SMART INDOOR NAVIGATION FOR MOBILE ROBOTS: A HARMONIC POTENTIAL-BASED APPROACH WITH ACCELERATED OVER-RELAXATION ITERATIVE METHOD
Abstract
Path planning for autonomous mobile robots remains a critical challenge, particularly in environments with obstacles and constraints. Efficient navigation requires a robust algorithm capable of generating smooth, collision-free trajectories while ensuring computational efficiency. This study addresses the problem of indoor mobile robot navigation by leveraging harmonic potential fields, a solution derived from Laplace’s equation, to formulate an effective path-planning strategy. Conventional numerical methods for solving Laplace’s equation, such as Successive Over-Relaxation and Accelerated Over-Relaxation, often require extensive computational resources, especially in large-scale environments. To overcome this limitation, this research introduces an improved iterative approach, the Explicit Decoupled Group Modified Accelerated Over-Relaxation (EDGMAOR) method, which enhances computational efficiency and convergence speed. The EDGMAOR method incorporates a half-sweep block approach, significantly reducing the number of computations required per iteration while maintaining accuracy. To validate the effectiveness of the proposed method, simulations were conducted in a static, enclosed environment with various configurations of obstacles. Different starting and goal positions were tested to assess the efficiency, accuracy, and computational cost of the generated paths. The results indicate that the EDGMAOR method outperforms conventional approaches by achieving faster convergence rates and reduced computational time, demonstrating its suitability for real-time robot pathfinding applications. Furthermore, the study highlights that with greater obstacles proliferation, the EDGMAOR method maintains its efficiency, as obstacle regions are automatically excluded from unnecessary computations. This characteristic makes the method particularly useful for complex indoor environments where real-time processing is crucial. In conclusion, this research establishes EDGMAOR as a practical and effective solution for solving mobile robot path-planning problems, providing a balance between computational speed, accuracy, and robustness. The findings contribute to the ongoing advancements in autonomous robotics and artificial intelligence-driven navigation systems, with potential applications in industrial automation, smart transportation, and defence sectors.
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References
C. Tang, B. Abbatematteo, J. Hu, R. Chandra, R. Martín-Martín, and P. Stone, “DEEP REINFORCEMENT LEARNING FOR ROBOTICS: A SURVEY OF REAL-WORLD SUCCESSES,” Annu. Rev. Control Robot. Auton. Syst., vol. 8, no. 1, pp. 153–188, May 2025. doi: https://doi.org/10.1146/annurev-control-030323-022510
D. Fernández Llorca et al., “TESTING AUTONOMOUS VEHICLES AND AI: PERSPECTIVES AND CHALLENGES FROM CYBERSECURITY, TRANSPARENCY, ROBUSTNESS AND FAIRNESS,” European Transport Research Review, vol. 17, no. 1, p. 38, Jul. 2025. doi: https://doi.org/10.1186/s12544-025-00732-x
M. Lan, S. Lai, T. H. Lee, and B. M. Chen, “A SURVEY OF MOTION AND TASK PLANNING TECHNIQUES FOR UNMANNED MULTICOPTER SYSTEMS,” Unmanned Systems, vol. 09, no. 02, pp. 165–198, Apr. 2021. doi: https://doi.org/10.1142/S2301385021500151
L. Zhang et al., “MOTION PLANNING FOR ROBOTICS: A REVIEW FOR SAMPLING-BASED PLANNERS,” Biomimetic Intelligence and Robotics, vol. 5, no. 1, p. 100207, Mar. 2025. doi: https://doi.org/10.1016/j.birob.2024.100207
B. Sundaralingam et al., “CUROBO: PARALLELIZED COLLISION-FREE ROBOT MOTION GENERATION,” in 2023 IEEE International Conference on Robotics and Automation (ICRA), IEEE, May 2023, pp. 8112–8119. doi: https://doi.org/10.1109/ICRA48891.2023.10160765
W. Xia, Y. Lu, W. Xu, and X. Xu, “DEEP REINFORCEMENT LEARNING BASED PROACTIVE DYNAMIC OBSTACLE AVOIDANCE FOR SAFE HUMAN-ROBOT COLLABORATION,” Manuf. Lett., vol. 41, pp. 1246–1256, Oct. 2024. doi: https://doi.org/10.1016/j.mfglet.2024.09.151
K. Katona, H. A. Neamah, and P. Korondi, “OBSTACLE AVOIDANCE AND PATH PLANNING METHODS FOR AUTONOMOUS NAVIGATION OF MOBILE ROBOT,” Sensors, vol. 24, no. 11, p. 3573, Jun. 2024. doi: https://doi.org/10.3390/s24113573
J. R. Sánchez-Ibáñez, C. J. Pérez-del-Pulgar, and A. García-Cerezo, “PATH PLANNING FOR AUTONOMOUS MOBILE ROBOTS: A REVIEW,” Sensors, vol. 21, no. 23, p. 7898, Nov. 2021. doi: https://doi.org/10.3390/s21237898
M. Badamasi Aremu, I. K. Kabir, G. Ahmed, and S. El-Ferik, “AUTONOMOUS MOBILE ROBOT PATH PLANNING TECHNIQUES—A REVIEW: CLASSICAL AND HEURISTIC TECHNIQUES,” IEEE Access, vol. 13, pp. 117999–118022, 2025. doi: https://doi.org/10.1109/ACCESS.2025.3579863
R. Daily and D. M. Bevly, “HARMONIC POTENTIAL FIELD PATH PLANNING FOR HIGH SPEED VEHICLES,” in 2008 American Control Conference, IEEE, Jun. 2008, pp. 4609–4614. doi: https://doi.org/10.1109/ACC.2008.4587222
Y. Liu, Y. Ren, J. Wang, L. Zhao, Q. Wang, and J. Shan, “PATH PLANNING FOR MOBILE ROBOT BASED ON IMPROVED ARTIFICIAL POTENTIAL FIELD METHOD,” in 2023 China Automation Congress (CAC), IEEE, Nov. 2023, pp. 4757–4762. doi: https://doi.org/10.1109/CAC59555.2023.10452131
H. J. Chou, P. L. Kuo, and J. S. Liu, “NUMERICAL STREAMLINE PATH PLANNING BASED ON LOG-SPACE HARMONIC POTENTIAL FUNCTION: A SIMULATION STUDY,” 2017 IEEE International Conference on Real-Time Computing and Robotics, RCAR 2017, vol. 2017-July, pp. 535–542, 2017. doi: https://doi.org/10.1109/RCAR.2017.8311918
Z. Guo, H. Yang, and D. Wang, “DEVELOPMENT AND APPLICATION OF POSITIONING AND QUEUE TRANSFORMATION TECHNOLOGY FOR MULTI-SMART CARS,” Proceedings of the 32nd Chinese Control and Decision Conference, CCDC 2020, pp. 3919–3924, 2020. doi: https://doi.org/10.1109/CCDC49329.2020.9164191
C. I. Connolly, “APPLICATIONS OF HARMONIC FUNCTIONS TO ROBOTICS,” IEEE International Symposium on Intelligent Control - Proceedings, vol. 199j2-Augus, no. 7, pp. 498–502, 1992. doi: https://doi.org/10.1109/ISIC.1992.225141
D. J. Evans, “GROUP EXPLICIT ITERATIVE METHODS FOR SOLVING LARGE LINEAR SYSTEMS,” Int. J. Comput. Math., vol. 17, no. 1, pp. 81–108, 1985. doi: https://doi.org/10.1080/00207168508803452
A. Sunarto, J. Sulaiman, and J. V. L. Chew, “COMPUTATIONAL HALF-SWEEP PRECONDITIONED GAUSS--SEIDEL METHOD FOR TIME-FRACTIONAL DIFFUSION EQUATIONS,” in Fractional Order Systems and Applications in Engineering, Elsevier, 2023, pp. 285–300. doi: https://doi.org/10.1016/B978-0-32-390953-2.00024-4
A. A. Dahalan and A. Saudi, “AN ITERATIVE TECHNIQUE FOR SOLVING PATH PLANNING IN IDENTIFIED ENVIRONMENTS BY USING A SKEWED BLOCK ACCELERATED ALGORITHM,” AIMS Mathematics, vol. 8, no. 3, pp. 5725–5744, 2022. doi: https://doi.org/10.3934/math.2023288
M. U. Alibubin, J. Sulaiman, F. A. Muhiddin, and A. Sunarto, “IMPLEMENTATION OF THE KSOR METHOD FOR SOLVING ONE-DIMENSIONAL TIME-FRACTIONAL PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO FINITE DIFFERENCE SCHEME TITLE OF MANUSCRIPT,” Journal of Advanced Research in Applied Sciences and Engineering Technology, vol. 48, no. 1, pp. 168–179, 2025. doi: https://doi.org/10.37934/araset.48.1.168179
J. V. L. Chew, E. Aruchunan, and J. Sulaiman, “EFFICIENCY EVALUATION OF HALF-SWEEP NEWTON-EGSOR METHOD TO SOLVE 1D NONLINEAR POROUS MEDIUM EQUATIONS,” Studies in Systems, Decision and Control, vol. 383, pp. 399–412, 2022. doi: https://doi.org/10.1007/978-3-030-79606-8_25
E. Aruchunan, Z. Siri, M. H. B. N. Aziz, M. H. B. A. Wahab, M. S. Muthuvalu, and J. Sulaiman, “SOLUTION OF PEAK JUNCTION TEMPERATURE WITH CRANK-NICOLSON AND SOR APPROACH,” Studies in Systems, Decision and Control, vol. 444, pp. 225–234, 2022. doi: https://doi.org/10.1007/978-3-031-04028-3_15
M. K. M. Akhir, M. Othman, J. Sulaiman, Z. A. Majid, and M. Suleiman, “NUMERICAL SOLUTION OF HELMHOLTZ EQUATION USING A NEW FOUR POINT EGMSOR ITERATIVE METHOD,” Applied Mathematical Sciences, vol. 5, no. 77–80, pp. 3991–4004, 2011.
A. R. Abdullah, “THE FOUR POINT EXPLICIT DECOUPLED GROUP (EDG) METHOD : A FAST POISSON SOLVER,” Int. J. Comput. Math., vol. 38, no. 1–2, pp. 61–70, 1991. doi: https://doi.org/10.1080/00207169108803958
N. A. Syafiq, M. Othman, N. Senu, and F. Ismail, “AN EXPERIMENTAL STUDY OF THE MODIFIED ACCELERATED OVERRELAXATION (MAOR) SCHEME ON STATIONARY HELMHOLTZ EQUATION,” J. Phys. Conf. Ser., vol. 1366, no. 1, p. 012093, Nov. 2019. doi: https://doi.org/10.1088/1742-6596/1366/1/012093
A. A. Dahalan and A. Saudi, “AN ITERATIVE TECHNIQUE FOR SOLVING PATH PLANNING IN IDENTIFIED ENVIRONMENTS BY USING A SKEWED BLOCK ACCELERATED ALGORITHM,” AIMS Mathematics, vol. 8, no. 3, pp. 5725–5744, 2023. doi: https://doi.org/10.3934/math.2023288
A. Ali, M. Abbas, and T. Akram, “NEW GROUP ITERATIVE SCHEMES FOR SOLVING THE TWO-DIMENSIONAL ANOMALOUS FRACTIONAL SUB-DIFFUSION EQUATION,” Journal of Mathematics and Computer Science, vol. 22, no. 2, pp. 119–127, 2020. doi: https://doi.org/10.22436/jmcs.022.02.03
A. A. Dahalan, A. Saudi, and J. Sulaiman, “ENHANCING AUTONOMOUS GUIDED VEHICLES WITH RED-BLACK TOR ITERATIVE METHOD,” Mathematics, vol. 11, no. 20, pp. 1–17, 2023 doi:. https://doi.org/10.3390/math11204393
P. Agarwal, A. Sunarto, J. V. L. Chew, J. Sulaiman, and S. Momani, “NEW PRECONDITIONING AND HALF-SWEEP ACCELERATED OVERRELAXATION SOLUTION FOR FRACTIONAL DIFFERENTIAL EQUATION,” J. King Saud Univ. Sci., vol. 35, no. 2, p. 102461, 2023. doi: https://doi.org/10.1016/j.jksus.2022.102461
G. B. Ekal, J. V. L. Chew, K. Ghazali, and J. Sulaiman, “HALF-SWEEP NEWTON-KSOR WITH WAVE VARIABLE TRANSFORMATION TO SOLVE FORCED POROUS MEDIUM EQUATIONS,” International Journal of Engineering Trends and Technology, vol. 72, no. 2, pp. 19–28, 2024. doi: https://doi.org/10.14445/22315381/IJETT-V72I2P103
M. Othman and A. R. Abdullah, “EFFICIENT FOUR POINTS MODIFIED EXPLICIT GROUP POISSON SOLVER,” Int. J. Comput. Math., vol. 76, no. 2, pp. 203–217, 2000. doi: https://doi.org/10.1080/00207160008805020
A. Saudi and J. Sulaiman, “HALF-SWEEP GAUSS-SEIDEL (HSGS) ITERATIVE METHOD FOR ROBOT PATH PLANNING.,” The 3rd Int. Conf. on Informatics and Technology (Informatics09), no. February 2019, pp. 27–28, 2009.
A. Hadjidimos, “ACCELERATED OVERRELAXATION METHOD,” Math. Comput., vol. 32, no. 141, pp. 149–157, 1978. doi: https://doi.org/10.1090/S0025-5718-1978-0483340-6
A. M. Saeed and N. M. AL-harbi, “GROUP SPLITTING WITH SOR/AOR METHODS FOR SOLVING BOUNDARY VALUE PROBLEMS: A COMPUTATIONAL COMPARISON,” European Journal of Pure and Applied Mathematics, vol. 14, no. 3, pp. 905–914, 2021. doi: https://doi.org/10.29020/nybg.ejpam.v14i3.4031
D. Young, “ITERATIVE METHODS FOR SOLVING PARTIAL DIFFERENCE EQUATIONS OF ELLIPTIC TYPE,” 1954. doi: https://doi.org/10.1088/1751-8113/44/8/085201
A. Saudi, “ROBOT PATH PLANNING USING FAMILY OF SOR ITERATIVE METHODS WITH LAPLACIAN BEHAVIOUR-BASED CONTROL,” 2015.
S.-F. Chen, “COLLISION-FREE PATH PLANNING,” 1997.
S. Sasaki, “PRACTICAL COMPUTATIONAL TECHNIQUE FOR MOBILE ROBOT NAVIGATION,” IEEE Conference on Control Applications - Proceedings, vol. 2, no. September, pp. 1323–1327, 1998. doi: https://doi.org/10.1109/CCA.1998.721675
C. I. Connolly, J. B. Burns, and R. Weiss, “PATH PLANNING USING LAPLACE’S EQUATION,” pp. 2102–2106, 1990. doi: https://doi.org/10.1109/ROBOT.1990.126315
A. A. Dahalan and A. Saudi, “PATHFINDING ALGORITHM BASED ON ROTATED BLOCK AOR TECHNIQUE IN STRUCTURED ENVIRONMENT,” AIMS Mathematics, vol. 7, no. 7, pp. 11529–11550, 2022. doi: https://doi.org/10.3934/math.2022643
L. H. Ali, J. Sulaiman, and A. Saudi, “ITERATIVE METHOD FOR SOLVING NONLINEAR FREDHOLM INTEGRAL EQUATIONS USING QUARTER-SWEEP NEWTON-PKSOR METHOD,” Lecture Notes in Electrical Engineering, vol. 983 LNEE, pp. 33–46, 2023. doi: https://doi.org/10.1007/978-981-19-8406-8_3
A. A. Dahalan, A. Saudi, and J. Sulaiman, “DEVELOPMENT OF PATH OPTIMIZATION USING QUARTER-SWEEP MODIFIED SUCCESSIVE OVER-RELAXATION ITERATIVE TECHNIQUE,” Lecture Notes in Networks and Systems, vol. 1056, pp. 411–425, 2024. doi: https://doi.org/10.1007/978-981-97-4892-1_35
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