Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2321–2333 | Cite as

A Novel and Reduced CPU Time Modeling and Simulation Methodology for Path Planning Based on Resistive Grids

  • Carlos Hernández-MejíaEmail author
  • Héctor Vázquez-Leal
  • Alfonso Sánchez-González
  • Ángel Corona-Avelizapa
Research Article - Electrical Engineering


In mobile robotics area, path planning has been considered as key part for expanding the intelligent properties because it faces the problem of finding collision-free motions for robot systems from one configuration to another. This problem deals with the challenge of searching trajectories that optimize some cost function as the minimum cumulative edge cost, i.e., the shortest path. In addition, it is necessary that path planning can be carried out with reduced CPU time in order to tackle more complex environments in real time. In this work, the analysis of different resistive grid (RG) configurations in order to achieve the shortest path is presented. Additionally, the use of an alternative technique to decrease computing time is introduced. As a result of this research, a modeling and simulation methodology is presented. This methodology is capable of modeling the environment, formulating the equilibrium equations, solving the system of equations and finding the path between the starting and ending points. The configuration space has been modeled with square, square with diagonals, square with center, hexagonal and hexagonal with center RGs. Besides, the formulation of the equilibrium equation has been established using modified nodal analysis. Furthermore, the solution of the system of equations has been carried out using multifrontal method. In addition, the local current comparison algorithm has been resorted in order to find the shortest path. Moreover, the impact of incorporating obstacles into the configuration space of the RGs is explored. As part of the exploration to reduce CPU times, the novel methodology has been expanded into high-level programming language, i.e., Python. Finally, new contributions of this work are expounded and discussed.


Resistive grids Path planning methods LCC algorithm Grid-based methods 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Siciliano, B.; Khatib, O. (eds.): Springer Handbook of Robotics. Springer, Berlin (2008)zbMATHGoogle Scholar
  2. 2.
    Kuric, I.; Bulej, V.; Saga, M.; Pokorny, M.: Development of simulation software for mobile robot path planning within multilayer map system based on metric and topological maps. Int. J. Adv. Rob. Syst. 14(6), 1–14 (2017)Google Scholar
  3. 3.
    Kallmann, M.; Kapadia, M.: Geometric and discrete path planning for interactive virtual worlds. In: ACM SIGGRAPH 2016 Courses, SIGGRAPH’16, pp. 12:1–12:29. ACM, New York (2016)Google Scholar
  4. 4.
    Guo, J.; Cheng, Y.; Guo, S.; Du, W.: A novel path planning algorithm for the vascular interventional surgical robotic doctor training system. In: 2017 IEEE International Conference on Mechatronics and Automation (ICMA), pp. 45–50 (2017)Google Scholar
  5. 5.
    Morimoto, T.K.; Cerrolaza, J.J.; Hsieh, M.H.; Cleary, K.; Okamura, A.M.; Linguraru, M.G.: Design of patient-specific concentric tube robots using path planning from 3-d ultrasound. In: 2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 165–168 (2017)Google Scholar
  6. 6.
    Choset, H.; Lynch, K.M.; Hutchinson, S.; Kantor, G.A.; Burgard, W.; Kavraki, L.E.; Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Cambridge (2005)zbMATHGoogle Scholar
  7. 7.
    Xiong, Y.; Ge, Y.; Liang, Y.; Blackmore, S.: Development of a prototype robot and fast path-planning algorithm for static laser weeding. Comput. Electron. Agric. 142, 494–503 (2017)CrossRefGoogle Scholar
  8. 8.
    Mohanan, M.; Salgoankar, A.: A survey of robotic motion planning in dynamic environments. Rob. Auton. Syst. 100, 171–185 (2018)CrossRefGoogle Scholar
  9. 9.
    Dajin, W.: A linear-time algorithm for computing collision-free path on reconfigurable mesh. Parallel Comput. 34(9), 487–496 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Bahar, M.; Ghiasi, A.; Bahar, H.: Grid roadmap based ANN corridor search for collision free, path planning. Scientia Iranica 19(6), 1850–1855 (2012)CrossRefGoogle Scholar
  11. 11.
    Tarassenko, L.; Blake, A.: Analogue computation of collision-free paths. In: Proceedings 1991 IEEE International Conference on Robotics and Automation, vol. 1, pp. 540–545 (1991)Google Scholar
  12. 12.
    Stan, M.; Burleson, W.: Analog VLSI for robot path planning. In: Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems Computers, vol. 2, pp. 915–919 (1992)Google Scholar
  13. 13.
    Stan, M.R.; Burleson, W.P.; Connolly, C.I.; Grupen, R.A.: Analog VLSI for robot path planning. Analog Integr Circuits Signal Process 6(1), 61–73 (1994)CrossRefGoogle Scholar
  14. 14.
    Althofer, K.; Fraser, D.A.; Bugmann, G.: Rapid path planning for robotic manipulators using an emulated resistive grid. Electron. Lett. 31(22), 1960–1961 (1995)CrossRefGoogle Scholar
  15. 15.
    Koziol, S.; Hasler, P.: Reconfigurable analog VLSI circuits for robot path planning. In: 2011 NASA/ESA Conference on Adaptive Hardware and Systems (AHS), pp. 36–43 (2011)Google Scholar
  16. 16.
    Koziol, S.; Hasler, P.; Stilman, M.: Robot path planning using field programmable analog arrays. In: 2012 IEEE International Conference on Robotics and Automation, pp. 1747–1752 (2012)Google Scholar
  17. 17.
    Marshall, G.F.; Tarassenko, L.: Robot path planning using VLSI resistive grids. In: 1993 Third International Conference on Artificial Neural Networks, pp. 163–167 (1993)Google Scholar
  18. 18.
    Marshall, G.F.; Tarassenko, L.: Robot path planning using resistive grids. In: 1991 Second International Conference on Artificial Neural Networks, pp. 149–152 (1991)Google Scholar
  19. 19.
    Hassouna, M.S.; Abdel-Hakim, A.E.; Farag, A.A.: Pde-based robust robotic navigation. In: The 2nd Canadian Conference on Computer and Robot Vision (CRV’05), pp. 176–183 (2005)Google Scholar
  20. 20.
    Namgung, I.: A global collision-free path planning using parametric parabola through geometry mapping of obstacles in robot work space. KSME J. 10(4), 443 (1996)CrossRefGoogle Scholar
  21. 21.
    Vazquez-Leal, H.; Marin-Hernandez, A.; Khan, Y.; Yildirim, A.; Filobello-Nino, U.; Castaneda-Sheissa, R.; Jimenez-Fernandez, V.: Exploring collision-free path planning by using homotopy continuation methods. Appl. Math. Comput. 219(14), 7514–7532 (2013)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Karpinska, J.; Tchon, K.: Continuation method approach to trajectory planning in robotic systems. In: 2011 16th International Conference on Methods Models in Automation Robotics, pp. 51–56 (2011)Google Scholar
  23. 23.
    Ortega, L.M.; Rueda, A.J.; Feito, F.R.: A solution to the path planning problem using angle preprocessing. Rob. Auton. Syst. 58(1), 27–36 (2010)CrossRefGoogle Scholar
  24. 24.
    Rashid, A.T.; Ali, A.A.; Frasca, M.; Fortuna, L.: Path planning with obstacle avoidance based on visibility binary tree algorithm. Rob. Auton. Syst. 61(12), 1440–1449 (2013)CrossRefGoogle Scholar
  25. 25.
    Nieto, J.; Slawinski, E.; Mut, V.; Wagner, B.: Online path planning based on rapidly-exploring random trees. In: 2010 IEEE International Conference on Industrial Technology, pp. 1451–1456 (2010)Google Scholar
  26. 26.
    Bry, A.; Roy, N.: Rapidly-exploring random belief trees for motion planning under uncertainty. In: 2011 IEEE International Conference on Robotics and Automation, pp. 723–730 (2011)Google Scholar
  27. 27.
    Kothari, M.; Postlethwaite, I.; Gu, D.W.: Multi-uav path planning in obstacle rich environments using rapidly-exploring random trees. In: Proceedings of the 48th IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, pp. 3069–3074 (2009)Google Scholar
  28. 28.
    Aghababa, M.P.: 3D path planning for underwater vehicles using five evolutionary optimization algorithms avoiding static and energetic obstacles. Appl. Ocean Res. 38, 48–62 (2012)CrossRefGoogle Scholar
  29. 29.
    Qu, H.; Xing, K.; Alexander, T.: An improved genetic algorithm with co-evolutionary strategy for global path planning of multiple mobile robots. Neurocomputing 120, 509–517 (2013)CrossRefGoogle Scholar
  30. 30.
    Lee, S.: Park., J.: Neural computation for collision-free path planning. J. Intell. Manuf. 2(5), 315–326 (1991)CrossRefGoogle Scholar
  31. 31.
    Zhang, Y.; wei Gong, D.; hua Zhang, J.: Robot path planning in uncertain environment using multi-objective particle swarm optimization. Neurocomputing 103, 172–185 (2013)CrossRefGoogle Scholar
  32. 32.
    Kanaya, M.; Cheng, G.X.; Watanabe, K.; Tanaka, M.: Shortest path searching for robot walking using an analog resistive network. In: Proceedings of IEEE International Symposium on Circuits and Systems—ISCAS ’94, vol. 6, pp. 311–314 (1994)Google Scholar
  33. 33.
    Roberts, G.; Sedra, A.: Spice. Oxford University Press, Oxford (1997)Google Scholar
  34. 34.
    Davis, T.: Direct Methods for Sparse Linear Systems. Fundamentals of AlgorithmsSociety for Industrial and Applied Mathematics, Philadelphia (2006)CrossRefzbMATHGoogle Scholar
  35. 35.
    Davis, T.A.: Algorithm 832: Umfpack v4.3—an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 196–199 (2004a)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Davis, T.A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 165–195 (2004b)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Ho, C.-W.; Ruehli, A.; Brennan, P.: The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. 22(6), 504–509 (1975)CrossRefGoogle Scholar
  38. 38.
    Schwarz, A.: Computer-Aided Design of Microelectronic Circuits and Systems: General Introduction and Analog-Circuit Aspects. Academic Press, New York (1987)zbMATHGoogle Scholar
  39. 39.
    Ogrodzki, J.: Circuit Simulation Methods and Algorithms. Electronic Engineering SystemsTaylor & Francis, London (1994)zbMATHGoogle Scholar
  40. 40.
    Langtangen, H.P.: A Primer on Scientific Programming with Python, 3rd edn. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  41. 41.
    Johansson, R.: Numerical Python: A Practical Techniques Approach for Industry, 1st edn. Apress, Berkely (2015)CrossRefGoogle Scholar
  42. 42.
    Ardiyanto, I.; Miura, J.: Real-time navigation using randomized kinodynamic planning with arrival time field. Rob. Auton. Syst. 60(12), 1579–1591 (2012)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Maestría en Ingeniería Electrónica y Computación, Facultad de Instrumentación y Ciencias AtmosféricasUniversidad VeracruzanaXalapaMéxico
  2. 2.Facultad de Instrumentación y Ciencias AtmosféricasUniversidad VeracruzanaXalapaMéxico
  3. 3.Universidad Politécnica Metropolitana de PueblaPueblaMéxico

Personalised recommendations