Design of a Chaotic Trajectory Generator Algorithm for Mobile Robots
This work addresses the problem of designing an
algorithm capable of generating chaotic trajectories for mobile robots.
Particularly, the chaotic behavior is induced in the linear and angular
velocities of a Khepera III differential mobile robot by infusing them
with the states of the H´enon chaotic map. A possible application,
using the properties of chaotic systems, is patrolling a work area.
In this work, numerical and experimental results are reported and
analyzed. In addition, two quantitative numerical tests are applied in
order to measure how chaotic the generated trajectories really are.
[1] L. Li, H. Peng, J. Kurths, Y. Yang and H. Schellnhuber, Chaos-order
transition in foraging behavior of ants. Proceedings of the National
Academy of Sciences of the United States of North America, 11(23), p.
83928397, 2014.
[2] Y. Nakamura and A. Sekiguchi, The Chaotic Mobile Robot. IEEE
Transactions on Robotics and Automation, p. 898904, 2001.
[3] L. Martins–Filho and E. Macau, Kinematic control of mobile robots.
ABCM Symposium Series in Mechatronics, Volumen 2, p. 258264,
2006.
[4] Volos, Kyprianidis and Stouboulos. A chaotic path planning generator
for autonomous mobile robots. Robotics and Autonomous Systems,
60(4), p. 651656, 2012.
[5] D. Curiac and C. Volosencu A 2D chaotic path planning for mobile
robots accomplishing boundary surveillance missions in adversarial
conditions. Communications in Nonlinear Science and Numerical
Simulation, 19(10), p. 36173627, 2014.
[6] M. Hnon, A Two-Dimensional Mapping with a Strange Atractor. Comm.
Math. Phys., 50(1), pp. 69-77, 1976.
[7] N. Torres, Caos en sistemas biol´ogicos. Matematicalia: Revista Digital
de Divulgacin Matem´atica de la Real Sociedad Matem´atica Espa˜nola,
1(3), 2005.
[8] A. Besicovitch, On linear sets of points of fractional dimension,
Mathematische Annalen, 101(1): p.161193, 1929.
[9] P. Suster and A. Jadlovsk´a, A. Neural tracking trajectory of the
mobile robot Khepera II internal model control structure. International
Conference Process, Czech Republic, Kouty nad Desnou, 2010
[10] G. A. Gottwald and I. Melbourne, A new test for chaos in deterministic
systems. Proceedings of the Royal Society of London A. Mathematical,
Physical and Engineering Sciences. The Royal Society, Vol. 460, pp.
603611, 2004.
[11] B. B. Mandelbrot, The fractal geometry of nature, Vol. 173. Macmillan,
1983
[12] K. Foroutan–Pour, P. Dutilleul, and D. Smith, Advances in the
implementation of the box-counting method of fractal dimension
estimation. Applied Mathematics and Computation, 105(2): 195210.
1999.
[1] L. Li, H. Peng, J. Kurths, Y. Yang and H. Schellnhuber, Chaos-order
transition in foraging behavior of ants. Proceedings of the National
Academy of Sciences of the United States of North America, 11(23), p.
83928397, 2014.
[2] Y. Nakamura and A. Sekiguchi, The Chaotic Mobile Robot. IEEE
Transactions on Robotics and Automation, p. 898904, 2001.
[3] L. Martins–Filho and E. Macau, Kinematic control of mobile robots.
ABCM Symposium Series in Mechatronics, Volumen 2, p. 258264,
2006.
[4] Volos, Kyprianidis and Stouboulos. A chaotic path planning generator
for autonomous mobile robots. Robotics and Autonomous Systems,
60(4), p. 651656, 2012.
[5] D. Curiac and C. Volosencu A 2D chaotic path planning for mobile
robots accomplishing boundary surveillance missions in adversarial
conditions. Communications in Nonlinear Science and Numerical
Simulation, 19(10), p. 36173627, 2014.
[6] M. Hnon, A Two-Dimensional Mapping with a Strange Atractor. Comm.
Math. Phys., 50(1), pp. 69-77, 1976.
[7] N. Torres, Caos en sistemas biol´ogicos. Matematicalia: Revista Digital
de Divulgacin Matem´atica de la Real Sociedad Matem´atica Espa˜nola,
1(3), 2005.
[8] A. Besicovitch, On linear sets of points of fractional dimension,
Mathematische Annalen, 101(1): p.161193, 1929.
[9] P. Suster and A. Jadlovsk´a, A. Neural tracking trajectory of the
mobile robot Khepera II internal model control structure. International
Conference Process, Czech Republic, Kouty nad Desnou, 2010
[10] G. A. Gottwald and I. Melbourne, A new test for chaos in deterministic
systems. Proceedings of the Royal Society of London A. Mathematical,
Physical and Engineering Sciences. The Royal Society, Vol. 460, pp.
603611, 2004.
[11] B. B. Mandelbrot, The fractal geometry of nature, Vol. 173. Macmillan,
1983
[12] K. Foroutan–Pour, P. Dutilleul, and D. Smith, Advances in the
implementation of the box-counting method of fractal dimension
estimation. Applied Mathematics and Computation, 105(2): 195210.
1999.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:78142", author = "J. J. Cetina-Denis and R. M. López-Gutiérrez and R. Ramírez-Ramírez and C. Cruz-Hernández", title = "Design of a Chaotic Trajectory Generator Algorithm for Mobile Robots", abstract = "This work addresses the problem of designing an
algorithm capable of generating chaotic trajectories for mobile robots.
Particularly, the chaotic behavior is induced in the linear and angular
velocities of a Khepera III differential mobile robot by infusing them
with the states of the H´enon chaotic map. A possible application,
using the properties of chaotic systems, is patrolling a work area.
In this work, numerical and experimental results are reported and
analyzed. In addition, two quantitative numerical tests are applied in
order to measure how chaotic the generated trajectories really are.", keywords = "Chaos, chaotic trajectories, differential mobile robot,
Henons map, Khepera III robot, patrolling applications.", volume = "12", number = "11", pages = "1021-8", }
