A Mathematical Approach Towards Random Road Profile Generation Based on Chaotic Signals of Chua's Circuit (Contemporary Mathematics, 2022)
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.
Keywords: road curvature, road profile, 3D curve generation, chaos theory, Chua's circuit, random number sequence