Ardalan Vahidi
email: avahidi@clemson.edu

Antonio Sciarretta
email: antonio.sciarretta@ifpen.fr

Energy Saving Potentials of Connected and Automated Vehicles

Keywords: connected vehicles, automated vehicles, eco-driving, optimal control, anticipative driving, collaborative driving

Connected and automated vehicles (CAV) are marketed for their increased safety, driving comfort, and time saving potential. With much easier access to information, increased processing power, and precision control, they also offer unprecedented opportunities for energy efficient driving. This paper is an attempt to highlight the energy saving potential of connected and automated vehicles based on first principles of motion, optimal control theory, and a review of the vast but scattered eco-driving literature. We explain that connectivity to other vehicles and infrastructure allows better anticipation of upcoming events, such as hills, curves, slow traffic, state of traffic signals, and movement of neighboring vehicles. Automation allows vehicles to adjust their motion more precisely in anticipation of upcoming events, and save energy. Opportunities for cooperative driving could further increase energy efficiency of a group of vehicles by allowing them to move in a coordinated manner. Energy efficient motion of connected and automated vehicles could have a harmonizing effect on mixed traffic, leading to additional energy savings for neighboring vehicles.

INTRODUCTION

The shift that we are witnessing toward vehicle connectivity and autonomy is going to be perhaps, the most disruptive since the early days of automobiles and could revolutionize movement of people and goods. According to IHS Automotive, the number of connected cars sold globally will grow more to 152 million across the globe by 2020, a six fold increase with respect to 2015 [START_REF] Mccarthy | Connected cars by the numbers[END_REF]. Another estimate puts the number of connected vehicles at 250 million vehicles by 2020 [START_REF] Gartner | [END_REF], a fourth of the billion cars that are in service today. In 2016 the US Department of Transportation issued a notice of proposed rule making, that if implemented would require Vehicle-to-Vehicle (V2V) connectivity on all new light-duty vehicles and is intended to reduce the number of car accidents (NHTSA, 2016b). Similar provisions and guidelines are envisioned for Vehicle-to-Infrastructure (V2I) communication [START_REF] Fhwa | Vehicle-to-Infrastructure Deployment Guidance and Products[END_REF]. With implementation of such mandates the number of connected cars with access to information and data will rapidly increase. On a different front, major auto manufacturers, technology firms, and startup companies have started a race toward building fully automated cars. Many automated functions such as adaptive cruise control and lane keeping assist are already available on several production vehicles. It is expected that first fully automated vehicles be available for sale before 2020 (Center for Sustainable Systems, 2016;[START_REF] Alexander-Kearns | The Impact of Vehicle Automation on Carbon Emissions[END_REF]. A projection is that 20-40% of vehicle sales be automated by 2030 and full penetration could happen in several stages over the next few decades [START_REF] Litman | Autonomous vehicle implementation predictions[END_REF].

This level of connectivity and autonomy will transform transportation of people and goods in several dimensions with important societal and economical impacts: improved safety, increased comfort, time saving potential, and more efficient road utilization are among the most widely discussed positive impacts of CAVs. Fully automated vehicles could improve mobility of young, elderly, and people with disability who are unable to drive today. Ride sharing and on-demand mobility services could gain more popularity due to reduced labor cost, influencing also urban planning and land use.

Energy use has not been the core consideration in development of connected and automated vehicles, but it could be impacted significantly. The impact could be positive or negative according to [START_REF] Brown | An analysis of possible energy impacts of automated vehicle[END_REF][START_REF] Wadud | Help or hindrance? the travel, energy and carbon impacts of highly automated vehicles[END_REF] which is summarized in Table 1. A careful scenario analysis in [START_REF] Wadud | Help or hindrance? the travel, energy and carbon impacts of highly automated vehicles[END_REF] shows vehicle automation could reduce energy use and green house gas emissions in half in an optimistic scenario or double them in a "dystopian nightmare", depending on the effects that come to dominate. Increased opportunities for eco-driving and platooning, traffic harmonization, vehicle light-weighting enabled by lower crash risk, vehicle right-sizing for number of travelers, de-emphasized vehicle performance, car-sharing and on-demand mobility, and reduced infrastructure footprint of automated vehicles all contribute to improved energy utilization according to [START_REF] Wadud | Help or hindrance? the travel, energy and carbon impacts of highly automated vehicles[END_REF]. But according to the same study, the increase in vehicle miles traveled due to lower travel costs, addition of new user groups (young, elderly, disabled), higher highway speeds, and increased vehicle features can also dramatically increase the energy footprint of vehicle automation. The outcomes depend on which scenarios prevail and proactive policy making is essential to steer the technology toward energy efficiency as also emphasized in [START_REF] Wadud | Help or hindrance? the travel, energy and carbon impacts of highly automated vehicles[END_REF][START_REF] Simon | Can transportation emission reductions be achieved autonomously?[END_REF][START_REF] Alexander-Kearns | The Impact of Vehicle Automation on Carbon Emissions[END_REF]. The authors of [START_REF] Greenblatt | Automated vehicles, on-demand mobility, and environmental impacts[END_REF] speculate that the aggregate energy and environmental impact of automated and on-demand mobility could be positive; but acknowledge a big shift from historical trends that needs to be carefully watched by policy makers and planners.

Table 1: Potential Impact of CAVs on a) energy intensity or user intensity according to [START_REF] Brown | An analysis of possible energy impacts of automated vehicle[END_REF] b) operational energy use by year 2050 according to [START_REF] Wadud | Help or hindrance? the travel, energy and carbon impacts of highly automated vehicles[END_REF].

Contributing Factors [START_REF] Brown | An analysis of possible energy impacts of automated vehicle[END_REF]) [START_REF] Wadud | Help or hindrance? the travel, energy and carbon impacts of highly automated vehicles[END_REF] platooning (-)10 % EI * (-) 2-10 % eco-driving (-)15-40 % EI (-) 20 % eco-routing (-) 5 % EI NA congestion mitigation NA (-)2-4% de-emphasized performance NA (-) 5-23 % vehicle light-weighting (-) 50 % EI (-) 5-23 % vehicle right-sizing (-) 12 † % UI * * (-) 20-45 % changed mobility services NA (-) 0-20 % infrastructure footprint NA (-) 2-5% reduced parking search (-) 4 % UI NA enabling electrification (-) 75 % FI * * * NA higher highway speeds (+) 30 % (+) 5-25 % increased features NA (+) 0-10 % travel cost reduction (+) 50 % UI (+) 5-60 % new user groups (+) 40 % UI (+) 2-10 % realizable with partial level 2 or 3 automation as they mostly rely on automated speed and steering control which can be overseen and overridden by a human driver.

Because CAVs are capable of sensing more accurately, processing more information, and can be more tightly controlled, they benefit more from information offered by connectivity and road preview. With higher penetration rate of CAVs, opportunities increase for vehicle to vehicle communication and cooperative control; which can lead to additional energy efficiency gains. Despite these prospects, connected and automated vehicle research and development have been mostly on software, sensing, and safety and there are limited results on energy efficiency potentials.

Over the past decade, various research groups have shown the positive influence of telematics, road preview, and connectivity on energy efficiency of conventional and hybrid vehicles through simulation and experimental investigations. For instance, in [START_REF] Manzie | Fuel economy improvements for urban driving: Hybrid vs. intelligent vehicles[END_REF] it is shown that as little as 7 seconds traffic look-ahead capability could have the same energy efficiency benefit as hybridization. Due to the complex nature of the problem (different vehicle configurations, variability of scenarios, and sensitivity to choice of algorithms) the reported values for energy efficiency benefits are scattered and a concerted effort is needed to summarize the findings and put them in context. Such a summary not only helps researchers in the field but can inform policy making in regulatory units.

We start by discussing the fundamentals of energy efficient driving based on a first principle energy analysis in Section 2. Our reference to eco-driving implies economic and not ecologic driving as they are not necessarily the same; lowering energy use is not equivalent to lowering emissions [START_REF] Mensing | Eco-driving: An economic or ecologic driving style?[END_REF]. As formalized in [START_REF] Sciarretta | Optimal ecodriving control: Energy-efficient driving of road vehicles as an optimal control problem[END_REF] and [START_REF] Saerens | Optimal Control Based Eco-Driving[END_REF] many eco-driving problems are optimal control problems; but to keep the paper readable to a more general audience we limit use of theory of optimal control to an appendix. The flow of the rest of the paper is shaped by the authors' past research on eco-driving and backed by the many papers that have emerged on the topic, mostly over the past decade. This is by no means a comprehensive review of existing literature as a wide range of publications exists. In particular we do not consider the topic of eco-routing and dynamic route guidance that have been discussed in several recent publications, for instance in [START_REF] Boriboonsomsin | Impacts of road grade on fuel consumption and carbon dioxide emissions evidenced by use of advanced navigation systems[END_REF][START_REF] Boriboonsomsin | Eco-routing navigation system based on multisource historical and real-time traffic information[END_REF][START_REF] Kubička | Performance of current eco-routing methods[END_REF][START_REF] De Nunzio | A model-based eco-routing strategy for electric vehicles in large urban networks[END_REF]. Nor we discuss opportunities for better traffic response signal control, ramp metering, and other infrastructure based controls that could also enhance energy efficiency.

In Section 3 the importance of anticipation for efficient driving is explained. In particular we discuss opportunities that arise for individual CAVs by anticipating future road slope and geometry, macroscopic state of traffic, color of upcoming traffic signals, and microscopic motion of their neighboring vehicles. This allows CAVs to more judiciously choose their velocity and lane to minimize wasteful braking and idling and also enables predictive powertrain control due to increased certainty about future vehicle motion. With increased penetration of CAVs, more opportunities arise for collaborative driving which could further enhance energy efficiency as discussed in Section 4. In particular we discuss platooning, cooperative adaptive cruise control, cooperative lane change and merge, and cooperative intersection control for a CAV fleet. The impact on mixed traffic is discussed briefly in Section 4.4, followed by conclusions in Section 5.

Fundamentals of Energy Efficient Driving

Energy used by a vehicle depends very much on the way its driven. There is a large body of scientific literature on energy efficient-or eco-driving [START_REF] Monastyrsky | Rapid computation of optimal control for vehicles[END_REF], [START_REF] Sciarretta | Optimal ecodriving control: Energy-efficient driving of road vehicles as an optimal control problem[END_REF], practical guides on hypermiling [START_REF] Hickman | Get the most from your car with these top 12 "hypermiling" tips[END_REF], and the potential impact on energy use and carbon emissions [START_REF] Barkenbus | Eco-driving: An overlooked climate change initiative[END_REF]. Connected and automated vehicles have the potential to excel at efficient driving because of their increased situational awareness and ability to execute more complex maneuvers more precisely. Before discussing specific scenarios where CAVs can save energy, here we take a closer look at fundamentals of energy efficient driving. We will consider only a vehicle's longitudinal motion governed by Newton's second law of motion and disregard the constraints imposed by the motion of surrounding vehicles:

m dv dt = F w -mg(sinθ +C rr cosθ) - 1 2 ρ a AC D v 2 (1)
where m is mass of the vehicle, including powertrain inertial effects, v is forward velocity. Here F w is chosen to be the sum of tractive or braking force at the wheels, thus decoupling the role of vehicle powertrain in the initial part of this discussion. In the term representing road loads, C rr is the coefficient of rolling resistance and θ is the road slope. In the term representing aerodynamic drag, ρ a is air density, A is vehicle front area, C D is aerodynamic drag coefficient.

The instantaneous power needed at the wheel is F w (t)v(t). Therefore, the net energy needed at the wheel, E w , to cover a distance s f in t f unit of time can then be calculated as:

E w = t f 0 F w (t)v(t)dt = s f 0 F w (t(s))ds = s f 0 m dv dt + mg(sinθ +C rr cosθ) + 1 2 ρ a AC D v 2 ds (2)
With the reasonable assumption that m, g, C rr , ρ a , and A are constants during a trip, integration yields:

E w = 1 2 m(v 2 f -v 2 0 ) + mg∆h + mgC rr ∆x + 1 2 ρ a A s f 0 C D (s)v 2 (s)ds (3)
where v 0 and v f are velocities at origin and destination respectively, ∆h is total elevation change during the trip, and ∆x is the horizontal distance covered. Here we assume the drag coefficient can vary along the road, due to potential for platooning or drafting which could reduce aerodynamic drag.

The first and the second terms in Equation ( 3) represent the change in kinetic and potential energy respectively and are dictated by initial and terminal conditions, so they do not offer opportunities for reducing E w . Note that road grade does not appear after integration; however we will explain later that because of constraints on velocity and powertrain output, the elevation profile along a trip can have a significant effect on energy use and prior knowledge of it can help save fuel via better constraint management. The term mgC rr ∆x represents the irreversible frictional loss and is a function of (horizontal) trip distance and C rr . So if there is a choice, one must choose shorter routes with lower C rr (concrete road over sand road) to save energy. With connectivity there may be opportunities to evaluate this term more accurately. The last term, the energy lost to aerodynamic drag, is the only term that can be influenced by the decisions along the route and therefore should be a core consideration in eco-driving. The energy needed at the wheel can be reduced by joining a tight platoon thus lowering C D . The vehicle velocity plays an important role and obviously lower speeds result in lower losses to drag. More specifically when C D is constant the drag term can be easily reorganized as follows [START_REF] Kubička | Performance of current eco-routing methods[END_REF]:

1 2 ρ a A s f 0 C D (s)v 2 (s)ds = 1 2 ρ a AC D ( v2 + σ 2 v )s f (4) where v = s f 0 v(s)ds s f
is the average velocity over position and

σ 2 v = s f 0 (v(s)-v) 2 ds s f
is its variance. Therefore to minimize drag losses it is best to drive with a low and constant (σ 2 v = 0) speed. Note also that at constant speed, the drag loss is proportional to s 3 f , therefore taking a road that is 10% shorter, reduces drag losses by 27% which can be significant at high speeds.

When the initial and final velocity are different, the velocity cannot be constant. Our optimal control analysis presented in the Appendix, indicates that in such a situation, it is best to accelerate (or decelerate) as quickly as possible to a constant low speed and then decelerate (or accelerate) quickly to the final desired speed (bang-singularbang solution). Note that we postpone the discussion of velocity and position constraints to Sections 3.1 and 3.3 respectively.

Depending on initial and final conditions, the required energy at wheel E w could be negative. Moreover d ds E w which is equal to the required wheel force F w , can be negative: for instance when decelerating to a stop ( dv dt < 0) or on downhill slopes (θ < 0) as inferred from Equation (1). When F w < 0, it is necessary to apply the brakes or rely on engine braking, thus wasting energy as heat. Even in hybrid and electric vehicles with recuperative brakes, a part of available braking energy is lost as heat. Therefore for eco-driving it is best to minimize situations in which F w < 0, in particular braking should be avoided when possible. This means that when deciding to slow down or to stop, it is best to coast with the engine disengaged (F w ≈ 0) and rely on rolling resistance and aerodynamic drag to slow the vehicle down. We note that coasting will increase the stopping distance which may not be always safe or desirable. Therefore anticipation of slow downs in advance, provides more time and opportunity for gradually reducing the speed. Vehicle connectivity could enable anticipative driving as discussed in more detail in Section 3. We also note that pure coasting may not be always energy optimal, for instance when traveling between two stops in a fixed time, the best final decelerating strategy is a combination of coasting and maximal braking as explained in the Appendix. This is classic problem that has been addressed in optimal control of trains that have to travel between two stations in a fixed amount of time [START_REF] Asnis | Solution of the problem of the energetically optimal control of the motion of a train by the maximum principle[END_REF][START_REF] Howlett | The optimal control of a train[END_REF].

When descending down a steep road and in a hypothetical scenario when there are no upper bounds on velocity, it is more energy efficient to coast down the hill (F w ≈ 0) allowing the velocity to increase toward the equilibrium imposed by rolling resistance and aerodynamic drag. Unfortunately this is very unsafe and often impractical due to road speed limits and the bounds imposed by preceding vehicles. However if the road profile is known in advance, the vehicle can start coasting early in anticipation of an imminent descent, allowing it to utilize the limited velocity band more effectively. An automated vehicle can execute such a maneuver more precisely than a human driven vehicle as explained in more detail in Section 3.1.

The above discussion was focused on increasing "wheel-to-distance" [START_REF] Sciarretta | Optimal ecodriving control: Energy-efficient driving of road vehicles as an optimal control problem[END_REF] energy efficiency and did not address "tank-to-wheel" energy efficiency which is powertrain dependent. The two problems are not entirely decoupled: for instance we showed that low constant velocities improve "wheel-to-distance" energy efficiency due to lower drag. A gasoline engine on the other hand is not most efficient at low loads seen at low speeds. The engine sweet spot is typically at relatively large engine loads. To strike a balance (running the engine efficiently and maintaining a low average speed), the engine could be periodically turned on at high load and then turn off; in a "pulse-and-glide" strategy as shown schematically in Figure 1. The effectiveness of pulse and glide algorithms is shown analytically in [START_REF] Gilbert | Vehicle cruise: Improved fuel economy by periodic control[END_REF], using theory of optimal control in [START_REF] Sciarretta | Fuel-optimal control of rendezvous maneuvers for passenger cars (treibstoffoptimale annäherung von straßenfahrzeugen)[END_REF][START_REF] Li | Strategies to minimize fuel consumption of passenger cars during car-following scenarios[END_REF], and experimentally in [START_REF] Lee | Vehicle Inertia Impact on Fuel Consumption of Conventional and Hybrid Electric Vehicles Using Acceleration and Coast Driving Strategy[END_REF] but overall the existing literature presents mixed and sometimes conflicting results. We note that pulse and glide may not be a practical eco-driving strategy because velocity variations are uncomfortable to passengers and disruptive to traffic. Also according to [START_REF] Lee | Vehicle Inertia Impact on Fuel Consumption of Conventional and Hybrid Electric Vehicles Using Acceleration and Coast Driving Strategy[END_REF] pulse and glide may not be an effective approach in vehicles with automatic transmission due to torque converter losses.

Figure 1: Eco driving between two stopping points. The combustion engine car starts with maximum acceleration, pulse-and-glides around its cruise speed, followed by coast down and final maximal braking to a stop. Parts of the image were created on https://icograms.com.

In hybrid vehicles, the battery energy storage buffer allows to (partially) decouple the engine load/speed from the wheel load/speed. Therefore the engine can be run more often near its sweet spot, even at low road loads and speeds. Moreover, regenerative brakes contribute to higher energy efficiency. Nevertheless, because the electromechanical energy conversion is always lossy, eco-driving practices can be beneficial even for hybrid vehicles. For instance using connectivity and road preview allows predictive utilization of the limited battery energy buffer to save energy [START_REF] Zhang | Role of terrain preview in energy management of hybrid electric vehicles[END_REF]. A pulse and glide strategy can save fuel in hybrids as well [START_REF] Lee | Vehicle Inertia Impact on Fuel Consumption of Conventional and Hybrid Electric Vehicles Using Acceleration and Coast Driving Strategy[END_REF] but may be undesirable.

The electric motor in electric vehicles is more efficient at lower torques and therefore the energy-optimal operation strategy, unlike for gasoline vehicles, is not pulse and glide [START_REF] Sciarretta | Optimal ecodriving control: Energy-efficient driving of road vehicles as an optimal control problem[END_REF][START_REF] Han | Safe-and eco-driving control for connected and automated electric vehicles using analytical state-constrained optimal solution[END_REF]. Analytical solutions based on optimal control theory show that the optimal speed profile for an electric vehicle is a parabolic function of time, quite different from that of gasoline engine vehicles [START_REF] Han | Safe-and eco-driving control for connected and automated electric vehicles using analytical state-constrained optimal solution[END_REF]. Here automated driving may provide an advantage in the ability to adhere to more complex speed profiles for energy saving.

Anticipation in Connected and Automated Driving

CAVs offer huge potentials for boosting road safety, capacity, and efficiency, because of their ability to process data from many more sources (e.g. V2X fused with on-board sensing) and their ability for more precise positioning and control than human drivers. While similar information can be processed, and provided to connected humandriven vehicles [START_REF] Barth | Energy and emissions impacts of a freeway-based dynamic eco-driving system[END_REF] [START_REF] Stahl | Supporting anticipation in driving through attentional and interpretational in-vehicle displays[END_REF]) (e.g. as optimal speed/lane advisories), only fully automated vehicles can be made to comply with and reliably follow real-time energy-efficient commands. Even in mixed-traffic that involves other non-automated vehicles, energy-efficient automated vehicles can have a positive impact on the energy efficiency of surrounding traffic as will be illustrated later. Automated cars have the potential to uncover the "driving signature" of their neighboring vehicles and predict their most likely actions. They can also anticipate probable locations of slow-downs by systematic evaluation of historical data. Connectivity between cars and infrastructure can make much more information available to each vehicle and the vehicles can form groups and act cooperatively. All of these advances, when put into an organized framework, can help better anticipation and enable improved traffic flow, increased safety, and reduced energy consumption.

Anticipating State of the Road

Prior knowledge of road speed limits, safe speeds on curved roads, and an estimate of average traffic speed allows for more energy efficient velocity transitions in anticipation of the change in velocity constraints. Speed limit is a standard feature on modern onboard navigation units. Road curvature may be extracted from navigation maps to calculate the likely (safe) speed on a curve. Curve speeds can also be crowdsourced from connected vehicle data. Average traffic speeds for upcoming segments of a trip can be queried from a Traffic Management Center (TMC) that operate based on local sensors and cameras or estimated from traffic feeds that mostly rely on crowdsourced information, such as feeds of Google, Here, Waze, and Inrix as of 2017. Dynamic spatiotemporal evolution of traffic speed can be estimated via a faster-than-real-time traffic simulation model which is initialized by current traffic speed, deterministically [START_REF] Asadi | The role of traffic flow preview for planning fuel optimal vehicle velocity[END_REF] or probabilistically [START_REF] Wan | Prediction on travel-time distribution for freeways using online expectation maximization algorithm[END_REF]. In absence of real-time traffic information services, time-and location-specific historical traffic data can be used as a baseline predictor [START_REF] Wan | Probabilistic anticipation and control in autonomous car following[END_REF]. Traffic speed can be imposed as a spatio-temporally varying upper bound on the CAV speed [START_REF] Asadi | The role of traffic flow preview for planning fuel optimal vehicle velocity[END_REF]. Speed limit, curve and traffic speeds can be unified [START_REF] Schepmann | Heavy vehicle fuel economy improvement using ultracapacitor power assist and preview-based MPC energy management[END_REF] into a single spatiotemporal bound on CAV velocity and used not only to optimize velocity transitions of a CAV but also inform its predictive powertrain control functions.

Another dominating factor in vehicle power demand is road grade, in particular on steep roads, and more so for heavier vehicles. While road grade does not explicitly impact E w as shown in Equation (3), it influences velocity and torque constraints and gear selection. Therefore advanced knowledge of the road grade, obtained from 3D road maps, is very beneficial in predictive powertrain control as shown for instance in [START_REF] Back | Predictive powertrain control for hybrid electric vehicles[END_REF][START_REF] Zhang | Role of terrain preview in energy management of hybrid electric vehicles[END_REF]. Additionally, due to constraints on velocity, prior knowledge of road grade will allow more judicious use of available velocity band and gear selection [START_REF] Terwen | Predictive powertrain control for heavy duty trucks[END_REF][START_REF] Fröberg | Explicit fuel optimal speed profiles for heavy trucks on a set of topographic road profiles[END_REF][START_REF] Huang | Using 3D road geometry to optimize heavy truck fuel efficiency[END_REF][START_REF] Hellström | Look-ahead control for heavy trucks to minimize trip time and fuel consumption[END_REF][START_REF] Hellström | Design of an efficient algorithm for fuel-optimal look-ahead control[END_REF][START_REF] Kamal | Ecological driving based on preceding vehicle prediction using MPC[END_REF][START_REF] Lu | Predictive transmission shift schedule for improving fuel economy and drivability using electronic horizon[END_REF]; for instance a vehicle can slow down in anticipation of a steep descent or speed up in preparation for a climb. The optimal solution can be non-trivial as shown for a heavy duty vehicle in [START_REF] He | Fuel consumption optimization of heavy-duty vehicles with grade, wind, and traffic information[END_REF]. Daimler already has a predictive cruise control function in production that adjust a heavy duty truck speed [START_REF] Freightliner | Freightliner trucks launches RunSmart Predictve Cruise for Cascadia[END_REF] and gear [START_REF] Barry | Trucks use GPS to anticipate hills, save fuel[END_REF] in anticipation of upcoming road grade to increase its energy efficiency by 3% on a highway. This level of achievable improvement is consistent with results in literature as summarized in Table 2. Predicted velocity transitions and road grade can reduce energy use also via predictive power split in hybrid powertrains [START_REF] Sun | Velocity predictors for predictive energy management in hybrid electric vehicles[END_REF], fuel cut-off [START_REF] Dornieden | Anticipatory energy-efficient longitudinal vehicle control[END_REF] and cylinder deactivation [START_REF] Sujan | System and method of cylinder deactivation for optimal engine torque-speed map operation[END_REF] in combustion engines, and thermal load management [START_REF] Braun | Looking forward: Predictive thermal management optimizes efficiency and dynamics[END_REF]. While such predictive powertrain control functions can be exercised in conventionally driven vehicles and some have been extensively studied, they will have a larger impact in CAVs. Real-time access to information due to connectivity and absence of a human driver in a CAV increases certainty of predictions and therefore effectiveness of predictive powertrain control as depicted schematically in Figure 2.

Anticipating Signal Phase and Timing

When driving on arterial roads, repetitive stops at traffic signals result in loss of energy due to braking and idling, engine and brake wear, and can be uncomfortable and frustrating for passengers. Some of these stops are unnecessary, in particular under light to medium traffic conditions, and are due to lack of information about the state of traffic lights. In an ideal connected urban area with Vehicle-to-Infrastructure (V2I) connectivity, Signal Phase and Timing (SPaT) can be broadcast to approaching vehicles; so that connected vehicles adjust their speed for a timely arrival at a green light as shown schematically in Figure 6. Vehicle autonomy further facilitates this scenario by taking the burden of speed adjustments away from human drivers. Eco-driving at signalized intersections and its impact on energy efficiency has been the topic of many papers in recent years. One of the earlier works was presented in [START_REF] Asadi | Predictive use of traffic signal state for fuel saving[END_REF] and expanded in [START_REF] Asadi | Predictive cruise control: Utilizing upcoming traffic signal information for improving fuel economy and reducing trip time[END_REF] and showed potential for significant fuel savings in a simulation study. These positive results have been corroborated in [START_REF] Mandava | Arterial velocity planning based on traffic signal information under light traffic conditions[END_REF][START_REF] Rakha | Eco-driving at signalized intersections using V2I communication[END_REF][START_REF] Mahler | An optimal velocity-planning scheme for vehicle energy efficiency through probabilistic prediction of traffic-signal timing[END_REF]) and many more publications that have followed them. Experimental results in isolated environments [START_REF] Xia | Field operational testing of eco-approach technology at a fixed-time signalized intersection[END_REF][START_REF] Jin | Power-based optimal longitudinal control for a connected eco-driving system[END_REF] and in real-world traffic conditions [START_REF] Mahler | Enhancing energy efficiency in connected vehicles via access to traffic signal information[END_REF][START_REF] Hao | Eco-Approach and Departure (EAD) Application for Actuated Signals in Real-World Traffic[END_REF][START_REF] Mahler | Cellular communication of traffic signal state to connected vehicles for eco-driving on arterial roads: system architecture and experimental results[END_REF] show that considerable fuel saving (5-15%) is possible with human drivers in the loop. Even more energy saving is expected in automated driving (or with automated cruise control) where vehicles can adjust their speeds more precisely and effortlessly.

The technology for transmitting traffic signal information to subscribing vehicles has been demonstrated in several research projects [START_REF] Koukoumidis | SignalGuru: leveraging mobile phones for collaborative traffic signal schedule advisory[END_REF], [START_REF] Xia | Field operational testing of eco-approach technology at a fixed-time signalized intersection[END_REF] and [START_REF] Mahler | Cellular communication of traffic signal state to connected vehicles for eco-driving on arterial roads: system architecture and experimental results[END_REF]. The SPaT information may be directly transmitted to vehicles within range using Dedicated Short Range Communications (DSRC) technology [START_REF] Hao | Eco-Approach and Departure (EAD) Application for Actuated Signals in Real-World Traffic[END_REF] or may become available by the traffic control center via cellular networks as shown in [START_REF] Mahler | Cellular communication of traffic signal state to connected vehicles for eco-driving on arterial roads: system architecture and experimental results[END_REF]. A software architecture for cellular communication of SPaT from a server to subscribing connected vehicles is described in [START_REF] Mahler | Cellular communication of traffic signal state to connected vehicles for eco-driving on arterial roads: system architecture and experimental results[END_REF]. Alternative means of inferring SPaT information via on-board cameras [START_REF] Koukoumidis | SignalGuru: leveraging mobile phones for collaborative traffic signal schedule advisory[END_REF] and via crowd-sourcing [START_REF] Fayazi | Traffic signal phase and timing estimation from low-frequency transit bus data[END_REF][START_REF] Fayazi | Crowdsourcing phase and timing of pre-timed traffic signals in the presence of queues: algorithms and back-end system architecture[END_REF] have also been proposed. Connected Signals (ConnectedSignals) is a company in Oregon, USA that has been attempting to build a SPaT information repository one city at a time and provides speed advisory to human drivers via a mobile app [START_REF] Marshall | Enlighten app uses AI to predict when lights will turn green[END_REF]. However a much needed real-time server that covers large urban areas is still missing. In absence of real-time SPaT information, it is still possible to use history of observation during daily commutes and to estimate the probability of a green or red over a future horizon, conditioned on the current color of the light [START_REF] Mahler | An optimal velocity-planning scheme for vehicle energy efficiency through probabilistic prediction of traffic-signal timing[END_REF]. Even when SPaT is available in real-time; the future color of the light is not known with certainty, for instance when the light is actuated by the state of loop detectors. In such a scenario one can still use historical trends, to predict the probability of a red or green over a future time horizon [START_REF] Bodenheimer | Enabling GLOSA for adaptive traffic lights[END_REF].

While simple logical rules, such as those in [START_REF] Asadi | Predictive use of traffic signal state for fuel saving[END_REF], can be effectively used when approaching a single traffic signal, optimizing the trajectory for a sequence of traffic lights can benefit from more formal methods. The velocity planning problem can be formulated as an optimal control problem where the goal could be minimizing or reducing energy consumption subject to the constraint imposed by red signals. Analytical solution, obtained using Pontryagin Minimum Principle, indicate that fuel optimal solution for a conventional vehicle1 is not intuitive and [START_REF] Scora | Comprehensive modal emissions model (CMEM), version 3.01. User guide[END_REF] fuel consumption model traffic) [START_REF] Kamalanathsharma | Network-wide impacts of vehicle eco-speed control in the vicinity of traffic signalized intersections[END_REF] S, network wide effect +26 1 fixed time signals, single lane at grade (100% CAV) INTEGRATION microsimulation package none varied CAVpenetration (≤50% VT-micro fuel consumption model CAV) * in simulated vicinity of signalized intersections and not an entire trip gain. † S: Simulation † † E: Experimental requires switching between maximum engine torque (pulse) and engine shut-down (glide) and could include a period of constant speed (cruise) [START_REF] Ozatay | Analytical solution to the minimum fuel consumption optimization problem with the existence of a traffic light[END_REF][START_REF] Wan | Optimal speed advisory for connected vehicles in arterial roads and the impact on mixed traffic[END_REF]. Obviously the resulting speed profile, while fuel optimal, is uncomfortable to drivers and may also be disruptive to surrounding traffic. Therefore alternative cost functions can be used that take into account passenger comfort; for instance penalizing a weighted sum of travel time and acceleration results in smoother trajectories and less braking, thus saving fuel. Optimizing for multiple lights ahead requires numerical solution methods; in [START_REF] Kamalanathsharma | Multi-stage dynamic programming algorithm for eco-speed control at traffic signalized intersections[END_REF] and [START_REF] Mahler | An optimal velocity-planning scheme for vehicle energy efficiency through probabilistic prediction of traffic-signal timing[END_REF], Dynamic Programming (DP) is utilized to solve the optimal control problem. In [START_REF] Mahler | An optimal velocity-planning scheme for vehicle energy efficiency through probabilistic prediction of traffic-signal timing[END_REF]) lack of deterministic information about the color of the light is handled by including probability of a green in the DP cost function and encourages vehicles to target probable green windows. Receding horizon optimization (model predictive control) has been used in [START_REF] Asadi | Predictive cruise control: Utilizing upcoming traffic signal information for improving fuel economy and reducing trip time[END_REF] and [START_REF] Kamal | Model predictive control of vehicles on urban roads for improved fuel economy[END_REF] and to obtain near optimal trajectories at signalized intersections. In [START_REF] He | Optimal vehicle speed trajectory on a signalized arterial with consideration of queue[END_REF] the queue is considered when calculating the optimal speed. Eco departure of geared vehicles at traffic signals is discussed in (Li et al., 2015b). In [START_REF] De Nunzio | Speed advisory and signal offsets control for arterial bandwidth maximization and energy consumption reduction[END_REF] speed advisory is proposed in conjunction with signal offsets control (green waving) for arterial bandwidth maximization and energy consumption reduction.

"Selfish" optimization that focuses on eco-driving of a single vehicle could be disruptive to the flow of following vehicles. In [START_REF] Homchaudhuri | Fast model predictive control-based fuel efficient control strategy for a group of connected vehicles in urban road conditions[END_REF], while still a vehicle centric optimization is solved, a more "considerate" cost function takes into account the preceding as well as the interest of the following vehicle. More specifically a "safety" term is introduced in the cost function of the host vehicle that penalizes sudden slow downs with respect to the velocity of the following vehicle.

Because this technology is unlikely to be implemented in every vehicle in the near future, it is important to evaluate the influence of equipped vehicles on other vehicles in mixed traffic flow. It is currently prohibitively difficult to do field experiments of a large number of CAVs in mixed traffic. Therefore traffic simulation tools have been used in most studies. The impact of traffic signal advisory on mixed traffic is studied, via microsimulations, in [START_REF] Xia | Dynamic eco-driving for signalized arterial corridors and its indirect network-wide energy/emissions benefits[END_REF][START_REF] Kamalanathsharma | Network-wide impacts of vehicle eco-speed control in the vicinity of traffic signalized intersections[END_REF][START_REF] Wan | Optimal speed advisory for connected vehicles in arterial roads and the impact on mixed traffic[END_REF]. In [START_REF] Kamalanathsharma | Network-wide impacts of vehicle eco-speed control in the vicinity of traffic signalized intersections[END_REF] and in [START_REF] Xia | Dynamic eco-driving for signalized arterial corridors and its indirect network-wide energy/emissions benefits[END_REF] the authors evaluate the influence of eco-driving or eco-speed control on the immediate neighboring vehicles. In [START_REF] Wan | Optimal speed advisory for connected vehicles in arterial roads and the impact on mixed traffic[END_REF] the impact of CAVs on mixed traffic near signalized intersections is studied in traffic microsimulations. The CAVs receive the timing of signals in advance and adjust their speed for a timely arrival at green. It is shown that CAVs not only improve their energy efficiency but as their penetration increases they reduce the energy consumption of conventional vehicles as well. With the increment of CAVs, other conventional vehicles are more likely to follow a smoother moving CAV. By their simple car following strategy, such conventional vehicles may reduce the chance of stopping at intersections as well.

Potential impact on energy efficiency is summarized in Table 3.

Anticipative Car Following

Human drivers are often reactive when following other cars as their view is often blocked by the preceding car and therefore their event horizon is very limited. In sudden slowdowns, they often fail to consider the vehicles approaching from behind. This is not only disruptive to traffic flow and is unsafe, but it can result in inefficient slow-down of multiple vehicles. Balancing the position dynamically with respect to the cars in the front and back is cognitively demanding for humans. Most autonomous cars without connectivity do not necessarily do better. Many are designed to behave like human-driven vehicles and could be reactive to the perception of their immediate surrounding which results in similar short-sighted decisions. In [START_REF] Mersky | Fuel economy testing of autonomous vehicles[END_REF] a simulation scenario depicts an automated vehicle that uses 3% more energy than a conventional vehicle baseline due to its aggressive car following strategy.

The challenge is anticipation of road events, although experienced drivers do exercise anticipation to some extent in driving [START_REF] Hoogendoorn | Empirics of multianticipative car-following behavior[END_REF] [START_REF] Stahl | Supporting anticipation in driving through attentional and interpretational in-vehicle displays[END_REF]. We pay attention to clues and drive accordingly. For example, if we observe that a lead vehicle is accelerating and decelerating erratically we increase our following distance or change lanes. If we observe that a following vehicle is tail-gating us we try to induce a larger gap or allow that vehicle to pass. But most of these precautions are practiced in an adhoc manner, are constrained by our limited sensory and cognitive limits [START_REF] Vanderbilt | Traffic: Why We Drive the Way We Do[END_REF], and are inconsistent across different drivers [START_REF] Ossen | Heterogeneity in car-following behavior: Theory and empirics[END_REF] and traffic scenarios. These cause poor local judgments that could lead to shock waves that slow us down to inefficient crawls. Today much more can be done: thanks to better sensing capabilities, CAVs have the potential to anticipate the motion of their preceding vehicle and finely adjust their speeds for a more steady and smooth motion. Additional information of the intent of preceding vehicles via V2V communication can enhance such anticipative car following.

While the main goal should be to robustly maintain a safe following distance to the preceding vehicle (imposed as position constraints); the inter-vehicle gap can be judiciously used as a degree of freedom to filter abrupt slow-downs and application of brakes [START_REF] Kamal | Smart driving of a vehicle using model predictive control for improving traffic flow[END_REF] and increase energy efficiency of the host vehicle as schematically shown in Figure 4. Smoother velocity transitions of the host vehicles are expected to positively influence the motion of upstream traffic, reduce the chance of a phantom jam, caused by small disturbance, [START_REF] Helbing | Traffic and related self-driven many-particle systems[END_REF][START_REF] Sugiyama | Traffic jams without bottlenecksexperimental evidence for the physical mechanism of the formation of a jam[END_REF][START_REF] Flynn | Self-sustained nonlinear waves in traffic flow[END_REF] and lower fuel used by the entire queue of vehicles as experimentally shown in [START_REF] Stern | Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments[END_REF][START_REF] Stern | Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments[END_REF].

Figure 4: Anticipative car following and lane selection. The white CAV receives the imminent intentions of its preceding yellow CAV or predicts it using past statistical data and plans its motion to minimize its acceleration and velocity deviation while enforcing safe gap constraints. The green CAV which is preceded by a bus anticipates right lane traffic slow down near a bus stop and proactively starts a lane change. Its goal could be minimizing a weighted sum of its acceleration and deviations from desired velocity and lane. Most parts of the image were created on https://icograms.com.

Because of shorter relevant time scales in car-following, a moving horizon optimization is a natural choice (as opposed to full trip optimization). One can penalize fuel used over a moving horizon or simplify the cost function by penalizing the vehicle deceleration in order to reduce braking events. For a vehicle with a combustion engine the fuel optimal car following strategy could be pulse and glide as shown in [START_REF] Sciarretta | Fuel-optimal control of rendezvous maneuvers for passenger cars (treibstoffoptimale annäherung von straßenfahrzeugen)[END_REF][START_REF] Li | Strategies to minimize fuel consumption of passenger cars during car-following scenarios[END_REF]Li et al., 2012); but a pulse and glide strategy is uncomfortable, and could be disruptive to traffic as alluded to in (Li et al., 2015a). Therefore it may be best to penalize acceleration and deceleration or use of brakes. Safety can be guaranteed by enforcing a speed dependent lower bound on inter-vehicle gap over the horizon (Li et al., 2011). Terminal constraints can also be enforced to prevent myopic decisions [START_REF] Dollar | Quantifying the impact of limited information and control robustness on connected automated platoons[END_REF][START_REF] Turri | A model predictive controller for non-cooperative eco-platooning[END_REF]. The main challenge that arises here is dependence of the inter-vehicle constraint on the position of the preceding vehicle which is typically unknown. Therefore despite a relatively simple control problem formulation, we are faced with a difficult prediction problem.

In absence of any information and when only instantaneous velocity or acceleration of the preceding vehicle is known, the position of the preceding vehicle can be projected over the horizon assuming that it travels with constant speed [START_REF] Mcdonough | Stochastic dynamic programming control policies for fuel efficient vehicle following[END_REF] or constant acceleration [START_REF] Han | Safe-and eco-driving control for connected and automated electric vehicles using analytical state-constrained optimal solution[END_REF]. Or perhaps it is reasonable to assume that acceleration of the preceding vehicle decays over the horizon to zero with some time constant [START_REF] Schepmann | Heavy vehicle fuel economy improvement using ultracapacitor power assist and preview-based MPC energy management[END_REF]. When information from the road and infrastructure is available as discussed in Sections 3.1 and 3.2 one can construct a deterministic profile that the preceding vehicle is expected to follow.

But often the main source of uncertainty is driving style of the preceding vehicle which induces reactive transitions by the host vehicles. In this context and in the broader context of driver modeling different modeling approaches have been used. For instance [START_REF] Lang | Prediction of preceding driver behavior for fuel efficient cooperative adaptive cruise control[END_REF] proposes fitting a nonlinear autoregressive model to historical data to predict the motion of preceding vehicle. In [START_REF] Kamal | Smart driving of a vehicle using model predictive control for improving traffic flow[END_REF] the future motion of a group of preceding vehicles is estimated via traffic microsimulations. Many have used Markov chain models to capture the statistics of velocity transitions. In essence, historical driving data from a particular driver is used to count transitions from a certain velocity (acceleration) to another and to then calculate the probability of such a transition [START_REF] Mcdonough | Modeling of vehicle driving conditions using transition probability models[END_REF].

One can then sample many potential velocity trajectories with associated probabilities and integrate them to obtain a probability distribution for the position of the preceding vehicle over a prediction horizon [START_REF] Zhang | Predictive cruise control with probabilistic constraints for eco driving[END_REF]. The inter-vehicle gap constraint can be enforced probabilistically (chance constraint) and then converted to a deterministic constraint as shown in [START_REF] Zhang | Predictive cruise control with probabilistic constraints for eco driving[END_REF][START_REF] Wan | Probabilistic anticipation and control in autonomous car following[END_REF]. Alternatively one can solve a stochastic moving horizon optimization as shown in [START_REF] Bichi | Stochastic model predictive control with driver behavior learning for improved powertrain control[END_REF][START_REF] Mcdonough | Stochastic dynamic programming control policies for fuel efficient in-traffic driving[END_REF][START_REF] Mcdonough | Stochastic dynamic programming control policies for fuel efficient vehicle following[END_REF][START_REF] Mcdonough | Stochastic fuel efficient optimal control of vehicle speed[END_REF][START_REF] Zhou | Rolling horizon stochastic optimal control strategy for acc and cacc under uncertainty[END_REF]. For instance, in [START_REF] Mcdonough | Stochastic dynamic programming control policies for fuel efficient in-traffic driving[END_REF] the host vehicle speed is adjusted, using stochastic Model Predictive Control (MPC), based on Markov chain predictions of traffic speed and road grade.

In an ideal scenario when all vehicles communicate, each vehicle can solve its own optimization problem and pass on its intended action to the vehicles that follow it [START_REF] Dollar | Quantifying the impact of limited information and control robustness on connected automated platoons[END_REF][START_REF] Zheng | Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies[END_REF]. This allows a host vehicle to know, with more certainty, the position of the preceding vehicle(s) over the optimization horizon and is believed to result in smoother flow and improved overall energy efficiency. Note that in this scenario, the vehicles are just sharing intentions and do not necessarily cooperate toward a common goal. Later in section 4.1 we discuss a cooperative cruise control scenario where the vehicles could cooperate toward a "social" optimum.

With a queue of communicating vehicles, this becomes a distributed MPC problem [START_REF] Zheng | Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies[END_REF] that is solved sequentially from the front to the back of the queue. Alternatively, a centralized optimization problem can be solved on a central server for all participating vehicles and its decisions communicated to each vehicle [START_REF] Besselink | Cyber-physical control of road freight transport[END_REF]; however a central coordination scheme is complex to implement, except maybe for freight transport, and is less likely to prevail in the authors' opinion. preview † S: Simulation † † E: Experimental A different approach is proposed in [START_REF] Kamal | Smart driving of a vehicle using model predictive control for improving traffic flow[END_REF] where it is assumed that all vehicles in a queue com-municate their immediate state (position, velocity, acceleration) but not their intentions. The host vehicle assumes a standard car following model for the preceding vehicles to anticipate their positions over its optimization horizon. A similar approach is discussed in [START_REF] Orosz | Connected cruise control: modelling, delay effects, and nonlinear behaviour[END_REF] and [START_REF] Li | Sequential parametric optimization for connected cruise control with application to fuel economy optimization[END_REF]. In a less than ideal scenario, when only a portion of the vehicles in a queue communicate, the position of non-communicating vehicles is inferred in [START_REF] Goodall | Microscopic estimation of arterial vehicle positions in a low-penetration-rate connected vehicle environment[END_REF] at signalized intersections. Communication delay make the problem even more complex and is discussed in [START_REF] Ge | Dynamics of connected vehicle systems with delayed acceleration feedback[END_REF][START_REF] Orosz | Connected cruise control: modelling, delay effects, and nonlinear behaviour[END_REF]. Packet drops resulting in stochastic delays in connected cruise control and the impact on string stability are discussed in [START_REF] Qin | Stability and frequency response under stochastic communication delays with applications to connected cruise control design[END_REF]. Table 4 highlights selected results that show the impact of anticipative car following on energy efficiency. As can be seen the reported gains vary significantly even for vehicles of the same size. This could be due to design and parameters of the car-following algorithms and scenario setups.

Anticipative Lane Selection and Merging

Most existing literature on eco-driving assume the vehicle maintains a single lane, reducing optimization of the vehicle motion to the choice of its velocity. In multi-lane roads, the freedom to choose a different lane provides a new dimension and many more possibilities for optimizing the motion (velocity) of the vehicle to safely improve its energy efficiency and even harmonize traffic. But every day driving experience indicates that choice of lane is a complex decision making problem, perhaps due to its combinatorial nature and typical lack of information about the average speed (or efficiency) of adjacent lanes. The same is true when merging into a highway from an on-ramp or exiting to an off-ramp. Lane selection can be a dilemma point for average drivers; aggressive lane change on the other hand can be unsafe and disruptive to the flow and efficiency of upstream traffic. Even "considerate" drivers who merge early, out of an ending lane reduce the road capacity and slow down traffic [START_REF] Mele | Why last-second lane mergers are good for traffic[END_REF].

In a connected and automated vehicle environment, more information about the intention of neighboring vehicles can become available via V2V communication, speed of each lane could be broadcast from roadside sensors, and therefore automated vehicles can change lanes more judiciously and smoothly. See an example scenario depicted schematically in Figure 4. A rather comprehensive survey of lane change/merge for CAVs can be found in (Rios-Torres and Malikopoulos, 2017b;[START_REF] Bevly | Lane change and merge maneuvers for and automated vehicles: A survey[END_REF]. One of the original formulations in this area can be found in (Kamal et al., 2015b[START_REF] Kamal | Efficient driving on multilane roads under a connected vehicle environment[END_REF] where choice of lane is an additional integer decision variable in the energy cost of the vehicle. Each CAV runs a microsimulation initialized by the current state of neighboring vehicles to determine the traffic scene over its optimization horizon. Lane and velocity of the vehicle are optimized accordingly. In [START_REF] Dollar | Predictive coordinated vehicle acceleration and lane selection using mixed integer programming[END_REF] the quadratic lane selection and velocity tracking cost function and the non-convex constraint set imposed by neighboring vehicles are converted to a mixed integer quadratic program and solved over a receding horizon. A hybrid optimization approach is presented in (Wang et al., 2015b). A scenario-based model predictive approach in [START_REF] Schildbach | Scenario model predictive control for lane change assistance on highways[END_REF] is intended for safe automated lane changing but also benefit energy efficiency. In [START_REF] Yu | A human-like game theory-based controller for automatic lane changing[END_REF] a game theoretic approach to automatic lane changing is proposed and is shown to outperform rule-based controllers.

Merging from ramps often causes breakdown and a phantom traffic jam in a highway. Today, solutions such as ramp metering are being used to remedy the situation [START_REF] Papageorgiou | Freeway ramp metering: An overview[END_REF][START_REF] Hegyi | Model predictive control for optimal coordination of ramp metering and variable speed limits[END_REF] which requires infrastructure investment and maintenance. With CAV technology the merge can be coordinated much more safely as experimentally shown in [START_REF] Hafner | Cooperative collision avoidance at intersections: Algorithms and experiments[END_REF] resulting in smoother traffic [START_REF] Letter | Efficient control of fully automated connected vehicles at freeway merge segments[END_REF][START_REF] Zhou | On the impact of cooperative autonomous vehicles in improving freeway merging: A modified intelligent driver model-based approach[END_REF] and higher energy efficiency (Rios-Torres and Malikopoulos, 2017a). The impact could go beyond individual vehicles; by reducing the chance of a phantom jam, the overall energy efficiency of traffic will improve. Table 5 summarizes the limited results that authors could find on the impact of lane selection on energy efficiency.

Increased Opportunities for Cooperative Driving

In a connected vehicle world, deliberate exchange of intentions by vehicles and infrastructure reduces the need for guesstimating the surrounding traffic patterns and therefore enables better coordination. Automated vehicles can cooperate rather than compete for right of way in urban areas and highways, thus contributing to harmony in motion and improved mobility and efficiency of a group of vehicles. Therefore "cooperation" in what follows, refers to sharing information and coordinating movements for a "common" good. Even with the best intentions of human drivers, cooperation among conventional vehicles is rather challenging due to often unknown plan of neighboring [START_REF] Kamal | Model predictive control of vehicles on urban roads for improved fuel economy[END_REF] yield reported gain for merging period only &merge † S: Simulation * equipped vehicles (all traffic) vehicles and complexity of coordination at speed. For instance, merging from a ramp into a highway lacks a clear protocol and is often done in "adhoc" manner in the hope that fast approaching vehicles act with "consideration". This is not only unsafe, but the need for frequent braking in dilemma zones increases energy use and could negatively impact traffic flow. Information sharing via connectivity allows establishing more systematic coordination protocols that increase safety and efficiency. Automated vehicles can be programmed to take full advantage of such protocols that may require precise movement coordination. We describe below cooperation in car following, merging, lane changing, and intersection crossing and also discuss their potential impact on efficiency of cooperating vehicles as well as benefits to mixed traffic.

Cooperative Car Following

Cooperative car following in which vehicles coordinate in longitudinal formations is perhaps the most researched topic in cooperative driving, under the contexts of platooning and cooperative adaptive cruise control. Tight platooning gained popularity in the 1990s for its potential to increase highway throughput. In a platoon of communicating and partially automated vehicles, such as in Figure 5, the gap between a group of following vehicles can be safely reduced to increase road capacity. Moreover at short following distances, the aerodynamic drag coefficient is smaller resulting in significant energy savings, in particular for heavy duty vehicles. Recognized research programs in the USA [START_REF] Browand | Fuel saving achieved in the field test of two tandem trucks[END_REF][START_REF] Bishop | Evaluation and testing of driver-assistive truck platooning: phase 2 final results[END_REF], Europe [START_REF] Kunze | Organization and operation of electronically coupled truck platoons on german motorways[END_REF][START_REF] Alam | An experimental study on the fuel reduction potential of heavy duty vehicle platooning[END_REF][START_REF] Alam | Fuel-efficient heavy-duty vehicle platooning[END_REF], and Japan [START_REF] Tsugawa | Results and issues of an automated truck platoon within the energy its project[END_REF] have demonstrated the feasibility of the technology in well documented road experiments as discussed in [START_REF] Tsugawa | A review of truck platooning projects for energy savings[END_REF] showing potential for 5-15% energy saving. Experimental results in [START_REF] Alam | An experimental study on the fuel reduction potential of heavy duty vehicle platooning[END_REF][START_REF] Alam | Fuel-efficient heavy-duty vehicle platooning[END_REF] show between 4 to 7 percent energy saving potential for a heavy truck. Over the years, important technical challenges such as platoon string stability [START_REF] Swaroop | String stability of interconnected systems[END_REF], communication needs [START_REF] Segata | Toward communication strategies for platooning: simulative and experimental evaluation[END_REF][START_REF] Willke | A survey of inter-vehicle communication protocols and their applications[END_REF], control design [START_REF] Swaroop | Constant spacing strategies for platooning in automated highway systems[END_REF]. [START_REF] Horowitz | Control design of an automated highway system[END_REF], and formation scheduling [START_REF] Larson | A distributed framework for coordinated heavy-duty vehicle platooning[END_REF][START_REF] Luo | Coordinated platooning with multiple speeds[END_REF] have been addressed. Today the technology has matured to the extent that major manufacturers and startup companies plan on delivering truck platooning solutions to the market in the near future with the goal of reducing energy and personnel cost [START_REF] Muoio | Here's how Tesla, Uber, and Google are trying to revolutionize the trucking industry[END_REF].

Over the past few years and with increased prospects for vehicle connectivity, Cooperative Adaptive Cruise Control (CACC), has gained popularity in the research community. CACC is essentially an enhanced Adaptive Cruise Control (ACC) system that, in addition to range sensor feedback, relies on wireless communication of the acceleration of the preceding vehicle(s) for feedforward control. V2V communication is intended to increase safety and allows string-stable reduction of the inter-vehicle gap for improved road utilization [START_REF] Naus | String-stable CACC design and experimental validation: A frequency-domain approach[END_REF]. With a correct design, velocity variations are much better attenuated than in ACC car following, as shown in road experiments with six equipped vehicles in [START_REF] Ploeg | Design and experimental evaluation of cooperative adaptive cruise control[END_REF]. Experimental results in [START_REF] Milanés | Cooperative adaptive cruise control in real traffic situations[END_REF] showed string stable operation of a CACC design at a short time headway of 0.6 seconds in scenarios where a production ACC design failed to maintain stability even though it was operating at larger 1.1 second headway. The 2011 Driving Challenge in Netherlands was a successful showcase of CACC technology by multiple teams. An overview of this competition is presented in [START_REF] Ploeg | Introduction to the special issue on the 2011 grand cooperative driving challenge[END_REF][START_REF] Van Nunen | Cooperative competition for future mobility[END_REF] and the details of each team's technical contribution is well documented in separate papers [START_REF] Geiger | Team AnnieWAY's entry to the 2011 grand cooperative driving challenge[END_REF][START_REF] Lidström | A modular CACC system integration and design[END_REF][START_REF] Kianfar | Design and experimental validation of a cooperative driving system in the grand cooperative driving challenge[END_REF][START_REF] Mårtensson | The development of a cooperative heavy-duty vehicle for the gcdc 2011: Team Scoop[END_REF][START_REF] Nieuwenhuijze | Cooperative driving with a heavy-duty truck in mixed traffic: Experimental results[END_REF][START_REF] Guvenc | Cooperative adaptive cruise control implementation of team Mekar at the grand cooperative driving challenge[END_REF]. CACC formations could positively or negatively impact surrounding traffic as demonstrated in a simulation study [START_REF] Van Arem | The impact of cooperative adaptive cruise control on traffic-flow characteristics[END_REF], for instance long formations may prevent those that intend to merge into a highway. But overall, CACC is expected to have a harmonizing impact on participating vehicles and on surrounding traffic, reducing braking events and lowering energy consumption. Despite these benefits there are few papers documenting the energy efficiency impact of CACC, for instance [START_REF] Lang | Prediction of preceding driver behavior for fuel efficient cooperative adaptive cruise control[END_REF]). It appears that reducing energy efficiency has been mostly the focus of truck platooning projects.

While the platoon and CACC terminologies are sometimes interchangeably used in the literature, there are some differentiating features. The original concept of a platoon relied on a designated lead vehicle and a hierarchical control structure from the lead to the following vehicles. This hierarchy is not needed in CACC car following and each vehicle can individually switch to its CACC mode as long as it receives messages communicated by its preceding vehicles. The information flow between vehicles can vary from one implementation to the other. A vehicle can receive information from the lead vehicle only, from its preceding vehicle only, or from multiple preceding vehicle as schematically shown in [START_REF] Orosz | Connected cruise control: modelling, delay effects, and nonlinear behaviour[END_REF] and [START_REF] Zheng | Influence of information flow topology on closed-loop stability of vehicle platoon with rigid formation[END_REF]. Depending on the information flow and content shared between vehicles, we can envision enhanced versions of current platooning and CACC practices. Ideally each vehicle will share its intended acceleration profile over a future horizon, rather than its instant acceleration, with all its following vehicles [START_REF] Dollar | Quantifying the impact of limited information and control robustness on connected automated platoons[END_REF][START_REF] Zheng | Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies[END_REF]. This reduces the uncertainty about the movement of preceding vehicles as was discussed in Section 3.3 aiding each vehicle to better plan its motion and reduce braking events. Note that in this scenario, cooperation is only via information sharing, and each vehicle optimizes its "selfish" cost function. In a true collaborative environment, a group of CAVs not only share information but look for the "social optimum" by optimizing a common cost function [START_REF] Zheng | Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies[END_REF] or by formation consensus rules [START_REF] Bernardo | Distributed consensus strategy for platooning of vehicles in the presence of time-varying heterogeneous communication delays[END_REF]. The common goal for instance could be reducing the fuel consumption of the entire fleet [START_REF] Besselink | Cyber-physical control of road freight transport[END_REF][START_REF] Lelouvier | Eco-platooning of autonomous electrical vehicles using distributed model predictive control[END_REF][START_REF] Homchaudhuri | Fast model predictive control-based fuel efficient control strategy for a group of connected vehicles in urban road conditions[END_REF], string stability [START_REF] Dunbar | Distributed receding horizon control of vehicle platoons: Stability and string stability[END_REF], or collision mitigation (Wang et al., 2015a). A common cost can still be optimized in a distributed fashion onboard each vehicle based on information communicated by neighboring vehicles to reach a consensus [START_REF] Dunbar | Distributed receding horizon control of vehicle platoons: Stability and string stability[END_REF][START_REF] Lelouvier | Eco-platooning of autonomous electrical vehicles using distributed model predictive control[END_REF]. In a centralized control framework described in [START_REF] Lelouvier | Eco-platooning of autonomous electrical vehicles using distributed model predictive control[END_REF], the common fuel cost is optimized on a central cloud server for a group of freight trucks and the decision is issued to low-level controllers of individual trucks. Table 6 summarizes some of the limited results on energy efficiency impact of cooperative car following, including platooning. [START_REF] Dollar | Quantifying the impact of limited information and control robustness on connected automated platoons[END_REF] S, microsimulation, combustion engine vehicles +50 10 CAVs follow lead vehicle, share partial info for drag reduction is not considered each CAV solves MPC, horizon=12 to 20 sec FTP fuel use evaluated using an engine map cycle compared against IDM car following following [START_REF] Browand | Fuel saving achieved in the field test of two tandem trucks[END_REF] E † † , truck platooning +8-11 2.4 km unused runway, Crows Landing two identical Freightliner tractors, 16 m trailers 90 km/h constant speed, 3-10 meter spacing [START_REF] Alam | Fuel-efficient heavy-duty vehicle platooning[END_REF] E, truck platooning, 45 km Swedish highway +4-6.5 Three 18 m, 37-39 ton Scania tractor-trailers wirelessly communicate vel., accel., parameters time headway=1 second [START_REF] Tsugawa | Results and issues of an automated truck platoon within the energy its project[END_REF] E, truck platooning on a test track +15 3 fully-automated 25 ton trucks & 1 light truck communicate vel,, accel., brake via DSRC 80 km/h constant speed, 4.7 meter gap [START_REF] Bishop | Evaluation and testing of driver-assistive truck platooning: phase 2 final results[END_REF] E, truck platooning on test track +7.0 2 Peterbilt tractors, full aerodynamic packages 16 m trailers weighing 30 ton high-speed oval track, banked turns 105 km/h and 10 m following distance † S: Simulation † † E: Experimental

Cooperative Lane Change and Merge

In Section 3.4 we discussed that individual CAVs can benefit from connectivity and autonomy and more safely and efficiently merge and change lanes. Additional gains are expected if CAVs cooperate, not only by sharing intentions but also by being "considerate" of neighboring vehicles as shown schematically in Figure 5. In such a cooperative scenario, each vehicle includes in its objective function, the impact of its decision on neighboring vehicles. Lane change and merge decisions can then be made in a distributed manner with each vehicle deciding (optimizing) its motion and sharing its intentions [START_REF] Nie | Decentralized cooperative lane-changing decision-making for connected autonomous vehicles[END_REF]. Alternatively, in a centralized framework, a single decision-making (optimization) problem is solved for a group of cooperative vehicles [START_REF] Cao | Cooperative vehicle path generation during merging using model predictive control with real-time optimization[END_REF]. Cooperative lane selection and merge not only contributes to efficiency of the cooperating fleet but can also have a positive harmonizing effect on surrounding traffic.

There is a large body of literature on lane change models for traffic microsimulations, such as the widely used MOBIL lane change model introduced in [START_REF] Kesting | General lane-changing model mobil for car-following models[END_REF]. However cooperative lane selection and merging for CAVs has only been recently discussed. In [START_REF] Awal | An efficient cooperative lane-changing algorithm for sensor-and communication-enabled automated vehicles[END_REF] a cooperative lane-changing algorithm is simulated that considers follower vehicles in current and target lanes when making a lane change decision. In [START_REF] Scarinci | Definition of a merging assistant strategy using intelligent vehicles[END_REF] a cooperative merging assistant is introduced to facilitate merging on ramp traffic and relying on vehicle connectivity. The simulations in [START_REF] Awal | An efficient cooperative lane-changing algorithm for sensor-and communication-enabled automated vehicles[END_REF] show improvement with respect to MOBIL, in terms of merge time and rate, wait time, fuel consumption, average velocity, and flow at the cost of slightly increased travel time for main road vehicles. In [START_REF] Scarinci | Analysis of traffic performance of a merging assistant strategy using cooperative vehicles[END_REF] a merging assistant system that relies on vehicle cooperation, reduces the number of "latemerging" vehicles and subsequent likelihood of flow break-downs. Different algorithms for cooperative merging have been proposed, for instance [START_REF] Mosebach | Merging control of cooperative vehicles[END_REF] proposes a decentralized control method and [START_REF] Cao | Cooperative vehicle path generation during merging using model predictive control with real-time optimization[END_REF] formulates in a model predictive control framework. A cooperative V2V "negotiation" process for lane changing is described in [START_REF] Lombard | On the cooperative automatic lane change: Speed synchronization and automatic "courtesy[END_REF] and [START_REF] Kazerooni | Interaction protocols for cooperative merging and lane reduction scenarios[END_REF] proposes interaction protocols for cooperative lane changing. A game theoretic perspective for cooperative lane changing is simulated in [START_REF] Zimmermann | Carrot and stick: A game-theoretic approach to motivate cooperative driving through social interaction[END_REF] for CAVs and incentives for cooperation are discussed. Experiments with 3 CAVs performing a semi-automated cooperative lane change maneuver are described in [START_REF] Raboy | Cooperative Control for Lane Change Maneuvers with Connected Automated Vehicles: A Field Experiment[END_REF] and show the potential for smoother velocity trajectories. The focus of the above results has not been energy efficiency and only [START_REF] Awal | An efficient cooperative lane-changing algorithm for sensor-and communication-enabled automated vehicles[END_REF] reports energy efficiency gains. However, we expect considerable energy saving from wide deployment of cooperative lane changing and merging system due to reduced braking events and harmonizing effect on traffic flow.

Cooperative Intersection Control

The coordination and optimal timing of traffic signals are by nature complex problems and backed by years of research in traffic engineering and operations research. Current signal timings are mostly scheduled offline, the optimized timings are then deployed as fix timetables for different times of the day. Many signals are actuated by traffic and have rules to override their pre-optimized timetables based on the state of their loop-detectors to reduce idling at intersections. While these traffic responsive control strategies calculate their timing in real-time [START_REF] Diakaki | A multivariable regulator approach to traffic-responsive network-wide signal control[END_REF], they act based on the immediate state of loop-detectors. On the other hand, smart traffic signal controllers in connected vehicle environments will do more than just signaling right of ways and act intelligently as hubs that sense, route, and harmonize the flow of arterial traffic. The research on uni-directional signal to vehicle communication for improving efficiency by providing speed advisory to individual vehicles was discussed in Section 3.2. Another research direction has focused on improving intersection flow by optimizing timing of traditional traffic signals informed by uni-directional communication from connected vehicles [START_REF] He | PAMSCOD: Platoon-based arterial multi-modal signal control with online data[END_REF]Kamal et al., 2015a). In addition, bi-directional vehicle-signal communication allows the geographical data of the connected vehicles to be also wirelessly transmitted in real-time to smart traffic signal controllers [START_REF] Goodall | Traffic signal control with connected vehicles[END_REF]. This increases energy efficiency and intersection flow as signals adjust their timings and vehicles their speeds [START_REF] De Nunzio | Speed advisory and signal offsets control for arterial bandwidth maximization and energy consumption reduction[END_REF].

Automated vehicles can further benefit from the communicated traffic signal information because they not only process the incoming information rather effortlessly but also can precisely control their speed and arrival time at a green light. The situation can get even better with 100% penetration of automated vehicles since a physical traffic light is not needed anymore as shown in concept papers by [START_REF] Dresner | A multiagent approach to autonomous intersection management[END_REF][START_REF] Ferreira | Self-organized traffic control[END_REF][START_REF] Ferreira | On the impact of virtual traffic lights on carbon emissions mitigation[END_REF]. Also because automated cars have much faster reaction times than human driven vehicles, the intersection controller can rapidly switch between phases [START_REF] Guler | Using connected vehicle technology to improve the efficiency of intersections[END_REF]. Some of the benefits of eliminating traffic signals in an all automated vehicle environment is discussed in [START_REF] Dresner | A multiagent approach to autonomous intersection management[END_REF] and demonstrated by interesting simulation results in a recent publication [START_REF] Tachet | Revisiting street intersections using slot-based systems[END_REF]. In [START_REF] Huang | Assessing the mobility and environmental benefits of reservation-based intelligent intersections using an integrated simulator[END_REF] the potential for 50% energy efficiency gain via such reservation-based intersection control systems is shown. In (Fayazi et al., 2017) increasing the intersection throughput is formalized as an Mixed Integer Linear Programming optimization problem. They show significant reduction in number of stops and fuel use compared to traditional intersection control schemes. In a one hour microsimulation case study it is shown that the number of stops can be reduced 100 times [START_REF] Fayazi | Mixed-integer linear programming for optimal scheduling of autonomous vehicle intersection crossing[END_REF]. Via a vehicle-in-the-loop experiment (Fayazi and Vahidi, 2017) they measure 20 % improvement in energy efficiency of a real-vehicle that interacts with the intersection controller and hundreds of simulated vehicles. The proposed MILP-based controller resides on a computational server and creates a live picture of evolving traffic conditions by tracking all subscribing vehicles. Based on the location and speed of all the vehicles, the controller optimally and regularly schedules the intersection access time for each vehicle. In addition to minimizing intersection delay and ensuring intersection safety, the desired arrival time of the vehicles is incorporated into the optimization problem in such a way that vehicles would not face extreme delay or expedition compared to their desired arrival times. In [START_REF] Ashtiani | Multi-intersection traffic management for autonomous vehicles via distributed mixed integer linear programming[END_REF] the concept is extended to multiple intersections. Simulations indicate benefits of such systems greatly increase if vehicles move in platoons, in certain cases doubling the arterial network capacity with the coordination of platoons and intersections [START_REF] Lioris | Doubling throughput in urban roads by platooning[END_REF]. In [START_REF] Jin | Platoon-based multi-agent intersection management for connected vehicle[END_REF] a platoon-based approach Figure 6: Schematic of a cooperative intersection. CAVs subscribe to an intersection control server as they approach the intersection, the controller assigns access times to each approaching vehicle allowing only vehicles of the same movement in the intersection area at the same time. In this schematic vehicles on movements X and O are grouped together when assigning acces times which reduces idling and saves energy. Most parts of the image were created on https://icograms.com.

shows up to 20% energy efficiency benefit with respect to signalized intersections, but under simulation conditions of [START_REF] Jin | Platoon-based multi-agent intersection management for connected vehicle[END_REF] energy efficiency was a little sacrificed to form platoons. Table 7 highlights some of the key results on energy benefits of cooperative intersection control.

Indirect Benefits Through Traffic Harmonization

Coordinated and smoother motion of CAVs could harmonize the surrounding traffic and contribute to energy efficiency of conventional vehicles, even at low penetration levels. While it is difficult to establish the network wide benefits experimentally, there are microsimulation case studies and isolated experiments that show such positive impacts. For instance in Section 3.2 we explained that according to [START_REF] Wan | Optimal speed advisory for connected vehicles in arterial roads and the impact on mixed traffic[END_REF]) traffic signal speed advisory can reduce the energy consumption of conventional vehicles at moderate penetration rates. Several papers have shown the harmonizing effect of automated cruise control on the upstream traffic [START_REF] Kamal | Smart driving of a vehicle using model predictive control for improving traffic flow[END_REF][START_REF] Koshizen | Traffic Congestion Mitigation Using Intelligent Driver Model (IDM) Combined with Lane Changes-Why Congestion Detection is So Needed?[END_REF] which is expected to positively influence energy efficiency of upstream traffic. CACC not only increases road utilization due to smaller gaps [START_REF] Van Arem | The impact of cooperative adaptive cruise control on traffic-flow characteristics[END_REF][START_REF] Naus | String-stable CACC design and experimental validation: A frequency-domain approach[END_REF][START_REF] Shladover | Impacts of cooperative adaptive cruise control on freeway traffic flow[END_REF], but is shown to attenuate velocity variations as shown in road experiments in [START_REF] Ploeg | Design and experimental evaluation of cooperative adaptive cruise control[END_REF][START_REF] Milanés | Cooperative adaptive cruise control in real traffic situations[END_REF]. These findings are corroborated by microsimulation studies, reported in [START_REF] Talebpour | Influence of connected and autonomous vehicles on traffic flow stability and throughput[END_REF], that show reduction of shock waves with increased penetration of connected and automated vehicles. In [START_REF] Nishi | Theory of jam-absorption driving[END_REF] a "theory for jam-absorption driving" is presented which is a method for driving a single car to attenuate a traffic shockwave, followed by experiments in [START_REF] Taniguchi | A demonstration experiment of a theory of jam-absorption driving[END_REF]. An interesting experiment with a group of 22 vehicles moving on circle, showed that a single automated vehicle using relatively simple control rules, could dissipates the phantom jam waves formed by the 21 human driven vehicles. This contributed to between 20 and 40 % improvement in average fuel economy of the fleet across the 3 experiments as measured using each vehicle's OBD-II port [START_REF] Stern | Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments[END_REF][START_REF] Stern | Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments[END_REF]. Harmonizing impact of CAVs in an open highway is demonstrated via interesting experiments in [START_REF] Ma | Freeway speed harmonization[END_REF]. Three CAVs were driven side-by-side in real shock-wave traffic near Washington DC and their influence was measured by three probe vehicles that were deployed downstream and upstream. It was observed that CAVs reduced the oscillation induced by the shock-waves and harmonized the traffic and is expected to have network-wide energy efficiency impact. Secondary effects due to reduced number of accidents, could further lower delays and loss of energy which is difficult to quantify. [START_REF] Scora | Comprehensive modal emissions model (CMEM), version 3.01. User guide[END_REF] fuel efficiency evaluation [START_REF] Jin | Platoon-based multi-agent intersection management for connected vehicle[END_REF] S, microsimulation in Sumo +11-21 1 intersection with 2 single lane approaches vehicles form platoons to pass intersection CMEM fuel efficiency evaluation [START_REF] Ferreira | On the impact of virtual traffic lights on carbon emissions mitigation[END_REF] S, Microsimulation in DIVERT [START_REF] Fernandes | Divert for realistic simulation of heterogeneous vehicular networks[END_REF]) +25 simulated entire network of Porto, Portugal (fuel) EMIT [START_REF] Cappiello | A statistical model of vehicle emissions and fuel consumption[END_REF]

Conclusions

This paper presented an overview of energy-efficient driving opportunities provided by connected and automated vehicles through first-principle analysis and a survey of eco-driving literature. Unprecedented access to information via advanced sensors and V2X communication, increased processing power, and precision positioning and control, enables connected and automated vehicles to plan and execute eco-driving maneuvers much better than a human driver. While there are limited previous studies on energy impact of CAVs, review of the eco-driving literature promises considerable benefits. In particular our conservative evaluation based on published experimental results indicates 3% energy saving from preview of static road information such as road grade in highway driving. Information from traffic signals via V2I, could lead to 10% energy saving in arterial driving. With full penetration of CAVs reservation based intersections could yield up to 20% savings. Anticipative car following has a more uncertain impact but could at least yield 3% gain or much higher depending on the driving scenario. Platooning for trucks could yield 7-10% gain due to drag reduction. Cooperative car following and lane selection for passenger cars could boost energy efficiency but there is a lack of experimental results to report. And the harmonizing impact of CAVs on traffic, even at low penetration levels, could result in 20% savings in stop and go driving.

Most of the benefits can be achieved without additional hardware costs and relying mainly on software and information. Higher energy efficiency is an attractive added feature of CAVs, beyond safety and comfort, that could accelerate their market adoption. With higher penetration, there will be system wide influences by such "eco-CAV"s, potentially lowering global energy use and contributing positively to the environment. Energy efficient driving of CAVs could be encouraged by proactive policy making countering alternative scenarios in which higher CAV-miles traveled at higher speeds increase global energy use. equations of motion can be written in the following state-space form:

       dt ds = 1 v dv ds = u t -u b -βv 2 -h(s) v (5)
where β = 1 m 0.5ρ a AC D and h(s) = g(sinθ +C rr cosθ). The boundary conditions are:

v(s 0 ) = v 0 , v(s f ) = v f , t(s 0 ) = 0, t(s f ) = t f
To keep the derivation applicable across a wide range of vehicles, we assume that a fraction η of the braking energy can be recuperated (η = 0 for conventional vehicles and η = 1 for vehicles with ideal regeneration). Therefore to optimize the "wheel-to-distance" energy expenditure, we minimize the following cost function, which is energy spent normalized by vehicle mass:

min u t ,u b J = s f 0 (u t -ηu b )ds (6)
subject to the equations of motion and their imposed boundary conditions. It is assumed that there are no bounds on the states over the control interval but 0 u t ūt and 0 u b ūb . Replacing for u t from Equation (5), we obtain:

J = 1 2 (v 2 f -v 2 0 ) + s f 0 h(s)ds + s f 0 (βv 2 + (1 -η)u b )ds (7)
The first two terms do not depend on the control input. Therefore we solve the following problem:

min u t ,u b s f 0 (βv 2 + γu b )ds (8)
where γ = 1η, so in absence of regeneration γ = 1. Following Pontryagin's Minimum Principle [START_REF] Kirk | Optimal control theory: an introduction[END_REF], the Hamiltonian H is formed as follows:

H = βv 2 + γu b + λ 1 v + µ u t -u b -βv 2 -h(s) v (9)
where λ and µ are the costates with the following dynamics:

       dλ ds = - ∂H ∂t = 0 ⇒ λ = constant dµ ds = - ∂H ∂v = -2βv + λ 1 v 2 + µ u t -u b -h(s) v 2 + βµ (10)
where boundary conditions for both λ and µ are free, since both states, t and v, are fixed at initial and final positions. We also note that λ is a constant over position, since its rate of change is zero while dynamics of µ is more complex.

The optimal inputs should minimize the Hamiltonian. Since H is an affine function of u t and u b and therefore

∂H ∂u t = µ v , ∂H ∂u b = γ - µ v
are independent of the inputs, the Hamiltonian is minimized at extreme values of the inputs, except for when the partial derivative of H with respect to the inputs is zero, in which a so-called singular interval may exist. Over a singular interval the inputs could assume a value within their constraints. The optimal traction force, denoted by u * t is:

u * t =      ūt µ/v < 0 u s t µ/v = 0 0 µ/v > 0 (11)
where u s t denotes the wheel traction during a possible singular interval. For a singular interval to exist, the condition µ v = 0 must be valid for a position interval rather than just at one point. Therefore over a singular interval we must have

d ds µ v = 1 v dµ ds - µ v 2 dv ds = 0 (12)
upon substitution from ( 5) and ( 10), the condition for existence of a singular interval simplifies to:

d ds µ v = -2β + λ v 3 + β µ v = 0 (13)
but since on a singular interval during traction µ v = 0, we conclude:

v s = λ 2β 1 3 (14)
which is a constant since optimal λ was shown to be a constant. As a result the traction force is u s t = βv 2 s + h(s). The optimal braking force, denoted by u * b is:

u * b = 0 µ/v < γ ūb µ/v > γ (15)
In other words there is no singular interval during braking: For a singular interval to exist during braking, the condition µ v = γ must be valid for a position interval rather than just at one point. Equation ( 13) indicates that during a braking singular interval the velocity has to be a constant. But we know that during braking the velocity cannot remain constant, hence there is no singular interval during a braking phase.

In summary Eq. ( 11) states that to minimize "wheel-to-distance" energy expenditure, the vehicle should decelerate or accelerate, as quickly as possible, to the constant speed of v sing and maintain that speed till close to destination. Optimal deceleration strategy starts by coasting but could end with a period of maximal braking even in absence of regeneration (γ = 1). With ideal regenerative brakes (γ = 0) the optimal strategy does not include a coasting phase. Values of v sing and λ will be smaller for longer trip times t f ; its value can be obtained after solving the two-point boundary value problem described by ( 5) and (10).

Figure 2 :

 2 Figure2: Eco driving in anticipation of upcoming hills, changes in speed limit, and slow traffic. The white CAV solves a dynamic program to find the fuel optimal velocity trajectory given road power demand and constraints. The image was created on https://icograms.com. Table 2: Summary of selected published results on energy efficiency gain enabled by road grade preview.

Figure 3 :

 3 Figure 3: Schematic of eco-driving with SPAT preview. Shaded triangles contain feasible paths to green intervals of the traffic light for the 3 vehicles moving from bottom left to top right. Most parts of the image were created on https://icograms.com.

Figure 5 :

 5 Figure 5: Collaborative car following and lane selection. The red trucks maintain a platoon formation relying on V2V communication and automated longitudinal control. The yellow truck communicates with the red trucks to join the platoon. In a collaborative lane change maneuver enabled by V2V communication, the white smaller truck leaves a gap for the yellow truck to change lane. Most parts of the image were created on https://icograms.com.

Table 3 :

 3 Summary of selected published results on energy efficiency gain enabled by SPaT anticipation with respect to conventional vehicles without SPaT information.

	Ref.	Methods and Conditions	Efficiency
			gain * (%)
	(Asadi and Vahidi, 2009)	S † , lone vehicle, 10 fixed time lights	+24-29
	(Asadi and Vahidi, 2011)	real SPaT: Greenville, SC timing cards
		1.7 L 4-cylinder gasoline engine,
		high fidelity vehicle model in PSAT (ANL)
	(Mandava et al., 2009)	S, 10 fixed time lights,	+12-14
		stochastic parameter variation
		passenger car and SUV, CMEM models (Scora and Barth, 2006)
	(Kamalanathsharma and Rakha, 2013)	S, 1 fixed time light	+20
		varying road conditions, random initialization
		Virginia Tech fuel consumption model (Rakha et al., 2011)
	(Mahler and Vahidi, 2014)	S, 3 fixed and variable timing lights	+16
		probabilistic SPaT, probabilistic planning
		Monte Carlo Evaluation (3000 scenarios)
	(Xia et al., 2012)	E † † , no traffic	+13
		1 fixed time signal, 4G cellular comm.
		2011 BMW 535i
	(Mahler, 2013)	E, real city traffic,	+9
	(Mahler et al., 2017)	real-time TMC data, 4G cellular comm.
		Mix of 10 fixed time and actuated signals
		2011 BMW 535i, 4 complying drivers
	(Hao et al., 2017)	E, real city traffic	+2-6
		coordinated actuated signals, DSRC comm.
		2008 Nissan Altima, 2 complying drivers
	(Koukoumidis et al., 2011)	E, real city traffic	+25
		2 fixed time lights
		camera SPaT estimation-V2V comm.
		2001 2.4L PT Cruiser, 1 complying driver
	(Wan et al., 2016)	S, network wide effect	+25
		4 fixed time signals, multi lane	(CAV)
		Paramics (Paramics, 2009) microsimulations, mixed traffic	+6
		50% CAVpenetration, 900 veh/hour/lane	(surronding
		polynomial fuel consumption model	traffic)
	(Xia et al., 2013)	S, network wide effect	+12.5
		11 fixed time signals, one lane	(CAV)
		Paramics microsimulations, mixed traffic	+7.5
		50% CAVpenetration, 300 veh/hour/lane	(all
		CMEM

Table 4 :

 4 Summary of selected published results on energy efficiency gain enabled by anticipative car following.

	Ref.	Methods and Conditions	Efficiency
			gain (%)
	(Manzie et al., 2007)	S † 1.6 ton vehicle	+13-35
		3 standard driving cycles for phantom lead vehicle	w.r.t.
		rule-based preview car following, horizon=50 sec	no preview
	(Zhang and Vahidi, 2011)	S, 2 ton vehicle
		recorded real-data for lead vehicle	+15
		winding road from Clemson, SC to Highland NC	w.r.t.
		chance constrained MPC, horizon=15 sec.	lead
		Markov chain prediction of lead vehicle velocity	vehicle
		fuel economy evaluated in Argonne PSAT (ANL)
	(Han et al., 2018)	S, 1.4 ton electric vehicle, no regeneration loss	+12-44
		3 real city driving profiles for lead vehicle	w.r.t.
		MPC, horizon=100 sec	lead
		Assumes constant acceleration for lead vehicle	vehicle
		physical polynomial model for energy use
	(Li and Peng, 2012)	S, 1.8 ton simulated vehicle with combustion engine	+0-32
		following lead car with constant speed	w.r.t
		optimal control yields pulse and glide strategy	lead
		efficiency gain is speed dependent	vehicle
	(Lang et al., 2014)	E † † , engine-in-the-loop simulations,	+6.5-22
		microsimulation + engine test bench measurement
		driver prediction: nonlinear autoregressive model
		prediction horizon=15 sec
		results depend on allowable inter-vehicle gap
	(McDonough et al., 2014)	E, real ego vehicle, 2007 Ford Edge	+3.6
		12 rounds city/highway driving on Michigan-39	w.r.t.
		following phantom vehicle with constant speed	lead
		stochastic DP policy calculated offline	vehicle
		restricted to ± 2 mph speed difference w.r.t. lead
		resulting strategy is pulse and glide
	(Turri et al., 2017)	E, real ego vehicle, 3.8L V6 engine, 8 speed trans.	+39-50
		Hyundai-Kia proving grounds, California	w.r.t.
		simulated lead vehicle with sinusoidal velocity	imperfect
		MPC tracking, perfect preview, horizon=6 sec.

Table 5 :

 5 Summary of selected published results on energy efficiency gain enabled by anticipative lane selection.

	Ref.	Methods and Conditions	Efficiency
			gain (%)
	(Kamal et al., 2016)	S † , microscopic simulations
		MPC velocity & lane selection, horizon=15 sec
		tested 2 cases, 2 km road, varying CAV levels
		at 50% penetration, w.r.t. conventional vehicles:	+14.3(12.9) *
		at 50% penetration, w.r.t. CACC vehicles:	+7.8(5.1) *
	(Dollar and Vahidi, 2018)	S † , microscopic simulations
		MPC velocity & lane selection converted to MIQP
		4 CAVs passing slow moving vehicle in a two lane scenario
		24 full-factorial simulations ordering the 4 CAVs
		Complete intent communication between neighboring vehicles
		w.r.t. a rule-based algorithm:	+8.4
	(Rios-Torres and Malikopoulos, 2017a)	S, micro-simulation in merging zone, 30 vehicles	+48
		optimal coordinated merging into a highway	w.r.t.
		fuel economy via polynomial metamodel in

Table 6 :

 6 Summary of selected published results on energy efficiency gain enabled by cooperative car following.

	Ref.	Methods and Conditions	Efficiency
			gain (%)
	(Lelouvier et al., 2017)	S † , group of five 1.2 ton electric vehicles	+10.5
		eco-platooning for reduced group consumption
		considered drag reduction
		nonlinear MPC, prediction horizon=120 sec
		studied centralized and distributed solutions

Table 7 :

 7 Summary of selected published results on energy efficiency gain enabled by cooperative intersection control.

	Ref.	Methods and Conditions	Efficiency
			gain (%)
	(Huang et al., 2012)	S † , microsiumlations in Paramics (Paramics, 2009)	+50%
		real-world road network, 3 intersections
		CMEM

The solution for hybrid and electric cars(Dib et al.,

2014) is different and could be more complex.

Appendix

We want to find the velocity profile that minimizes the "wheel-to-distance" energy losses, going from velocity of v 0 to v f over a specified time of t f and distance of s f . Here we break down the wheel force F w to tractive force F t and braking force F b . Considering the tractive acceleration, u t = F t m , and braking deceleration u b = F b m as the two inputs, and choosing position as the independent variable, the

ACKNOWLEDGMENT

The first author was a scientific visitor at IFP Energies Nouvelles, Rueil-Malmaison, France May-August 2017 during which this paper was written. He thankfully acknowledges the support and sponsorship provided by IFPEN. The authors thank, Dr. Jihun Han, for his suggestions on the organization of the paper.