Abstract
The main concerns in handling a self-directed path finding is that we must address the obstacle avoidance issue in which the mobile robot has to create a bump-free route in order to surpass the efficiency of its movement from any departure position to the destination position in the areas concerned. This study seeks to solve the problem by elucidating it iteratively through a numerical approach. The solution builds on the potential field approach, that uses the equation of Laplace to restrict the formation of potential functions across regions in which the mobile robot operates. This article proposes an iterative method for the resolution of mobile robot path finding problem, namely Explicit Group Modified Accelerated Over-Relaxation (EGMAOR). The experiment demonstrates that, by applying a finite difference method, the mobile robot is competent to produce a collision-free trail from any start to specific target point. In addition, the findings of the model verified that numerical techniques could provide an accelerated solution and have produced smoother path than earlier work on the same issue.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Connolly CI, Burns JB, Weiss R (1990) Path planning using Laplace’s equation. In: Proceedings of IEEE international conference of robotics automation, pp 2102–2106
Akishita S, Hisanobu T, Kawamura S (1993) Fast path planning available for moving obstacle avoidance by use of Laplace potential. In: Proceedings of IEEE international conference of intelligent robots system, pp 673–678
Sasaki S (1998) A practical computational technique for mobile robot navigation. In: Proceedings of IEEE international conference of control applications, pp 1323–1327
Barraquand J, Langlois B, Latombe JC (1992) Numerical potential field techniques for robot path planning. IEEE Trans Syst Man Cybern 22(2):224–241
Connolly CI, Gruppen R (1993) On the applications of harmonic functions to robotics. J Robot Syst 10(7):931–946
Khatib O (1985) Real-time obstacle avoidance for manipulators and mobile robots. IEEE Trans Robot Autom 1:500–505
Karonava M, Zhelyazkov D, Todorova M, Penev I, Nikolov V, Petkov V (2015) Path planning algorithm for mobile robot. Recent Res Appl Comput Sci:26–29
Hachour O (2008) Path planning of autonomous mobile robot. Int J Syst Appl Eng Develop 4(2):178–190
Saudi A, Sulaiman J (2013) Robot path planning using Laplacian behaviour-based control (LBBC) via half-sweep SOR. In: Proceedings of the international conference on technological advances in electrical, electronics and computer engineering. Konya, Turkey, pp 424–429
Saudi A, Sulaiman J, Hijazi MHA (2014) Fast robot path planning with laplacian behaviour-based control via four-point explicit decoupled group SOR. Recent J Appl Sci 9(6):354–360
Saudi A, Sulaiman J (2012) Robot path planning using four point-explicit group via nine-point Laplacian (4EG9L) iterative method. Int Symp Robot Intell Sens 41:182–188
Pedersen MD, Fossen TI (2012) Marine vessel path planning and guidance using potential flow. In: Proceedings of 9th IFAC conference of manoeuvring AMD control of marine craft, pp 188–193
Liang X, Wang H, Li D, Liu C (2014) Three-dimensional path planning for unmanned aerial vehicles based on fluid flow. In: Proceedings of IEEE aerospace conference, pp 1–13
Motonaka K, Watanabe K, Maeyama S (2014) 3-dimensional kinodynamic motion planning for an X4-Flyer using 2-dimensional harmonic potential fields. In: 14th international conference of control automation system, pp 1181–1184
Shi C, Zhang M, Peng J (2007) Harmonic potential field method for autonomous ship navigation. In: 7th international conference of telecommunication (ITST’07), pp 1–6
Vallvé J, Andrade-Cetto J (2015) Potential information fields for mobile robot exploration. Robot Autonom Syst 69:68–79
Masoud AA, Al-Shaikhi A (2015) Time-sensitive, sensor-based, joint planning and control of mobile robots in cluttered spaces: a harmonic potential approach. In: 54th IEEE conference of decision control (CDC), pp 2761–2766
Evans LC (1998) Partial differential equations. American Mathematical Society, Providence
Ibrahim A (1993) The study of the iterative solution of boundary value problem by the finite difference method. PhD thesis, Universiti Kebangsaan Malaysia
Sulaiman J, Hasan MK, Othman M (2007) Red-Black EDGSOR iterative method using triangle element approximation for 2D Poisson equations. In: Gervasi O, Gavrilova M. (eds) Computer science applied 2007. Lecture notes in computer science (LNCS 4707). Springer-Verlag, Berlin, pp 298–308
Evans DJ (1985) Group explicit iterative methods for solving large linear systems. Int J Comput Math 17:81–108
Evans DJ, Yousif WS (1986) Explicit group iterative methods for solving elliptic partial differential equations in 3-space dimensions. Int J Comput Math 18:323–340
Martins MM, Yousif WS, Evans DJ (2002) Explicit group AOR method for solving elliptic partial differential equations. Neural Parall Sci Comput 10(4):411–422
Hadjidimos A (1978) Accelerated overrelaxation method. Math Comput 32(141):149–157
Dahalan AA, Sulaiman J (2016) Half-sweep two parameter alternating group explicit iterative method applied to fuzzy poisson equation. Appl Math Sci 10(2):45–57
Dahalan AA, Shattar NA, Sulaiman J (2016) Implementation of half-sweep age method using seikkala derivatives approach for 2D fuzzy diffusion equation. J Eng Appl Sci 11(9):1891–1897
Dahalan AA, Sulaiman J (2015) Approximate solution for 2 dimensional fuzzy parabolic equations in QSAGE iterative method. Int J Math Anal 9(35):1733–1746
Dahalan AA, Aziz NSA, Sulaiman J (2016) Performance of quarter-sweep successive over relaxation iterative method for two-point fuzzy boundary value problems. J Eng Appl Sci 11(7):1456–1463
Sulaiman J, Othman M, Hassan MK (2009) A new quarter-sweep arithmetics mean (QSAM) method to solve diffusion equations. Cham J Math 2(1):93–103
Muthuvalu MS, Sulaiman J (2010) Quarter-sweep arithmetic mean (QSAM) iterative method for second kind linear Fredholm integral equations. Appl Math Sci 4(59):2943–2953
Acknowledgements
This research was supported by Ministry of Education (MOE) through Fundamental Research Grant Scheme (FRGS/1/2018/ICT02/UPNM/03/1). The researchers declare that the publication of this study has no conflict of interest.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Dahalan, A.A., Saudi, A. (2022). Self-directed Mobile Robot Path Finding in Static Indoor Environment by Explicit Group Modified AOR Iteration. In: Ab. Nasir, A.F., Ibrahim, A.N., Ishak, I., Mat Yahya, N., Zakaria, M.A., P. P. Abdul Majeed, A. (eds) Recent Trends in Mechatronics Towards Industry 4.0. Lecture Notes in Electrical Engineering, vol 730. Springer, Singapore. https://doi.org/10.1007/978-981-33-4597-3_3
Download citation
DOI: https://doi.org/10.1007/978-981-33-4597-3_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-33-4596-6
Online ISBN: 978-981-33-4597-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)