Table of Links

Abstract and Introduction

Vehicle Modeling

The Nonlinear Feedback Control

OD Corridors and Desired Orientations

Boundary and Safety Controllers

Simulation Results

Conclusion

Appendix A: Collision Detection

Appendix B: Transformed ISO-Distance curves

Appendix C: Local Density

Appendix D: Safety Controller Details

Appendix E: Controller Parameters

References

III. THE NONLINEAR FEEDBACK CONTROL

Two nonlinear controllers are employed as the kernel for real-time decision making by each vehicle while moving on the roundabout or the connected straight branches, respectively.

A. Nonlinear Controller for Straight (Horizontal) Roads

A nonlinear feedback controller (NLFC) is developed in [11] to control vehicles on a straight (horizontal) lane-free road that uses the vehicle’s state variables and its distance from other adjacent vehicles. This controller was designed for the continuous-time model (1) and guarantees some properties, including avoiding collisions, boundary violation, negative speed, and exceeding the allowable maximum speed. Also, when there is sufficient space, vehicles reach the desired longitudinal speeds, while accelerations, orientations, lateral speeds, and steering angles tend to zero (on an open straight road). The feedback law reads [11]:

B. Nonlinear Controller for Circular Roads

For vehicle control on the roundabout, we employ an NLFC presented in [12], which is specialized for circular roads, e.g. ring-roads or roundabouts, whose structure is similar to the NLFC for straight roads. It rigorously guarantees (in continuous time) the avoidance of collisions, boundary violation, and exceeding the maximum allowable angular speed, tracking the desired angular speed, convergence of acceleration and orientation (deviation from circular angle) to zero. The feedback law reads:

where

Furthermore, the distance definition, and consequently the iso-distance “aura” surrounding each vehicle, should be changed according to the desired deviation. This calls for a transformation that is described in Appendix B and leads to modified iso-distance curves (aura) around the vehicle, as depicted in Fig. 4, where the curved ellipses surrounding the ego vehicle are aligned with the vehicle's orientation to avoid wasting lateral space around the vehicle while ensuring safety.

It must be emphasized that the iso-distance ellipses extend all around each vehicle. This implies that, based on the NLFCs, “forces” are exerted to each vehicle from obstacles around them. While repulsion from front vehicles is typical in lane-based driving, the NLFCs for lane-free driving also produce “nudging” forces due to obstacles that may be positioned on the left or right or rear side of the vehicle. Beyond safety implications, vehicle nudging was found to have a beneficial impact on the macroscopic properties of the emerging traffic flow [38],[39].

The centre of all mentioned auras, from the ellipses defined for straight or skewed movements to the curved ellipses for the circular movement, is on the middle of the rear axle as introduced in (1). Thus, they cover a smaller area in front of the ego vehicle, compared to the rear part. Having different orientations and moving forward, vehicles have higher collision risk at their front part in crowded situations. To reduce this risk,

we move the centre of aura to the middle point of the front axle. Thus, the inter-vehicle distance is calculated based on the position of the middle of the front axle.

C. Adaptive Desired Speed