A FAST PATH PLANNING METHOD OF ROBOT FOR SURVEILLANCE MISSIONS BASED ON CHAOS

Salah Nasr, Hassen Mekki, and Kais Bouallegue

References

  1. [1] D.R. Corbett, D.W. Gage, and D.D. Hackett, Robotic commu-nications and surveillance – The DARPA LANdroids program,Australasian Joint Conf. on Artificial Intelligence, Springer,Berlin, Heidelberg, 2011, 749–758.
  2. [2] L.S. Martins-Filho and E.E. Macau, Patrol mobile robots andchaotic trajectories, Mathematical Problems in Engineering,2007, ID 61543, 1–13.
  3. [3] P. Sooraska and K. Klomkarn, “No-CPU chaotic robots: Fromclassroom to commerce, IEEE Circuits and Systems Magazine,10(1), 2010, 46–53.
  4. [4] D.W. Kim, T.A. Lasky, and S.A. Velinsky, Autonomous multi-mobile robot system: Simulation and implementation usingfuzzy logic, International Journal of Control, Automation andSystems, 11(3), 2013, 545–554.
  5. [6], [38],the chaotic path planning with a mirror mapping methoddoes not require a map of the terrain and it is more efficientthan the random walk algorithm.The comparison results of the two proposed chaoticsystems for all space cases are depicted in Fig. 7. In thisfigure, the simulation of the robot trajectory of each chaoticsystem with different workspace dimensions is presented.Furthermore, in Table 1, time analysis and terrain coverageor its coverage rate (C) for the two dynamical systems arecompared. We note that the double-scroll Lorenz systemshows smaller values of the coverage rate (C) as regardsthe other system. The multi-scroll chaotic system has asignificantly higher value of the coverage rate (bold valuesin Table 1). As a result, from the two proposed chaoticsystems, the multi-scroll chaotic system has better resultsor performance coverage, especially when we increase theworkspace dimensions, which is obvious in Fig. 7(d), where89.86% of the workspace shows to be covered by the mobilerobot, compared to Fig. 7(c), where only 29.82% of theworkspace shows to be covered, using the double scrollin the same iterative time and with the same workspacedimensions.Furthermore, to better explain the effectiveness ofour approach, the terrain coverage using the proposedapproach in more complex space with obstacle avoidanceis depicted in Fig. 8. In this figure, the reference coveragetrajectory (left figure) and the real coverage trajectory(right figure) of the robot are presented. As it is shown,it is clear that the robot successfully joins the referencecoverage path even in the presence of boundary conditionsand obstacles. However, thisn work can prove to be very473Figure 7. Coverage trajectory of the mobile robot using the flatness controller, mirror mapping method and double-scroll andmulti-scroll chaotic system in different spaces dimensions: (a) using double-scroll in the 50 m × 50 m workspace; (b) usingmulti-scroll in the 50 m × 50 m workspace; (c) Using double-scroll in the 100 m × 100 m workspace; and (d) using multi-scrollin the 100 m × 100 m workspace.Figure 8. Reference coverage trajectory (left figure) and actual coverage trajectory (right figure) of mobile robot in differentcomplex workspaces.helpful for the resolution of the coverage problem for theintroduced surveillance tasks.7. ConclusionThe paper provides a new approach or method to generatepaths for mobile robots accomplishing military missionssuch as surveillance or patrolling. Using the chaotic sys-tems as a primary source of chaotic movement combinedwith the flatness controller, the reference path is altered,in each boundary condition or obstacles, without compro-mising the overall goals of the patrolling mission. The ob-tained trajectory emulates an unpredictable motion when474chased by predators. Moreover, the coverage rate andtime in which the robot covers the workspace using themulti-scroll chaotic system, in different study cases, hasbeen studied providing very satisfactory results in compar-ison to the use of the double-scroll chaotic system.Finally, the results of this work guarantee that theapplication of chaotic systems as solutions for robots tra-jectory control methods represents a very interesting taskfor researchers of both scientific fields.References[1] D.R. Corbett, D.W. Gage, and D.D. Hackett, Robotic commu-nications and surveillance – The DARPA LANdroids program,Australasian Joint Conf. on Artificial Intelligence, Springer,Berlin, Heidelberg, 2011, 749–758.[2] L.S. Martins-Filho and E.E. Macau, Patrol mobile robots andchaotic trajectories, Mathematical Problems in Engineering,2007, ID 61543, 1–13.[3] P. Sooraska and K. Klomkarn, “No-CPU chaotic robots: Fromclassroom to commerce, IEEE Circuits and Systems Magazine,10(1), 2010, 46–53.[4] D.W. Kim, T.A. Lasky, and S.A. Velinsky, Autonomous multi-mobile robot system: Simulation and implementation usingfuzzy logic, International Journal of Control, Automation andSystems, 11(3), 2013, 545–554.[5] H. Lee, E.-J. Jung, B.-J. Yi, and Y. Choi, Navigation strat-egy of multiple-mobile robot systems based on the null-spaceprojection method, International Journal of Control, Automa-tion and Systems, 9(2), 2011, 384–390.[6] M. Kapanoglu, M. Ozkan, O. Parlaktuna, et al., Pattern-basedgenetic algorithm approach to coverage path planning formobile robots, Int. Conf. on Computational Science, Springer,Berlin Heidelberg, 2009, 33–42.
  6. [7] L. Feifei and L. Fei, Time-jerk optimal planning of indus-trial robot trajectories, International Journal of Robotics andAutomation, 31(1), 2016, 1–7.
  7. [8] M. Shayestegan, M.H. Marhaban, S. Shafie, and A.S.B. Din,Fuzzy logic-based robot navigation in static environment withdead cycle obstacles, International Journal of Robotics andAutomation, 28(4), 2013.
  8. [9] C. Luo and S.X. Yang, A bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environments, IEEE Transactions onNeural Networks, 19(7), 2008, 1279–1298.
  9. [10] J. Zhang, H. Lv, D. He, L. Huang, Y. Dai, and Z. Zhang,Discrete bioinspired neural network for complete coverage pathplanning, International Journal of Robotics and Automation,32(2), 2017.
  10. [11] Y. Nakamura and A. Sekiguchi, The chaotic mobile robot,IEEE Transactions on Robotics and Automation, 17(6), 2001,898–904.
  11. [12] R.L. Devaney and J.-P. Eckmann, An introduction to chaoticdynamical systems, Physics Today, 40, 1987, 72.
  12. [13] C.K. Volos, N. Doukas, I. Kyprianidis, I. Stouboulos, andT. Kostis, Chaotic autonomous mobile robot for militarymissions, In Proceedings of the 17th International Conferenceon Communications, 2013, 197–202.
  13. [14] C. Li, F. Wang, L. Zhao, Y. Li, and Y. Song, An improvedchaotic motion path planner for autonomous mobile robotsbased on a logistic map, International Journal of AdvancedRobotic Systems, 10(6), 2013, 273.
  14. [15] X. Zang, S. Iqbal, Y. Zhu, X. Liu, and J. Zhao, Applicationsof chaotic dynamics in robotics, International Journal ofAdvanced Robotic Systems, 13(2), 2016, 60.
  15. [16] E.N. Lorenz, Deterministic nonperiodic flow, Journal of theAtmospheric Sciences, 20(2), 1963, 130–141.
  16. [17] O.E. R¨ossler, An equation for continuous chaos, Physics LettersA, 57(5), 1976, 397–398.
  17. [18] A. Arneodo, P. Coullet, and C. Tresser, Possible new strangeattractors with spiral structure, Communications in Mathe-matical Physics, 79(4), 1981, 573–579.
  18. [19] N. Salah, B. Kais, M. Hassen, and V. S, Controlling mobilerobot based on multi-scroll dynamic chaotic systems, Inter-national Journal of Control Theory and Applications, 10(34),2017, 31–42.
  19. [20] E.D. Markus, J.T. Agee, and A.A. Jimoh, Trajectory controlof a two-link robot manipulator in the presence of gravity andfriction, AFRICON, 2013, (ieeexplore.ieee.org, 2013), 1–5.
  20. [21] E. Markus, J. Agee, A. Jimoh, N. Tlale, and B. Zafer, Flatnessbased control of a 2 DOF single link flexible joint manipulator,SIMULTECH (pdfs.semanticscholar.org), 2012, 437–442.
  21. [22] E.D. Markus, J.T. Agee, and A.A. Jimoh, Flat control ofindustrial robotic manipulators, Robotics and AutonomousSystems, 87, 2017, 226–236.
  22. [23] R. Siegwart, I.R. Nourbakhsh, and D. Scaramuzza, Introductionto autonomous mobile robots, (Cambridge MA: MIT Press,2011).
  23. [24] H. Abidi, M. Chtourou, K. Kaaniche, and H. Mekki, Visualservoing based on efficient histogram information, InternationalJournal of Control, Automation and Systems, 15(4), 1746–1753, 2017.
  24. [25] R. Siegwart and I.R. Nourbakhsh, Introduction to autonomousmobile robots, Bradford Book, Intelligent robotics and au-tonomous agents series, 2004.
  25. [26] S.-O. Lee, Y.-J. Cho, M. Hwang-Bo, B.-J. You, and S.-R. Oh,A stable target-tracking control for unicycle mobile robots,(ieeexplore.ieee.org)/RSJ Int. Conf. on Intelligent Robots andSystems, 2000 (IROS 2000) IEEE, 2000, Vol. 3, 1822–1827.
  26. [27] C.C. De Wit and O. Sordalen, Exponential stabilization of mo-bile robots with nonholonomic constraints, IEEE Transactionson Automatic Control, 37(11), 1992, 1791–1797.
  27. [28] E.R. Trejo-Guerra, C. Cruz-Hernandez, C. Sanchez-Lopez,and M. Fakhfakh, Current conveyor realization of synchro-nized Chua’s circuits for binary communications, (ieeex-plore.ieee.org), DTIS, 2008, 1–4.
  28. [29] S. Vaidyanathan, Analysis and adaptive synchronization oftwo novel chaotic systems with hyperbolic sinusoidal andcosinusoidal nonlinearity and unknown parameters, Journal ofEngineering Science and Technology Review – jestr.org, 6(4),2013, 53–65.
  29. [30] S.H. Strogatz, Nonlinear dynamics and chaos: With applica-tions to physics, biology, chemistry, and engineering, Comput-ers in Physics, 8(5), 1994, 532–532.
  30. [31] L.O. Chua and E.W. Szeto, High-order non-linear circuitelements: Circuit-theoretic properties, International Journalof Circuit Theory and Applications, 11(2), 1983, 187–206.
  31. [32] A. Hegazi, H. Agiza, and M. El-Dessoky, Adaptive synchro-nization for R¨ossler and Chua’s circuit systems, InternationalJournal of Bifurcation and Chaos, 12(07), 2002, 1579–1597.
  32. [33] K. Bouallegue, Generation of multi-scroll chaotic attractorsfrom fractal and multi-fractal processes, 2011 Fourth Int. Work-shop on Chaos-Fractals Theories and Applications (IWCFTA),(ieeexplore.ieee.org), 2011, 398–402.
  33. [34] Y. Gao, Q. Li, X. Li, and G. Qian, Construction of multi-scrollchaotic attractors with exponential function, 2016 IEEE Int.Conf. on Digital Signal Processing (DSP), (ieeexplore.ieee.org),2016, 542–544.
  34. [35] S. Rasappan and S. Vaidyanathan, Hybrid synchronizationof n-scroll chaotic Chua circuits using adaptive backsteppingcontrol design with recursive feedback, Malaysian Journal ofMathematical Sciences, 7(2), 2013, 219–246.
  35. [36] F. Nicolau and W. Respondek, Multi-input control-affine sys-tems linearizable via one-fold prolongation and their flatness,2013 IEEE 52nd Annual Conf. on Decision and Control (CDC),(ieeexplore.ieee.org), 2013, 3249–3254.
  36. [38],the chaotic path planning with a mirror mapping methoddoes not require a map of the terrain and it is more efficientthan the random walk algorithm.The comparison results of the two proposed chaoticsystems for all space cases are depicted in Fig. 7. In thisfigure, the simulation of the robot trajectory of each chaoticsystem with different workspace dimensions is presented.Furthermore, in Table 1, time analysis and terrain coverageor its coverage rate (C) for the two dynamical systems arecompared. We note that the double-scroll Lorenz systemshows smaller values of the coverage rate (C) as regardsthe other system. The multi-scroll chaotic system has asignificantly higher value of the coverage rate (bold valuesin Table 1). As a result, from the two proposed chaoticsystems, the multi-scroll chaotic system has better resultsor performance coverage, especially when we increase theworkspace dimensions, which is obvious in Fig. 7(d), where89.86% of the workspace shows to be covered by the mobilerobot, compared to Fig. 7(c), where only 29.82% of theworkspace shows to be covered, using the double scrollin the same iterative time and with the same workspacedimensions.Furthermore, to better explain the effectiveness ofour approach, the terrain coverage using the proposedapproach in more complex space with obstacle avoidanceis depicted in Fig. 8. In this figure, the reference coveragetrajectory (left figure) and the real coverage trajectory(right figure) of the robot are presented. As it is shown,it is clear that the robot successfully joins the referencecoverage path even in the presence of boundary conditionsand obstacles. However, thisn work can prove to be very473Figure 7. Coverage trajectory of the mobile robot using the flatness controller, mirror mapping method and double-scroll andmulti-scroll chaotic system in different spaces dimensions: (a) using double-scroll in the 50 m × 50 m workspace; (b) usingmulti-scroll in the 50 m × 50 m workspace; (c) Using double-scroll in the 100 m × 100 m workspace; and (d) using multi-scrollin the 100 m × 100 m workspace.Figure 8. Reference coverage trajectory (left figure) and actual coverage trajectory (right figure) of mobile robot in differentcomplex workspaces.helpful for the resolution of the coverage problem for theintroduced surveillance tasks.7. ConclusionThe paper provides a new approach or method to generatepaths for mobile robots accomplishing military missionssuch as surveillance or patrolling. Using the chaotic sys-tems as a primary source of chaotic movement combinedwith the flatness controller, the reference path is altered,in each boundary condition or obstacles, without compro-mising the overall goals of the patrolling mission. The ob-tained trajectory emulates an unpredictable motion when474chased by predators. Moreover, the coverage rate andtime in which the robot covers the workspace using themulti-scroll chaotic system, in different study cases, hasbeen studied providing very satisfactory results in compar-ison to the use of the double-scroll chaotic system.Finally, the results of this work guarantee that theapplication of chaotic systems as solutions for robots tra-jectory control methods represents a very interesting taskfor researchers of both scientific fields.References[1] D.R. Corbett, D.W. Gage, and D.D. Hackett, Robotic commu-nications and surveillance – The DARPA LANdroids program,Australasian Joint Conf. on Artificial Intelligence, Springer,Berlin, Heidelberg, 2011, 749–758.[2] L.S. Martins-Filho and E.E. Macau, Patrol mobile robots andchaotic trajectories, Mathematical Problems in Engineering,2007, ID 61543, 1–13.[3] P. Sooraska and K. Klomkarn, “No-CPU chaotic robots: Fromclassroom to commerce, IEEE Circuits and Systems Magazine,10(1), 2010, 46–53.[4] D.W. Kim, T.A. Lasky, and S.A. Velinsky, Autonomous multi-mobile robot system: Simulation and implementation usingfuzzy logic, International Journal of Control, Automation andSystems, 11(3), 2013, 545–554.[5] H. Lee, E.-J. Jung, B.-J. Yi, and Y. Choi, Navigation strat-egy of multiple-mobile robot systems based on the null-spaceprojection method, International Journal of Control, Automa-tion and Systems, 9(2), 2011, 384–390.[6] M. Kapanoglu, M. Ozkan, O. Parlaktuna, et al., Pattern-basedgenetic algorithm approach to coverage path planning formobile robots, Int. Conf. on Computational Science, Springer,Berlin Heidelberg, 2009, 33–42.[7] L. Feifei and L. Fei, Time-jerk optimal planning of indus-trial robot trajectories, International Journal of Robotics andAutomation, 31(1), 2016, 1–7.[8] M. Shayestegan, M.H. Marhaban, S. Shafie, and A.S.B. Din,Fuzzy logic-based robot navigation in static environment withdead cycle obstacles, International Journal of Robotics andAutomation, 28(4), 2013.[9] C. Luo and S.X. Yang, A bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environments, IEEE Transactions onNeural Networks, 19(7), 2008, 1279–1298.[10] J. Zhang, H. Lv, D. He, L. Huang, Y. Dai, and Z. Zhang,Discrete bioinspired neural network for complete coverage pathplanning, International Journal of Robotics and Automation,32(2), 2017.[11] Y. Nakamura and A. Sekiguchi, The chaotic mobile robot,IEEE Transactions on Robotics and Automation, 17(6), 2001,898–904.[12] R.L. Devaney and J.-P. Eckmann, An introduction to chaoticdynamical systems, Physics Today, 40, 1987, 72.[13] C.K. Volos, N. Doukas, I. Kyprianidis, I. Stouboulos, andT. Kostis, Chaotic autonomous mobile robot for militarymissions, In Proceedings of the 17th International Conferenceon Communications, 2013, 197–202.[14] C. Li, F. Wang, L. Zhao, Y. Li, and Y. Song, An improvedchaotic motion path planner for autonomous mobile robotsbased on a logistic map, International Journal of AdvancedRobotic Systems, 10(6), 2013, 273.[15] X. Zang, S. Iqbal, Y. Zhu, X. Liu, and J. Zhao, Applicationsof chaotic dynamics in robotics, International Journal ofAdvanced Robotic Systems, 13(2), 2016, 60.[16] E.N. Lorenz, Deterministic nonperiodic flow, Journal of theAtmospheric Sciences, 20(2), 1963, 130–141.[17] O.E. R¨ossler, An equation for continuous chaos, Physics LettersA, 57(5), 1976, 397–398.[18] A. Arneodo, P. Coullet, and C. Tresser, Possible new strangeattractors with spiral structure, Communications in Mathe-matical Physics, 79(4), 1981, 573–579.[19] N. Salah, B. Kais, M. Hassen, and V. S, Controlling mobilerobot based on multi-scroll dynamic chaotic systems, Inter-national Journal of Control Theory and Applications, 10(34),2017, 31–42.[20] E.D. Markus, J.T. Agee, and A.A. Jimoh, Trajectory controlof a two-link robot manipulator in the presence of gravity andfriction, AFRICON, 2013, (ieeexplore.ieee.org, 2013), 1–5.[21] E. Markus, J. Agee, A. Jimoh, N. Tlale, and B. Zafer, Flatnessbased control of a 2 DOF single link flexible joint manipulator,SIMULTECH (pdfs.semanticscholar.org), 2012, 437–442.[22] E.D. Markus, J.T. Agee, and A.A. Jimoh, Flat control ofindustrial robotic manipulators, Robotics and AutonomousSystems, 87, 2017, 226–236.[23] R. Siegwart, I.R. Nourbakhsh, and D. Scaramuzza, Introductionto autonomous mobile robots, (Cambridge MA: MIT Press,2011).[24] H. Abidi, M. Chtourou, K. Kaaniche, and H. Mekki, Visualservoing based on efficient histogram information, InternationalJournal of Control, Automation and Systems, 15(4), 1746–1753, 2017.[25] R. Siegwart and I.R. Nourbakhsh, Introduction to autonomousmobile robots, Bradford Book, Intelligent robotics and au-tonomous agents series, 2004.[26] S.-O. Lee, Y.-J. Cho, M. Hwang-Bo, B.-J. You, and S.-R. Oh,A stable target-tracking control for unicycle mobile robots,(ieeexplore.ieee.org)/RSJ Int. Conf. on Intelligent Robots andSystems, 2000 (IROS 2000) IEEE, 2000, Vol. 3, 1822–1827.[27] C.C. De Wit and O. Sordalen, Exponential stabilization of mo-bile robots with nonholonomic constraints, IEEE Transactionson Automatic Control, 37(11), 1992, 1791–1797.[28] E.R. Trejo-Guerra, C. Cruz-Hernandez, C. Sanchez-Lopez,and M. Fakhfakh, Current conveyor realization of synchro-nized Chua’s circuits for binary communications, (ieeex-plore.ieee.org), DTIS, 2008, 1–4.[29] S. Vaidyanathan, Analysis and adaptive synchronization oftwo novel chaotic systems with hyperbolic sinusoidal andcosinusoidal nonlinearity and unknown parameters, Journal ofEngineering Science and Technology Review – jestr.org, 6(4),2013, 53–65.[30] S.H. Strogatz, Nonlinear dynamics and chaos: With applica-tions to physics, biology, chemistry, and engineering, Comput-ers in Physics, 8(5), 1994, 532–532.[31] L.O. Chua and E.W. Szeto, High-order non-linear circuitelements: Circuit-theoretic properties, International Journalof Circuit Theory and Applications, 11(2), 1983, 187–206.[32] A. Hegazi, H. Agiza, and M. El-Dessoky, Adaptive synchro-nization for R¨ossler and Chua’s circuit systems, InternationalJournal of Bifurcation and Chaos, 12(07), 2002, 1579–1597.[33] K. Bouallegue, Generation of multi-scroll chaotic attractorsfrom fractal and multi-fractal processes, 2011 Fourth Int. Work-shop on Chaos-Fractals Theories and Applications (IWCFTA),(ieeexplore.ieee.org), 2011, 398–402.[34] Y. Gao, Q. Li, X. Li, and G. Qian, Construction of multi-scrollchaotic attractors with exponential function, 2016 IEEE Int.Conf. on Digital Signal Processing (DSP), (ieeexplore.ieee.org),2016, 542–544.[35] S. Rasappan and S. Vaidyanathan, Hybrid synchronizationof n-scroll chaotic Chua circuits using adaptive backsteppingcontrol design with recursive feedback, Malaysian Journal ofMathematical Sciences, 7(2), 2013, 219–246.[36] F. Nicolau and W. Respondek, Multi-input control-affine sys-tems linearizable via one-fold prolongation and their flatness,2013 IEEE 52nd Annual Conf. on Decision and Control (CDC),(ieeexplore.ieee.org), 2013, 3249–3254.[37] M. Fliess, J. L´evine, P. Martin, and P. Rouchon, Flatnessand defect of non-linear systems: Introductory theory andexamples, International Journal of Control, 61(6), 1995, 1327–1361.[38] E. Gonzalez, O. Alvarez, Y. Diaz, C. Parra, and C. Bustacara,BSA: A complete coverage algorithm, Proc. of the 2005 IEEEInt. Conf. on Robotics and Automation, 2005, ICRA 2005,(ieeexplore.ieee.org), 2005, 2040–2044.475

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