Stability and Equilibrium Analysis of Laneless Traffic with Local Control Laws

In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis representing the direction of motion and the X-axis representing the lateral or the direction perpendicular to the direction of motion. Different influence graphs are used to model the interaction between the vehicles in these two directions. The instantaneous accelerations of each car, in both X and Y directions, are functions of the measurements from the neighbouring cars according to these influence graphs. The stability and equilibrium spacings of the car formation is analyzed for usual traffic situations such as steady flow, obstacles, lane changing and rogue drivers arbitrarily changing positions inside the formation. Conditions are derived under which the formation maintains stability and the desired intercar spacing for each of these traffic events. Simulations for some of these scenarios are included.Comment: 8 page

Stability and String Stability Analysis of Formation Control Architectures for Platooning.

This thesis presents theoretical results for stability and string stability of formation control architectures for platooning. We consider three important interconnection topologies for vehicles travelling in a straight line as a string: leader following, cyclic and bidirectional. For the leader following topology we discuss modifications that allow reduced coordination requirements. In the first case we consider the use of the leader velocity as the state to be broadcast to the followers, rather than the standard use of the leader position. This selection yields a formation control architecture that achieves string stability even under time delays in the state broadcast, while reducing typical coordination requirements of leader following architectures. For the second modification we change the way in which the leader position is sent across the string to every follower. This technique keeps some of the good transient properties of the standard leader following architecture but eliminates most of the coordination requirements for the followers. However, we show that this technique does not provide string stability when time delays are present in the communication. The second topology that we discuss is a cyclic one, where the first member of the platoon is forced to track the last one. We discuss two strategies: one where the inter-vehicle spacings may follow a constanttime headway spacing policy and one where an independent leader broadcasts its position to every member of a cyclic platoon. For both strategies we obtain closed form expressions for the transfer functions from disturbances to inter-vehicle spacings. These expressions allow us to show that if the design parameters are not properly chosen, the vehicle platoon may become unstable when the string size is greater than a critical number. On the contrary, if the design parameters are well chosen, both architectures can be made stable and string stable for any size of the platoon. The final topology that we consider is bidirectional, where every member of the platoon, with the exception of the first and last, use measurements of the two nearest neighbours to control their position within the string. Although the derivations are more complex than in the two previous unidirectional cases, we obtain closed form epressions for the dynamics of the platoon. These expressions are in the form of simple transfer functions from disturbances to vehicles. They allow us to obtain stability results for any size of the platoon and understand the behaviour of the least stable pole location as the string size increases. All of the results obtained are illustrated by numerical examples and ad-hoc simulations

Stability and String Stability Analysis of Formation Control Architectures for Platooning.

This thesis presents theoretical results for stability and string stability of formation control architectures for platooning. We consider three important interconnection topologies for vehicles travelling in a straight line as a string: leader following, cyclic and bidirectional. For the leader following topology we discuss modifications that allow reduced coordination requirements. In the first case we consider the use of the leader velocity as the state to be broadcast to the followers, rather than the standard use of the leader position. This selection yields a formation control architecture that achieves string stability even under time delays in the state broadcast, while reducing typical coordination requirements of leader following architectures. For the second modification we change the way in which the leader position is sent across the string to every follower. This technique keeps some of the good transient properties of the standard leader following architecture but eliminates most of the coordination requirements for the followers. However, we show that this technique does not provide string stability when time delays are present in the communication. The second topology that we discuss is a cyclic one, where the first member of the platoon is forced to track the last one. We discuss two strategies: one where the inter-vehicle spacings may follow a constanttime headway spacing policy and one where an independent leader broadcasts its position to every member of a cyclic platoon. For both strategies we obtain closed form expressions for the transfer functions from disturbances to inter-vehicle spacings. These expressions allow us to show that if the design parameters are not properly chosen, the vehicle platoon may become unstable when the string size is greater than a critical number. On the contrary, if the design parameters are well chosen, both architectures can be made stable and string stable for any size of the platoon. The final topology that we consider is bidirectional, where every member of the platoon, with the exception of the first and last, use measurements of the two nearest neighbours to control their position within the string. Although the derivations are more complex than in the two previous unidirectional cases, we obtain closed form epressions for the dynamics of the platoon. These expressions are in the form of simple transfer functions from disturbances to vehicles. They allow us to obtain stability results for any size of the platoon and understand the behaviour of the least stable pole location as the string size increases. All of the results obtained are illustrated by numerical examples and ad-hoc simulations

Modelling supported driving as an optimal control cycle: Framework and model characteristics

Driver assistance systems support drivers in operating vehicles in a safe, comfortable and efficient way, and thus may induce changes in traffic flow characteristics. This paper puts forward a receding horizon control framework to model driver assistance and cooperative systems. The accelerations of automated vehicles are controlled to optimise a cost function, assuming other vehicles driving at stationary conditions over a prediction horizon. The flexibility of the framework is demonstrated with controller design of Adaptive Cruise Control (ACC) and Cooperative ACC (C-ACC) systems. The proposed ACC and C-ACC model characteristics are investigated analytically, with focus on equilibrium solutions and stability properties. The proposed ACC model produces plausible human car-following behaviour and is unconditionally locally stable. By careful tuning of parameters, the ACC model generates similar stability characteristics as human driver models. The proposed C-ACC model results in convective downstream and absolute string instability, but not convective upstream string instability observed in human-driven traffic and in the ACC model. The control framework and analytical results provide insights into the influences of ACC and C-ACC systems on traffic flow operations.Comment: Submitted to Transportation Research Part C: Emerging Technologie