Cover
Vol. 21 No. 1 (2025)

Published: September 19, 2025

Pages: 199-209

Original Article

Mobile Robot Navigation with Obstacles Avoidance by Witch of Agnesi Algorithm with Minimum Power

Abstract

Obstacle avoidance in mobile robot path planning represents an exciting field of robotics systems. There are numerous algorithms available, each with its own set of features. In this paper a Witch of Agnesi curve algorithm is proposed to prevent a collision by the mobile robot’s orientation beyond the obstacles which represents an important problem in path planning, further, to achieve a minimum arrival time by following the shortest path which leads to minimizing power loss. The proposed approach considers the mobile robot’s platform equipped with the LIDAR 360o sensor to detect obstacle positions in any environment of the mobile robot. Obstacles detected in the sensing range of the mobile robot are dealt with by using the Witch of Agnesi curve algorithm, this establishes the obstacle’s apparent vertices’ virtual minimum bounding circle with minimum error. Several Scenarios are implemented and considered based on the identification of obstacles in the mobile robot environment. The proposed system has been simulated by the V-REP platform by designing several scenarios that emulate the behavior of the robot during the path planning model. The simulation and experimental results show the optimal performance of the mobile robot during navigation is obtained as compared to the other methods with minimum power loss and also with minimum error. It’s given 96.3 percent in terms of the average of the total path while the Bezier algorithm gave 94.67 percent. While in experimental results the proposed algorithm gave 93.45 and the Bezier algorithm gave 92.19 percent.

References

  1. A. T. Rashid, A. Abdulkareem, A. L. Fortuna, A. Rashid, A. A. Ali, and M. Frasca, “Path planning and obstacle avoidance based on shortest distance algorithm,” Iraq Journal of Electrical and Electronic Engineering, no. 1, pp. 2–7, 2017.
  2. J. Villagra and H. Mounier, “High velocity wheeled mobile robots,” IFAC Elsevier Journal, vol. 38, no. 1, 2005.
  3. A. T. Rashid, A. A. Ali, M. Frasca, and L. Fortuna, “Path planning with obstacle avoidance based on visibility bi- nary tree algorithm,” Robotics and Autonomous Systems, vol. 61, no. 12, pp. 1440–1449, 2013.
  4. P. Bhattacharya and M. L. Gavrilova, “Voronoi diagram in optimal path planning,” in 4th International Sympo- sium on Voronoi Diagrams in Science and Engineering, vol. 1, 2007.
  5. R. Wein, J. P. V. D. Berg, and D. Halperin, “The visibility–voronoi complex and its applications,” Else- vier Journal, vol. 36, pp. 66–87, 2007.
  6. S. Garrido, L. Moreno, D. Blanco, and P. Jurewicz, “Path planning for mobile robot navigation using voronoi dia- gram and fast marching,” University Carlos of Madrid, vol. 36, no. 1, pp. 66–87, 2007.
  7. V. Waghmare, P. S. Chandel, P. A. Patil, S. S. Waghade, T. A. Komalkar, and P. Marbate, “Motion planning using voronoi diagram with constraints,” International Journal of Advanced Research in Computer Science and Soft- ware Engineering, vol. 5, no. 1, pp. 604–608, 2015. 208 | Issa, Almukhtar, Thabit & Rashid
  8. A. F. Marhoon, “Path planning with polygonal obstacles avoidance based on the virtual circles of the visible ver- tices,” Southern Technical University, no. 10, pp. 61–67, 2017.
  9. B. A. Issa and A. T. Rashid, “Multi-robot control for a static polygon formation using neighbor-leader algo- rithm,” Journal of King Saud University - Computer and Information Sciences, no. 19, pp. 1–11, 2020.
  10. B. A. Issa and A. T. Rashid, “Static polygon formation in the leader-follower robotic system by utilizing rp lidar sensor in an unknown environment,” Journal of Engineering Science and Technology Transactions of Electrical Engineering, vol. 16, pp. 398–414, February 2021.
  11. V. P. Tran, M. Garratt, and I. R. Petersen, “Distributed obstacle and multi-robot collision avoidance in uncertain environments,” arXiv, pp. 1–12, 2018.
  12. F. Zhou, B. Song, and G. Tian, “B´ezier curve based smooth path planning for mobile robot,” Journal of In- formation and Computational Science, vol. 8, no. 12, pp. 2441–2450, 2011.
  13. J. Guo, Y. Gao, and G. Cui, “Path planning of mobile robot based on improved potential field,” Information Technology Journal, vol. 12, no. 11, pp. 2188–2194, 2013.
  14. Z. Ibrahim, A. Rashid, and A. Marhoon, “Path plan- ning algorithm for mobile robot navigation in a dynamic environment based on motion prediction and tangency graph,” in 2017 IEEE First International Conference on Recent Trends of Engineering Science and Sustainability, vol. 978, pp. 1–6, 2017.
  15. H. T. Nguyen, H. X. Le, and V. Nam, “Path planning and obstacle avoidance approaches for mobile robot,” In- ternational Journal of Computer Science Issues, vol. 13, no. 4, pp. 1–10, 2016.
  16. A. Fujimori, H. Kubota, N. Shibata, and Y. Tezuka, “Leader-follower formation control with obstacle avoid- ance using sonar-equipped mobile robots,” Proceedings of the Institution of Mechanical Engineers. Part I: Jour- nal of Systems and Control Engineering, vol. 228, no. 5, pp. 303–315, 2014.
  17. O. Khatib, “Real-time obstacle avoidance for manipu- lators and mobile robots,” in Proceedings - IEEE In- ternational Conference on Robotics and Automation, pp. 500–505, 1985.
  18. A. T. Rashid, “Leader follower tracking with obstacle avoidance using circular paths algorithm,” Iraqi Journal of Electrical and Electronic Engineering, vol. 16, no. 2, pp. 29–47, 2016.
  19. O. Montiel, U. Orozco-Rosas, and R. Sep´ulveda, “Path planning for mobile robots using bacterial potential field for avoiding static and dynamic obstacles,” Expert Sys- tems with Applications, vol. 42, no. 12, pp. 5177–5191, 2015.
  20. A. A. Aldair, M. T. Rashid, and A. T. Rashid, “Naviga- tion of mobile robot with polygon obstacles avoidance based on quadratic bezier curves,” Iranian Journal of Science and Technology - Transactions of Electrical En- gineering, vol. 43, no. 4, pp. 757–771, 2019.
  21. M. A. M. Norrazi, W. Y. R. Yap, I. M. H. Sanhoury, M. Tousizadeh, M. M. Mahmood, and S. H. M. Amin, “Formations strategies for obstacle avoidance with multi- agent robotic system,” in Communications in Computer and Information Science, vol. 376, pp. 232–245, 2013.
  22. A. S. Brand˜ao, M. Sarcinelli-Filho, R. Carellit, and T. F. Bastos-Filho, “Decentralized control of leader-follower formations of mobile robots with obstacle avoidance,” in IEEE 2009 International Conference on Mechatronics ICM 2009, 2009.
  23. B. N. AbdulSamed, A. A. Aldair, and A. Al-Mayyahi, “Robust trajectory tracking control and obstacles avoid- ance algorithm for quadrotor unmanned aerial vehi- cle,” Journal of Electrical Engineering and Technology, vol. 15, no. 2, pp. 855–868, 2020.
  24. B. A. Issa, A. T. Rashid, and M. T. Rashid, “Leader- neighbor algorithm for polygon static formation control,” in 2020 International Conference on Electrical, Commu- nication, and Computer Engineering (ICECCE), pp. 1–6, IEEE, 2020.
  25. K. Nawade, V. A. Apoorv, and S. B. K. Rout, “Geo- metrical approach to online trajectory generation ob- stacle avoidance and footstep planning for a humanoid robot,” in 15th IEEE-RAS International Conference on Humanoid Robots, pp. 1–6, 2015.
  26. D. Nazari, M. Abadi, and M. H. Khooban, “Design of op- timal mamdani-type fuzzy controller for nonholonomic wheeled mobile robots,” Journal of King Saud Univer- sity - Engineering Sciences, vol. 27, no. 1, pp. 92–100, 2015.
  27. E. Masehian, “A voronoi diagram–visibility graph–potential field compound algorithm for 209 | Issa, Almukhtar, Thabit & Rashid robot path planning,” Journal of Robotic Systems, vol. 21, no. 6, pp. 275–300, 2004.
  28. M. Hamani and A. Hassam, “Mobile robot navigation in unknown environment using improved apf method,” in The 13th International Arab Conference on Information Technology ACIT’2012, pp. 453–458, 2012.
  29. W. Chen, X. Wu, and Y. Lu, “An improved path planning method based on artificial potential field for a mobile robot,” CYBERNETICS AND INFORMATION TECH- NOLOGIES, vol. 15, no. 2, pp. 181–191, 2015.
  30. M. S. Alam, M. U. Rafique, and M. U. Khan, “Mobile robot path planning in static environments using particle swarm optimization,” International Journal of Computer Science and Electronics Engineering (IJCSEE), vol. 3, no. 3, 2015.
  31. A. Y. Guanghui Li, Yusuke Tamura and H. Asama, “Ef- fective improved artificial potential field-based regres- sion search method for autonomous mobile robot path planning,” International Journal of Mechatronics and Automation, vol. 3, no. 3, 2013.
  32. M. G. V. P. Tran and I. R. Petersen, “Distributed obstacle and multi-robot collision avoidance in uncertain envi- ronments,” The School of Engineering and Information Technology, University of New South Wales, Australia and Ian R. Petersen is with the Research School of Engi- neering, Australian National University, vol. 543, no. 13, pp. 1–12, 2018.
  33. A. A. T. Weerakoon, K. Ishii and F. Nassiraei, “An artifi- cial potential field based mobile robot navigation method to prevent from deadlock,” JAISCR, vol. 5, no. 3, pp. 189– 203, 2015.
  34. V. K. B. J. Kaur and G. Singh, “Robotic path planning us- ing the intelligent control,” in International Conference on Advances in Electrical and Electronics Engineering, pp. 197–199, 2011.
  35. E. Galceran and M. Carreras, “A survey on coverage path planning for robotics,” Robotics and Autonomous Systems, vol. 61, no. 12, pp. 1258–1276, 2013.
  36. A. M. E. H. H. Adeli, M. H. N. Tabrizi and M. Jahed, “Path planning for mobile robots using iterative artificial potential field method,” IJCSI International Journal of Computer Science, vol. 8, no. 4, pp. 28–32, 2011.
  37. P. Raja and S. Pugazhenthi, “Optimal path planning of mobile robots: A review,” International Journal of Physical Sciences, vol. 7, no. 9, pp. 1314–1320, 2012.
  38. M. F. A. Turky, A. Abdulkareem and L. Fortuna, “Path planning with obstacle avoidance based on visibility bi- nary tree algorithm,” Robotics and Autonomous Systems, vol. 61, no. 12, pp. 1440–1449, 2013.
  39. T. Wang, “Path planning approach in unknown environ- ment,” International Journal of Automation and Com- puting, vol. 7, no. August, pp. 310–316, 2010.
  40. I. M. I. Hassani and C. Rekik, “Robot path planning with avoiding obstacles in known environment using free segments and turning points algorithm,” Mathematical Problems in Engineering, vol. 20, 2018.
  41. S. Tao and J. Tan, “Path planning with obstacle avoid- ance based on normalized r-functions,” Journal of Robotics, vol. 20, 2018.
  42. Y. Z. M. A. Kamel and S. Member, “Decentralized leader-follower formation control with obstacle avoid- ance of multiple unicycle mobile robots,” in Canadian Conference on Electrical and Computer Engineering, vol. 32, pp. 406–411, 2015.
  43. M. A. M. Norrazi, W. Y. R. Yap, I. M. Sanhoury, M. Tou- sizadeh, M. M. Mahmood, and S. H. Amin, “Formations strategies for obstacle avoidance with multi agent robotic system,” in Intelligent Robotics Systems: Inspiring the NEXT: 16th FIRA RoboWorld Congress, FIRA 2013, Kuala Lumpur, Malaysia, August 24-29, 2013. Proceed- ings 16, pp. 232–245, Springer, 2013.
  44. R. C. A. S. Brandao, M. Sarcinelli-Filho and T. F. Bastos- Filho, “Decentralized control of leader-follower forma- tions of mobile robots with obstacle avoidance,” in 2009 IEEE International Conference on Mechatronics, vol. 11, 2009.
  45. Z. Ying and L. I. Xu, “Leader-follower formation control and obstacle avoidance of multi-robot based on artificial potential field,” IEEE Journal, vol. 34, no. 122, pp. 4355– 4360, 2015.
  46. R. C. Spencer, “Properties of the witch of ag- nesi—application to fitting the shapes of spectral lines,” Journal of the Optical Society of America, vol. 30, no. 9, p. 415, 1940.
  47. J. M. K. Alexander, “Decision theory meets the witch of agnesi,” Journal of Philosophy, vol. 109, no. 12, pp. 712– 727, 2012.