulaiman. Half-Sweep Arithmetic Mean method with composite trapezoidal scheme for solving linear Fredholm integral equations. Applied Mathematics and Computation, 217(12), 2011, pp. 5442-5448.

[15] M. S. Muthuvalu and J. Sulaiman. An implementation of the 2-point block arithmetic mean iterative method for first kind linear Fredholm integral equations. World Journal of Modelling and Simulation, 8(4), 2012, pp. 293-301.

[16] O. Khatib. Real-time obstacle avoidance for manipulators and mobile robots. In Proceedings of the IEEE International Conference on Robotics and Automation, Mar 25-28, 1985, St. Louis, USA, vol. 2, 1985, pp. 500-505.

[17] P. Szulczynski, D. Pazderski and K. Kozlowski. Real-time obstacle avoidance using harmonic potential functions. Journal of Automation Mobile Robotics and Intelligent Systems, 5: 59-66.

[18] R. Kress. Numerical Analysis. New York: Springer-Verlag, 1998.

[19] S. Akishita, S. Kawamura, and K. Hayashi. Laplace potential for moving obstacle avoidance and approach of a mobile robot. In Japan-USA Symposium on Flexible Automation, July 9-13, 1990, Kyoto, Japan, pp. 139-142.

[20] S. Garrido, L. Moreno, D. Blanco, and M. F. Martin. Robotic motion using harmonic functions and finite elements. Journal of Intelligent and Robotic Systems, 59(1), 2010, pp. 57-73.

[21] X. Liang, H. Wang, D. Li, and C. Liu. Three-dimensional path planning for unmanned aerial vehicles based on fluid flow. In Proceedings of the IEEE Aerospace Conference, March 1-8, 2014, Big Sky, USA, pp. 1-13.