A Mathematical Approach Towards Random Road Profile Generation Based on Chaotic Signals of Chua's Circuit

Authors

  • Sina Milani School of Engineering, RMIT University, Melbourne, Australia
  • Aidin Momtaz Department of Physics, Isfahan University of Technology, Isfahan, Iran
  • Sarah Amini Department of Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran
  • Kasra Amini FLOW and Fluid Physics Laboratory, Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden
  • Shekoufeh Sadeghi Department of Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran
  • Ehsan Qoreishi Department of Physics, Isfahan University of Technology, Isfahan, Iran
  • Sanaz Haddadian System and Circuit Technology Group, Heinz Nixdorf Institute, University of Paderborn, Paderborn, Germany

DOI:

https://doi.org/10.37256/cm.3120221151

Keywords:

road curvature, road profile, 3D curve generation, chaos theory, Chua's circuit, random number sequence

Abstract

In response to application demands in vehicle dynamics and control, traffic engineering, urban planning, and logistics, the generation of an adequate artificial road profile in terms of the diversity of geometric scenarios has been addressed in the current manuscript. The underlying mathematical principles for generating a geometrically comprehensive, yet logically meaningful, 3D road profile have been taken from high and unbiased sweeping factors of random number sequences over their domain of interest.  And to generate such random number sequences, the mathematically manipulated output signal of a well-established chaotic system has been utilized, namely that of the Chua's circuit. Having defined the target road profile mathematically with all its geometrical complexities, a suitable scheme derived from the mentioned chaotic signal has been used to generate the required random number sequences as defining parameters of the road profile. The scheme has been otherwise tested and proven to show the demanded level of randomness in literature. Several attempts have been made to create a diverse range of road profiles, considering the constraints imposed by vehicle dynamics. To generate the road geometries, the limitations imposed by the vehicle's motion, such as the limitations on corresponding curvatures, slopes, and banking angles are negotiated, in terms of vehicle dynamics and available tire-road friction forces, by evaluating how close a vehicle will be to its tire force capacity limits as it travels on sections of the generated road.

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Published

2022-02-21

How to Cite

1.
Milani S, Momtaz A, Amini S, Amini K, Sadeghi S, Qoreishi E, Haddadian S. A Mathematical Approach Towards Random Road Profile Generation Based on Chaotic Signals of Chua’s Circuit. Contemp. Math. [Internet]. 2022 Feb. 21 [cited 2024 May 28];3(1):34-59. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1151