Path Planning and Tracking for Overtaking Maneuvers of Autonomous Vehicles in Analogy to Supersonic Compressible Fluid Flow

Given the undoubtable similarities between the dynamic behavior of the vehicular traffic flow in terms of its response to boundary condition alterations dictated in the form of obstacles, and the specific case of supersonic compressible fluid flow fields, the current manuscript addresses developing a target trajectory for the overtaking maneuver of autonomous vehicles. The path-planning is pursued in analogy to the governing principles of the supersonic compressible fluid flow fields, with the specific definition of a physically meaningful dimensionless group, namely the Traffic Mach number (MT), which grants the initial access point to the said set of fundamental equations. This practical application is a follow-up to the primarily established proof-of-concept level introduction and analysis of the more general case of collision avoidance for autonomously driven vehicles in accordance with the supersonic compressible fluid flow field, where the Traffic Mach number was first introduced. The proposed trajectory is then taken to the next block of the investigation, namely the tracking and control aspects of the maneuvering vehicle’s dynamics. The path tracking controller is designed based on sliding mode control technique and the algorithm is applied on a 7-DOF simulation model, used for validation and discussion of results. The proposed method is shown to be suitable for overtaking maneuvers of autonomous vehicles, whilst meeting the criteria for a relative velocity from the constant-velocity vehicle ahead of the road in the supersonic regime based on the defined Traffic Mach number. The results are then presented, first, in the scope of the aerodynamics field configuration and their verifications, followed by the vehicle dynamics remarks showing the practicality of the proposed method in terms of vehicle motion. It is observed that the distance corresponding to the delayed maneuver maximizes at highest velocities of the ego vehicle, consistent with the highest MT values, yet in all simulated cases, the control system of the vehicle model was capable of performing the maneuver based on the assigned trajectories through the present model.