Constrained optimization and distributed computation based car following control of a connected and autonomous vehicle platoon

Motivated by the advancement in connected and autonomous vehicle technologies, this paper develops a novel car-following control scheme for a platoon of connected and autonomous vehicles on a straight highway. The platoon is modeled as an interconnected multi-agent dynamical system subject to physical and safety constraints, and it uses the global information structure such that each vehicle shares information with all the other vehicles. A constrained optimization based control scheme is proposed to ensure an entire platoon’s transient traffic smoothness and asymptotic dynamic performance. By exploiting the solution properties of the underlying optimization problem and using primal-dual formulation, this paper develops dual based distributed algorithms to compute optimal solutions with proven convergence. Furthermore, the asymptotic stability of the unconstrained linear closed-loop system is established. These stability analysis results provide a principle to select penalty weights in the underlying optimization problem to achieve the desired closed-loop performance for both the transient and the asymptotic dynamics. Extensive numerical simulations are conducted to validate the efficiency of the proposed algorithms.     

Coordinated platooning with multiple speeds

In a platoon, vehicles travel one after another with small intervehicle distances; trailing vehicles in a platoon save fuel because they experience less aerodynamic drag. This work presents a coordinated platooning model with multiple speed options that integrates scheduling, routing, speed selection, and platoon formation/dissolution in a mixed-integer linear program that minimizes the total fuel consumed by a set of vehicles while traveling between their respective origins and destinations. The performance of this model is numerically tested on a grid network and the Chicago-area highway network. We find that the fuel-savings factor of a multivehicle system significantly depends on the time each vehicle is allowed to stay in the network; this time affects vehicles’ available speed choices, possible routes, and the amount of time for coordinating platoon formation. For problem instances with a large number of vehicles, we propose and test a heuristic decomposed approach that applies a clustering algorithm to partition the set of vehicles and then routes each group separately. When the set of vehicles is large and the available computational time is small, the decomposed approach finds significantly better solutions than does the full model.     

Optimal vehicle trajectory planning in the context of cooperative merging on highways

One of the main triggers of traffic congestion on highways is vehicle merging at on-ramps. The development of automated procedures for cooperative vehicle merging is aimed to ensure safety and alleviate congestion problems. In this work, a longitudinal trajectory planning methodology is presented, developed to assist the merging of vehicles on highways; it achieves safe and traffic-efficient merging, while minimizing the engine effort and passenger discomfort through the minimization of acceleration and its first and second derivatives during the merging maneuver. The problem is formulated as a finite-horizon optimal control problem and is solved analytically. This enables the solution to be stored on-board, saving computational time and rendering the methodology suitable for practical applications. The tunable weights, used for taking into account the different optimization criteria, may serve as parameters to match the individual driver’s preferences. The proposed methodology is first developed for a pair of cooperating vehicles, a merging one and its putative leader. Moreover, an alternative solution procedure via a time-variant Linear-Quadratic Regulator approach is also presented. A Model Predictive Control (MPC) scheme is utilized to compensate possible disturbances in the trajectories of the cooperating vehicles, whereby the analytical optimal solution is applied repeatedly in real time, using updated measurements, until the merging procedure is actually finalized. Subsequently, the methodology is generalized for a set of vehicles inside the merging area. Various numerical simulations illustrate the validity and applicability of the method.     

Predictive path following with arrival time awareness for waterborne AGVs

Large ports are seeking innovative logistical ways to improve their competitiveness world-wide. This article proposes waterborne AGVs, inspired by conventional automated guided vehicles and autonomous surface vessels, for transport over water. A predictive path following with arrival time awareness controller is proposed for such waterborne AGVs. The controller is able to achieve smooth tracking and energy efficiency with arrival time awareness for transport oriented applications. Tracking errors are conveniently formulated with vessel dynamics modeled in connected reference path coordinate systems and a coordinate transformation at switching coordinate systems. Binary decision variables and logic constraints based on an along-track state are proposed for modeling switches in the framework of Model Predictive Control (MPC) so that overshoots are avoided. Moreover, timing-aware along-track references are generated by a two-level double integrator scheme. The lower level is embedded in online MPC optimizations for smooth tracking. The higher level solves a mixed-integer quadratic programming problem considering distance-to-go and time-to-go before each MPC optimization. References over the next prediction horizon are generated being aware of the requirements on arrival time. Furthermore, successive linearizations of nonlinear vessel dynamics about a shifted previous optimal system trajectory are implemented to maintain a trade-off between computational complexity and optimality. Simulation results of two industrially relevant Inter Terminal Transport case studies illustrate the effectiveness of the proposed modeling and control design for waterborne AGVs.     

The simple platoon advancement model of its technologies applied to vehicle control at signalised intersections

The Simple Platoon Advancement (SPA) Model describes a conceptual system whose principal objective is to increase the throughput of vehicles at signalised intersections. This is achieved through a novel combination of Intelligent Transport System (ITS) technologies including Automatic Cruise Control, Lane Departure Avoidance, and Collision Avoidance. These are combined in SPA so that vehicles are progressed through signalised intersections under automated control. All of the vehicles in a stationary queue are moved instantly at the start‐of‐green as a closely‐spaced platoon. Dispersion occurs after all vehicles are in motion. Throughput of the SPA model is determined analytically and comparisons are made between the SPA model and a valid representation of current road traffic behaviour. These comparisons show that theoretically a SPA system can progress nearly twice as many vehicles past the stopline as can be seen in today's road network. Other benefits of a conceptual SPA system are improved safety and a reduction in delay per vehicle.     

Evaluation of a model predictive control framework for motorway traffic involving conventional and automated vehicles

A Model Predictive Control (MPC) strategy for motorway traffic management, which takes into account both conventional control measures and control actions executed by vehicles equipped with Vehicle Automation and Communication Systems (VACS), is presented and evaluated using microscopic traffic simulation. A stretch of the motorway A20, which connects Rotterdam to Gouda in the Netherlands, is taken as a realistic test bed. In order to ensure the reliability of the application results, extensive speed and flow measurements, collected from the field, are used to calibrate the site’s microscopic traffic simulation model. The efficiency of the MPC framework, applied to this real sizable and complex network under realistic traffic conditions, is examined for different traffic conditions and different penetration rates of equipped vehicles. The adequacy of the control application when only VACS equipped vehicles are used as actuators, is also considered, and the related findings underline the significance of conventional control measures during a transition period or in case of increased future demand.     

Multi-scale perimeter control approach in a connected-vehicle environment

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors).     

Eco-driving advisory strategies for a platoon of mixed gasoline and electric vehicles in a connected vehicle system

As electric vehicles (EVs) have gained an increasing market penetration rate, the traffic on urban roads will tend to be a mix of traditional gasoline vehicles (GVs) and EVs. These two types of vehicles have different energy consumption characteristics, especially the high energy efficiency and energy recuperation system of EVs. When GVs and EVs form a platoon that is recognized as an energy-friendly traffic pattern, it is critical to holistically consider the energy consumption characteristics of all vehicles to maximize the energy efficiency benefit of platooning. To tackle this issue, this paper develops an optimal control model as a foundation to provide eco-driving suggestions to the mixed-traffic platoon. The proposed model leverages the promising connected vehicle technology assuming that the speed advisory system can obtain the information on the characteristics of all platoon vehicles. To enhance the model applicability, the study proposes two eco-driving advisory strategies based on the developed optimal control model. One strategy provides the lead vehicle an acceleration profile, while the other provides a set of targeted cruising speeds. The acceleration-based eco-driving advisory strategy is suitable for platoons with an automated leader, and the speed-based advisory strategy is more friendly for platoons with a human-operated leader. Results of numerical experiments demonstrate the significance when the eco-driving advisory system holistically considers energy consumption characteristics of platoon vehicles.     

Vehicle sorting for platoon formation: Impacts on highway entry and throughput

Automated highway systems (AHS) are intended to increase the throughput and safety of roadways through computer control, communication and sensing. In the “platoon” concept for AHS, vehicles travel on highways in closely spaced groups. To maximize benefits, it is desirable to form platoons that are reasonably large (five or more vehicles), and it is also desirable to ensure that platoons remain intact for considerable distances. This paper develops and evaluates strategies for organizing vehicles into platoons at highway entrances, with the objective of maximizing the distance that platoons stay intact, so that they do not need to be regrouped into new platoons on the highway itself. Fundamentally, this entails grouping vehicles according to their destination. We evaluate various strategies in which vehicles are sorted on entrance ramps, with respect to platoon sizes, throughput and platoon formation time.     

A conceptualization of vehicle platoons and platoon operations

Vehicle platooning, a coordinated movement strategy, has been proposed to address a range of current transport challenges such as traffic congestion, road safety, energy consumption and pollution. But in order to form platoons in an ad-hoc manner the vehicles have to ‘speak the same language’, which is in current practice limited to vehicles of particular manufacturers. There is no standard language yet. Also in research, while the current literature focuses on platoon control strategies, intra-platoon communication, or platooning impacts on traffic, the conceptualization of platooning objects and their operations remained unattended. This paper aims to fill this fundamental gap by developing a formal model of platooning concepts. The paper proposes an ontological model of platooning objects and properties and abstract basic building blocks of platoon operations that can then be aggregated to complex platooning behavior. The presented ontological model provides the logical reasoning to support vital decision-making during platoon lifecycles. The ontological model is implemented and demonstrated.     

Application of intervention analysis for assessing the effectiveness of CO pollution control legislation in India

An Intervention Analysis Model (IAM) (Box and Tiao, 1975) was developed to study the impact of the ‘intervention' brought in by the Government of India (GoI), to control the CO pollution caused by the vehicular exhaust emissions, by the enforcement of the emission standards for the vehicles, on the mean level of the time-series of CO concentration. The study was conducted for an Air Quality Control Region (AQCR) comprising of an urban road intersection in Delhi, India, where almost 100% CO is contributed by vehicular traffic. Application of the model suggests that the ‘intervention' has not been effective in bringing down the desired change; some likely causes of which have also been mentioned.     

Characterising Green Light Optimal Speed Advisory trajectories for platoon-based optimisation

Conceptually, a Green Light Optimal Speed Advisory (GLOSA) system suggests speeds to vehicles, allowing them to pass through an intersection during the green interval. In previous papers, a single speed is computed for each vehicle in a range between acceptable minimum and maximum values (for example between standstill and the speed limit). This speed is assumed to be constant until the beginning of the green interval, and sent as advice to the vehicle. The goal is to optimise for a particular objective, whether it be minimisation of emissions (for environmental reasons), fuel usage or delay. This paper generalises the advice given to a vehicle, by optimising for delay over the entire trajectory instead of suggesting an individual speed, regardless of initial conditions – time until green, distance to intersection and initial speed. This may require multiple acceleration manoeuvres, so the advice is sent as a suggested acceleration at each time step. Such advice also takes into account a suitable safety constraint, ensuring that vehicles are always able to stop before the intersection during a red interval, thus safeguarding against last-minute signal control schedule changes. While the algorithms developed primarily minimise delay, they also help to reduce fuel usage and emissions by conserving kinetic energy. Since vehicles travel in platoons, the effectiveness of a GLOSA system is heavily reliant on correctly identifying the leading vehicle that is the first to be given trajectory advice for each cycle. Vehicles naturally form a platoon behind this leading vehicle. A time loop technique is proposed which allows accurate identification of the leader even when there are complex interactions between preceding vehicles. The developed algorithms are ideal for connected autonomous vehicle environments, because computer control allows vehicles’ trajectories to be managed with greater accuracy and ease. However, the advice algorithms can also be used in conjunction with manual control provided Vehicle-to-Infrastructure (V2I) communication is available.     

Prediction of vehicle CO2 emission and its application to eco-routing navigation

Transportation sector accounts for a large proportion of global greenhouse gas and toxic pollutant emissions. Even though alternative fuel vehicles such as all-electric vehicles will be the best solution in the future, mitigating emissions by existing gasoline vehicles is an alternative countermeasure in the near term. The aim of this study is to predict the vehicle CO₂ emission per kilometer and determine an eco-friendly path that results in minimum CO₂ emissions while satisfying travel time budget. The vehicle CO₂ emission model is derived based on the theory of vehicle dynamics. Particularly, the difficult-to-measure variables are substituted by parameters to be estimated. The model parameters can be estimated by using the current probe vehicle systems. An eco-routing approach combining the weighting method and k-shortest path algorithm is developed to find the optimal path along the Pareto frontier. The vehicle CO₂ emission model and eco-routing approach are validated in a large-scale transportation network in Toyota city, Japan. The relative importance analysis indicates that the average speed has the largest impact on vehicle CO₂ emission. Specifically, the benefit trade-off between CO₂ emission reduction and the travel time buffer is discussed by carrying out sensitivity analysis in a network-wide scale. It is found that the average reduction in CO₂ emissions achieved by the eco-friendly path reaches a maximum of around 11% when the travel time buffer is set to around 10%.     

Stop-and-go traffic analysis: Theoretical properties,environmental impacts and oscillation mitigation

This study aims (i) to analyze theoretical properties of a recently proposed describing-function (DF) based approach (Li and Ouyang, 2011; Li et al., 2012) for traffic oscillation quantification, (ii) to adapt it for estimating fuel consumption and emission from traffic oscillation and (iii) to explore vehicle control strategies of smoothing traffic with advanced technologies. The DF approach was developed to predict traffic oscillation propagation across a platoon of vehicles following each other by a nonlinear car-following law with only the leading vehicle’s input. We first simplify the DF approach and prove a set of properties (e.g., existence and uniqueness of its solution) that assure its prediction is always consistent with observed traffic oscillation patterns. Then we integrate the DF approach with existing estimation models of fuel consumption and emission to analytically predict environmental impacts (i.e., unit-distance fuel consumption and emission) from traffic oscillation. The prediction results by the DF approach are validated with both computer simulation and field measurements. Further, we explore how to utilize advantageous features of emerging sensing, communication and control technologies, such as fast response and information sharing, to smooth traffic oscillation and reduce its environmental impacts. We extend the studied car-following law to incorporate these features and apply the DF approach to demonstrate how these features can help dampen the growth of oscillation and environmental impact measurements. For information sharing, we convert the corresponding extended car-following law into a new fixed point problem and propose a simple bisecting based algorithm to efficiently solve it. Numerical experiments show that these new car-following control strategies can effectively suppress development of oscillation amplitude and consequently mitigate fuel consumption and emission.     

Stochastic optimal path problem with relays

This paper studies the optimal path problem for travelers driving with vehicles of a limited range, such as most battery electric vehicles currently available in the market. The optimal path in this problem often consists of several relay points, where the vehicles can be refueled to extend its range. We propose a stochastic optimal path problem with relays (SOPPR), which aims at minimizing a general expected cost while maintaining a reasonable arrival probability. To account for uncertainty in the road network, the travel speed on a road segment is treated as a discrete random variable, which determines the total energy required to traverse the segment. SOPPR is formulated in two stages in this paper. In the first stage, an optimal routing problem is solved repeatedly to obtain the expected costs and arrival probabilities from any node to all refueling nodes and the destination. With this information, the second stage constructs an auxiliary network, on which the sequence of refueling decisions can be obtained by solving another optimal path problem. Label-correcting algorithms are developed to solve the routing problems in both stages. Numerical experiments are conducted to compare the stochastic and deterministic models, to examine the impact of different parameters on the routing results, and to evaluate the computational performance of the proposed algorithms.     

Length-based vehicle classification using event-based loop detector data

Length-based vehicle classification is an important topic in traffic engineering, because estimation of traffic speed from single loop detectors usually requires the knowledge of vehicle length. In this paper, we present an algorithm that can classify vehicles passing by a loop detector into two categories: long vehicles and regular cars. The proposed algorithm takes advantage of event-based loop detector data that contains every vehicle detector actuation and de-actuation “event”, therefore time gaps between consecutive vehicles and detector occupation time for each vehicle can be easily derived. The proposed algorithm is based on an intuitive observation that, for a vehicle platoon, longer vehicles in the platoon will have relatively longer detector occupation time. Therefore, we can identify longer vehicles by examining the changes of occupation time in a vehicle platoon. The method was tested using the event-based data collected from Trunk Highway 55 in Minnesota, which is a high speed arterial corridor controlled by semi-actuated coordinated traffic signals. The result shows that the proposed method can correctly classify most of the vehicles passing by a single loop detector.     

Effect of signal coordination on traffic emission

This study investigates the effect of traffic signal coordination on emissions and compares it with their effects on operational performance measures of delay and stops. Various platoon ratios are obtained by simulating cycle lengths and offsets. Our results indicate that the impact of the cycle length on delay is more significant than those on stops and emissions for under-saturation traffic conditions. Given a fixed cycle length, increasing the platoon ratio can reduce delay, stops, and emissions, with reduction in emissions being correlated with stops than delay. The effect on emissions from the platoon arrival with respect to the onset of green or red indication is identified. With the same cycle length and platoon ratio, the early arrival situation, when the leading vehicles of a platoon encounters the red signal, can generate more emissions than are associated with late platoon arrival, when the last few vehicles in a platoon are stopped at the intersection by the onset of the red signal.     

Design,analysis and performance evaluation of a third order distributed protocol for platooning in the presence of time-varying delays and switching topologies

This paper is concerned with the problem of designing a decentralized consensus protocol for platooning of non-identical vehicles in the presence of heterogeneous time-varying communication delays. The proposed control protocol makes use of a state feedback and to this aim drivetrain dynamics are modeled as third-order linear systems. Necessary and sufficient conditions for convergence and exponential stability, derived by using an appropriate Krasovskii functional, demonstrate the ability of the platoon in reaching the required regime with an exponentially bounded behavior. The proposed LMI-based approach allows to estimate both delay margin and decay rate. Moreover, convergence is proven under switching communication network topologies by means of a Lyapunov-Razumikhin function, and the assessment of a string stable behavior has been also theoretically investigated. High-fidelity simulations with Plexe show the effectiveness of the theoretical results in different driving conditions and in the presence of external disturbances and communication impairment. Different communication channel models are used in the validation stage to further prove robustness of the proposed methodology with respect hard delay and packets losses.