Platoon Stability Research Articles

An auction mechanism for platoon leader determination in single-brand cooperative vehicle platooning

Cooperative vehicle platooning enabled by connected automated vehicle (CAV) technology has been identified to bring energy savings and driving-effort reduction. However, the intrinsic difference of gained benefits between the leading vehicle and the following vehicles hampers the spontaneous platooning via peer-to-peer coordination. This study proposes an auction mechanism that determines the leader–follower positioning together with the associated benefits, for facilitating the formation and maintaining the behavioral stability of vehicle platoons in a distributed way. We theoretically prove that there is no mechanism to achieve an efficient outcome in an ex post equilibrium, requiring individual rationality and budget balance. In this regard, we provide a truthful ε-approximate auction mechanism that deploys a linear transfer function, which guarantees that the implemented outcome is an efficient approximate dominant strategy equilibrium.

String Stability of Mixed Platoon Under Cooperative AdaptiveCruise Control

String Stability of Mixed Platoon Under Cooperative AdaptiveCruise Control

Study on stability and scalability of vehicular platoon with a bidirectional ring interconnection

This paper studies the stability and scalability of the platoon where multiple vehicles move in a closed roadway and are coupled in a bidirectional ring. Each vehicle regulates its longitudinal motion based on bidirectional asymmetric control with triple asymmetry factors. By exploiting Hermite stability criterion, we derive necessary and sufficient conditions of stability for the n-vehicle platoon. Based on parametric robustness analysis, necessary and sufficient conditions of scalably asymptotic stability are further obtained, meaning that the stability is independent of the number of vehicles in the platoon. It is proved that symmetric spacing feedback is necessary for scalably asymptotic stability and the first spatial mode is the least stable among all the non-zero modes. Numerical computations show that the stability region in the space of feedback gains is favourable when the asymmetry level on speed gain is small and the asymmetry level on acceleration gain is large, whereas it may deteriorate rapidly when these two asymmetry factors have different signs.

Analysis of the Intra-Platoon Message Delivery Delay in a Platoon of Vehicles

A platoon of connected and automated vehicles (CAVs) is one of the promising autonomous-driving applications. Vehicles in a platoon need timely delivery of road-safety information in order to alter their speeds in time and thus maintain the stability of the platoon. The intra-platoon message delivery delay is a critical metric that has a big impact on the maintenance of a platoon's stability. It depends on several system parameters, such as the number of vehicles in a platoon, the intra-platoon spacing, and the distribution of non-platoon vehicles. This paper studies the analysis of the intra-platoon message delivery delay in a platoon of CAVs moving on a highway road. A theoretical analytical model is derived to investigate the impacts of major system parameters on the intra-platoon message delivery delay. The derived analytical model considers a V2V hop-by-hop communication mode and takes into account the effects of both platoon and non-platoon vehicle nodes on channel access contention. The effect of hidden vehicle nodes is also considered. The derived analytical model is validated through simulation results and the impacts of major system parameters on the intra-platoon message delivery delay are investigated through numerical results. The derived analytical model can be used to provide reasonable reference values for system parameter setting in order to maintain the stability of an autonomous-driving platoon.

Control of connected vehicles with event-triggered transmission and prescribed energy budget

This paper is concerned with event-triggered cooperative control of a platoon of connected vehicles via vehicular ad hoc networks (VANETs). To reduce communications among vehicles, we introduce a hybrid event-triggered transmission mechanism based on both time elapsed and state error. The effect of time-varying transmission delay and communication energy constraint can be also taken into account in the system modeling and design procedures. The on-board sensors use different power levels to transmit information resulting in different packet loss rates. The vehicular platoon system is proved to be exponentially mean-square stable under the hybrid event-triggering scheme and a constant time headway spacing policy. A framework for co-design of the hybrid event triggering scheme and the output feedback controller is given to guarantee platoon stability and spacing-error convergence along the stream. Numerical simulations are given to demonstrate the effectiveness of proposed method.

From homogeneous to heterogeneous traffic flows: [formula omitted] String stability under uncertain model parameters

This paper shows that the heterogeneity of drivers’ and vehicles characteristics makes platoons, on average, more string-unstable. However, the string instability degree of unstable platoons is much higher in a homogeneous flow than in a heterogeneous one. These results are based on an L∞ characterization of string stability, which is shown to be the most appropriate one from a traffic safety viewpoint. Mechanisms and conditions are discussed in which an L2 characterization is not able to capture the amplification of a speed drop through a string of vehicles. An analytical sufficient condition for the L∞ string stability of heterogeneous vehicles, which move according to a general class of car-following models, is derived. Above all, a thorough comparison of L∞ and L2 string stability characterizations between a homogeneous and a heterogenous flow, is performed. To this aim, the Lp norms of heterogeneous platoons are calculated within a quasi-Monte Carlo framework. The variability of the Lp norm values due to the platoon length, the equilibrium speed, and the probability distribution model of the uncertain vehicle parameters, is analysed. Overall, it is shown that the platoon stability behaviour sensibly changes with the shape and the correlation structure of vehicle model parameter distributions. Therefore, traffic heterogeneity needs to be modelled in order to correctly characterize the string stability of a mixed traffic flow.

Centralized and Distributed Control Framework Under Homogeneous and Heterogeneous Platoon

Platooning vehicles are beneficial in comfortable driving, safety, and enhanced transportation efficiency. Platooning vehicles with cooperative adaptive cruise control (CACC) mode can potentially result in a small distance between vehicles with assured string stability. This CACC-based platoon control can be realized by vehicle-to-vehicle (V2V) or vehicle-to-everything (V2X) communication between vehicles. In this regard, the distributed control framework is widely used. It claims robustness to communication uncertainties since each vehicle has its controller. With the rapid research on V2X, the centralized framework is another option for the platooning vehicle control framework. This paper investigates and analyzes the centralized and distributed control framework under platoon uncertainty. In most of the papers, the platoon uncertainty is considered as road slope and vehicle dynamics model. In this paper, the platoon uncertainty refers to the platoon types, namely homogeneous and heterogeneous platoon. The analytical platoon stability is studied for both frameworks under different platoon types. It gives the minimum time gap boundary to guarantee string stability for both frameworks. The numerical string stability is performed by the simulation to verify the analytical. The simulation is done using the integrated PreScan and Matlab/Simulink. Then, the robustness of both frameworks is evaluated under latency and packet loss. Finally, the performance of both frameworks is also evaluated.

Vehicle Platooning With Non-Ideal Communication Networks

The performance and effectiveness of a vehicle platoon rely on the topology of information flow and quality of communications, such as delays and dropouts. In this paper, we investigate the homogeneous and constant-time-headway-spacing-policy-based vehicle platoon longitudinal control problem, where communication impairments including the limited communication range, random packet losses, and time-varying communication delays are considered. Here, internal stability characterizes the system stability without disturbance while string stability is concerned with the error amplification when the vehicle platoon is affected by external disturbances. First, for the case when each vehicle utilizes the position, velocity, and acceleration information of multiple preceding and following vehicles, we obtain sufficient conditions to guarantee the internal stability of the vehicle platoon system based on the stability of matrix polynomials and the matrix eigenvalue perturbation theory. Then, considering random packet losses, we find that the effectiveness of platoon control relies on the frequency of packets being successfully received, or the delay till a new packet is received. We also obtain the upper bound for delays on all communication links such that the internal stability of the vehicle platoon can still be maintained when time-varying communication delays are within the bound. The $L_2$ -string stability is also analyzed through the transfer function for both ideal communication cases, and cases with uniform and constant delays. Extensive simulink-based numerical results validate our analysis, which reveals how communication impairments affect platoon control with a realistic information flow topology.

Time-Dependent Performance Analysis of the 802.11p-Based Platooning Communications Under Disturbance

Platooning is a critical technology to realize autonomous driving. Each vehicle in platoons adopts the IEEE 802.11p standard to exchange information through communications to maintain the string stability of platoons. However, one vehicle in platoons inevitably suffers from a disturbance resulting from the leader vehicle acceleration/deceleration, wind gust and uncertainties in a platoon control system, i.e., aerodynamics drag and rolling resistance moment etc. Disturbances acting on one vehicle may inevitably affect the following vehicles and cause that the spacing error is propagated or even amplified downstream along the platoon, i.e., platoon string instability. In this case, the connectivity among vehicles is dynamic, resulting in the performance of 802.11p in terms of packet delay and packet delivery ratio being time-varying. The effect of the string instability would be further deteriorated once the time-varying performance of 802.11p cannot satisfy the basic communication requirement. Unlike the existing works which only analyze the steady performance of 802.11p in vehicular networks, we will focus on the impact of disturbance and construct models to analyze the time-dependent performance of 802.11p-based platooning communications. The effectiveness of the models is validated through simulation results. Moreover, the time-dependent performance of 802.11p is analyzed through numerical results and it is validated that 802.11p is able to satisfy the communication requirement under disturbance.

String Stability of a Vehicular Platoon With the Use of Macroscopic Information

The paper investigates the possibility of using macroscopic information to improve control performance of a vehicular platoon composed of autonomous vehicles. A mesoscopic traffic modeling framework is proposed, and closed loop String Stability is achieved by exploiting Input-to-State Stability (ISS) for the analysis of the platoon. Examples of mesoscopic control laws are illustrated and simulations show the effectiveness of our approach in ensuring String Stability and improving the platoon behavior.

Stability Analysis of Vehicle Platooning With Limited Communication Range and Random Packet Losses

Control performance of vehicle platooning relies on the information flow topology and quality of wireless communications. In this article, we investigate the constant-time-headway-spacing-policy-based vehicle platooning problem, where multiple predecessors' information is used by the following vehicles and communication impairments, i.e., limited communication range and random packet losses, are considered. In this article, first, when the leading vehicle moves at a constant speed, we obtain the sufficient and necessary conditions on sampling time, control gains, and internal lag, to ensure the stability of the vehicle platoon based on matrix polynomials' stability for ideal communications. Second, for time-independent homogeneous random packet losses, we provide the upper bound for the loss rate to maintain convergence in expectation by matrix eigenvalue perturbation theory when no input is set for lossy information. We also provide sufficient conditions to guarantee mean-square convergence for heterogeneous time-independent random packet losses and show the convergence time for any given accuracy and probability. Third, when historically latest information is used for input, the sufficient and necessary conditions are provided to ensure the internal stability and string stability by Markov jump linear system theory. Furthermore, we discuss the controller design when no feasible solution exists to guarantee the string stability. Extensive numerical results validate our analysis.

Multi look‐ahead consensus of vehicular networks in the presence of random data missing

This study deals with internal and string stability analyses of vehicular platoons with centralized multi-look ahead network topology in the presence of communication and parasitic delays and random data missing. In vehicular networks, because of huge amount of information exchanged between vehicles and highway infrastructures, some adverse effects such as data missing and communication delay are unavoidable in practical implementation. In this study, a third-order dynamical model is used to describe the longitudinal dynamics of each following vehicle, and the constant spacing strategy is used to adjust the inter-vehicle spacing. By considering communication and parasitic delays and random data missing, the closed-loop dynamics of platoon is derived. Afterward, by using the Lyapunov–Krasovskii theorem, sufficient conditions assuring the internal stability are introduced. In continuance, the string stability of platoon under the aforementioned effects is studied. It will be shown that the proposed controller always guarantees the string stability of platoon without any limitations. Several simulation results are provided to show the effectiveness of the proposed approaches.

A Distributed Adaptive Triple-Step Nonlinear Control for a Connected Automated Vehicle Platoon With Dynamic Uncertainty

Connected automated vehicle (CAV) platoon control is becoming increasingly prevalent because of its unique advantages in reducing fuel consumption and improving traffic efficiency. A novel control framework for CAV platoon control is designed in this article. First, a model predictive control (MPC)-based method is proposed to obtain the optimal velocity of the whole platoon, in which both reducing fuel consumption and improving transport efficiency are taken into account in the optimization process. Then, a distributed adaptive triple-step nonlinear control strategy is investigated from the perspective of multiagent system control. The adaptive performance of the control strategy can guarantee the string stability of the CAV platoon under the premise of the existence of dynamic uncertainties. Various simulation conditions with heterogeneous dynamic disturbances are designed to validate the proposed control strategy, and the results show that the proposed control strategy can be robust to dynamic disturbances while ensuring the string stability of the CAV platoon.

Computation of Time Delay Stability Margin for the Automated Vehicular Platoon

Due to the limited band width and congestion of communication channels in the wireless vehicle-to-vehicle (V2V) communication, time delay inevitably arises and dramatically leads to the disturbances for the automated vehicular platoon. This paper focuses on computing the exact time delay stability margin. In this study, we treat this problem as a stability issue of a consensus system with time delay, where each vehicle in the platoon is recognized as a node, and the interconnected information flow is represented as a graph. Then, the distributed controller is designed by combining the states of the vehicle itself and its neighbouring vehicles. Furthermore, the stability of the entire platoon is analysed according to the characteristic equation of the closed-loop system, and a necessary and sufficient condition for the exact time delay stability margin is obtained. Especially, for the automated vehicular platoon with undirected topology, it is revealed that exact time delay stability margin is determined by the largest eigenvalue of the augmented Laplacian matrix. Furthermore, a rapid method for finding exact time delay stability margin is proposed. Finally, numerical simulations demonstrate that this work generates exact and satisfactory time delay stability margin for the automated vehicular platoon.

Distributed Adaptive Event-Triggered Control and Stability Analysis for Vehicular Platoon

This paper is concerned with the stability of the vehicular platoon consisting of a leader and multiple cooperative autonomous driving followers. The objective of the platoon control is to ensure all vehicles traveling at the same speed while maintaining a safety spacing. To achieve the objective, a novel control framework consisting of the distributed adaptive event-triggered observer and the car-following control protocol is proposed for the vehicular platoon control. The condition that only few following vehicles can access the information of the leader is considered. In order to design controllers while avoid using any global information, such as the system matrix and the state of the leader, a distributed event-triggered observer is proposed, such that each vehicle can observe the dynamics of the leader. Based on this observer, both collision avoidance and limited communication source of each vehicle are simultaneously considered in the design of the observer. It is shown that under the proposed control framework, the platoon can achieve asymptotical stable, meanwhile, the amount of transmission data and communication cost among vehicles can be reduced. Finally, numerical simulations are presented to show the applicability of the obtained results.

Robust optimal control and identification of adaptive cruise control systems in the presence of time delay and parameter uncertainties

This article deals with the robust optimal control and identification of uncertain adaptive cruise control systems. Both measurement delay and engine’s lag are investigated in system modeling and control design. The control structure consists of two steps. In the first step, by using a new approach, the uncertain parameters of longitudinal dynamics of each vehicle is identified. Afterwards, at the second step, by using the relative position and velocity measurement with respect to ahead vehicle, a robust control against size changing of platoon is presented to assure the internal stability, string stability, and safety of heterogeneous vehicular platoons. A cost function involving important metrics internal stability, maximum overshoot, and settling time is introduced, and the particle swarm optimization algorithm is used to find the optimal values of control parameters minimizing the cost function. It will be shown that the proposed robust controller guarantees the internal stability, string stability, and safety of adaptive cruise control systems in the presence of measurement and parasitic delays. Several simulation results are provided to show the effectiveness of the proposed approaches.

String Stability of Homogenous Vehicle Platoons Based on Cooperative Extended State Observers

We study platoon control of homogeneous vehicles with linear third-order longitudinal dynamics with the constant time headway (CTH) policy. In order to ensure string stability with a small time headway, a distributed control law based on extended state observers is proposed. The controller of each follower vehicle only depends on its own velocity, acceleration, inter-vehicle distance and velocity difference with respect to its immediate predecessor. First, a dynamic model based on velocity differences between adjacent vehicles is established. Then cooperative extended state observers are designed to estimate the acceleration differences between adjacent vehicles, based on which distributed cooperative controllers are designed. By analyzing the transfer function of inter-vehicle distances errors, the sufficient conditions to ensure string stability are presented. It is shown that for any given positive time headway, the parameters of distributed cooperative state observers and controllers can be properly designed so that the inter-vehicle distance errors are not amplified during the backward propagation along the platoon. The effectiveness of the cooperative control law is demonstrated by simulations.

An Auction Mechanism for Platoon Leader Determination in Single-Brand Cooperative Vehicle Platooning

Cooperative vehicle platooning enabled by connected automated vehicle (CAV) technology has been identified to bring energy savings and driving-effort reduction. However, the intrinsic difference of gained benefits between the leading vehicle and the following vehicles hampers the spontaneous platooning via peer-to-peer coordination. This study proposes an auction mechanism that determines the leader-follower positioning together with the associated benefits, for facilitating the formation and maintaining the behavioral stability of vehicle platoons in a distributed way. We theoretically prove that there is no mechanism to achieve an efficient outcome in an ex post equilibrium, requiring individual rationality and budget balance. In this regard, we provide a truthful $\epsilon-$approximate auction mechanism that deploys a linear transfer function, which guarantees that the implemented outcome is an efficient approximate dominant strategy equilibrium.

Reducing time headway in platoons under the MPF topology in the presence of communication delays

Abstract For platoons under the multiple-predecessor following (MPF) topology, communication delays can compromise both the internal stability and string stability. The most straightforward solution to guarantee stability is by increasing the time headway. On the other hand, time headway plays a significant role in road capacity and increasing its value is in contrast with the idea of platooning. In this study, internal stability and string stability of platoons suffering from communication delays are investigated and a lower bound for the time headway is proposed. Using this bound, platoons do not need to massively increase the time headway in order to compensate for the effects of communications delays. Finally, we evaluate the proposed lower bound on the time headway and the simulation results demonstrate its effectiveness.

Platoon Stability Conditions Under Inter-vehicle Additive Noisy Communication Channels

This paper studies the behavior of a platoon control system under the presence of inter-vehicle noisy communication channels. A set of homogeneous vehicles modelled as LTI systems with a predecessor-following topology is analyzed. Our main contribution is to study the stochastic scenario when additive white noise is affecting the communication between agents. We aim to provide conditions for mean square string stability and look over its relationship with the mean and variance of the tracking error. Finally, through computational analysis, we discuss the scalability, convergence and boundedness properties related to string stability in stochastic multi-agent systems.