## Abstract

This paper examines both mathematical formulation and practical implementation of an ecological adaptive cruise controller (ECO-ACC) with connected infrastructure. Human errors are typical sources of accidents in urban driving, which can be remedied by rigorous control theories. Designing an ECO-ACC is, therefore, a classical research problem to improve safety and energy efficiency. We add two main contributions to the literature. First, we propose a mathematical framework of an *online* ECO-ACC for plug-in hybrid electric vehicle (PHEV). Second, we demonstrate ECO-ACC in a real world, which includes other human drivers and uncertain traffic signals on a 2.6 (km) length of the corridor with eight signalized intersections in Southern California. The demonstration results show, on average, 30.98% of energy efficiency improvement and 8.51% additional travel time.

## 1 Introduction

Research on autonomous driving vehicles has gained significant attention from both academia and industry, supported by abundant finance and human resources. Advanced computing, sensing, and communication technologies facilitate a foreseeable future of fully autonomous driving in urban areas. In general, there are three major perspectives in the area of automotive and vehicular research: *safety*, *drive comfort*, and *energy*. Each perspective has a profound body of literature [1,2] and they are often jointly investigated within specific driving scenarios. Energy efficiency is the major focus of this paper, although we also take into account safety and drive comfort. In particular, we leverage vehicle-to-infrastructure connectivity to enhance the energy efficiency of a plug-in hybrid electric vehicle (PHEV) in the urban driving scenarios.

In the broad area of control systems, improving energy efficiency is a common goal. It is often achieved by penalizing control efforts and/or by explicitly minimizing an energy cost. In automotive and vehicular research, as recommended by International Energy Agency [3], “ecological driving” (or “Eco-driving”) has been a primary research subject over decades, with a definite goal: *driving in an energy-efficient manner*. Eco-driving typically pursues ecological driving styles such as driving slowly and accelerating and braking gradually (Fig. 1).

There exist variants of approaches for enhancing the energy efficiency of driving. Examples include providing fuel economy information to drivers to adapt their driving style [4,5], factorizing major sources of fuel consumption [6,7] (such as transient engine operations), and reducing un-necessary accelerations/braking [8,9]. In particular, a rich body of literature has focused on smoothing velocity trajectories as a cost-effective metric [10,11] and enhanced the efficiency of adaptive cruise controller (ACC). ACC often applies predictive control methods, such as model predictive control [12], for its capability of evaluating future positions of other vehicles [13]. Then smoothing velocity trajectories, together with predicting trajectories of a preceding vehicle, allows smooth car-following performances [14–16].

Meantime, low carbon emission vehicles, in particular, Plug-in Hybrid Electric Vehicles have shown their benefit in fuel economy compared to conventional internal combustion vehicles [17]. With their potential of enhancing energy efficiency [18], Eco-driving algorithms for PHEVs have gained close attention [19–22]. However, Eco-driving for PHEVs is challenging, since PHEVs have two power-generating sources and diverse configurations, e.g., series, parallel, and power-split. These complex powertrains introduce additional degrees-of-freedom [23] that increase the state space and control input space, adding nonlinearities that make optimal eco-driving computationally challenging.

Therefore, optimizing the speed profile is often separated from optimizing the vehicle powertrain control in a hierarchical structure [24]; in this way, only vehicle dynamics is considered in the velocity optimization. In Ref. [25], the authors simultaneously optimize the speed profile and powertrain control using approximation and Pontryagin's minimum principle. However, powertrain dynamics is often simplified to the extent that model fidelity is lost (e.g., a linear approximation). Alternatively, especially for a fixed route, a speed reference is precomputed *offline* (using, e.g., dynamic programming [23,26]) and used as a look-up table *online*. Despite these efforts, *online* speed planning with high-fidelity PHEV powertrain dynamics and time-varying traffic information remains an open problem. We address this problem in this paper.

In a separate domain, vehicle-infrastructure integration technologies have enhanced the potential of eco-driving [27] for further energy savings by understanding traffic conditions and traffic signal information, such as traffic signal phase and timing (SPaT) [28,29]. In particular, the SPaT information consists of two main parts: (i) the current signal phase (red, green, yellow) and (ii) the remaining time duration for the current signal phase. With SPaT, the Eco-driving controller is able to determine an energy-optimal velocity trajectory within these green waves [23,26] or for smooth-stop at red [30] if inevitable, which are active research area [31–34].

There are remaining gaps in the Eco-driving research. First, Eco-driving research has a limited control/planning horizon which is often set to 3–4 s [35]. Consequently, the traffic signal information is often partially used, e.g., one upcoming intersection, for rapid computation [29]. Second, PHEV powertrains add additional degrees-of-freedom, which hinders expeditious computation. Thus, Eco-driving controllers often end up using a simple model [25], restricting delicate cost evaluations. Third, Eco-driving controllers are often limited to fixed traffic signal schedules, remaining difficult to expand on dynamic traffic signal schedules (e.g., by dynamic traffic control systems). Finally, developing a comprehensive module that simultaneously achieves multiple objectives, i.e., safety, long-term fuel savings with time-varying traffic signal schedules, precise evaluations of PHEV energy consumption, and real-time computations, remains unsolved.

This paper is the first attempt to fulfill these research gaps, by making connections between these different perspectives of eco-driving. Namely, adaptive cruise controller for *safety*, low carbon vehicles for *energy efficient powertrains*, and green light optimal speed advisory systems for *long-sighted ecological velocity planning*. Recall, these connections inevitably increase the problem complexity, and consequently, computational challenges arise, and we also address these issues.

Still, thorough verification and validations are crucial before the dispatch of automated vehicles on-roads, which require rigorous tests. To this end, hardware-in-the-loop (HIL) simulations are actively exploited for their reproducibility and their capability of measuring a genuine value from a physical device, instead of a simulated one. Typically, HIL is composed of a few (i) physical devices that (either partially or fully) represent a system plant and (ii) real-time software that simulates virtual environments [36]. For autonomous driving in urban areas (with traffic and traffic lights), use-cases of HIL include safety analysis of longitudinal control with ACC [37,38], stability analysis of vehicle platooning [39,40], and fuel economy analysis for connected and automated vehicles [41,42]. HIL is widely exploited and is a promising approach to verifying theoretical algorithms for autonomous driving. However, real-world driving has millions of unknown factors that simulations cannot perfectly emulate, such as pedestrians, random behaviors of other drivers, extreme weather and traffic conditions, and sensing errors and noises. Consequently, existing case studies for Eco-driving on-road are mostly limited to speed advisory systems for human drivers [43,44]. Specifically, to the authors' knowledge, no published literature performs on-road tests of an automated vehicle controller that communicates with traffic lights to validate an Eco-driving controller.

We add two key contributions to the literature as follows:

We propose a mathematical and structural framework for

*online*ecological longitudinal control of PHEV with communication to traffic lights. In particular, our framework addresses multiple practical challenges including limited communication ranges, time-varying traffic signal schedules, guaranteed safety, random vehicle queues, delicate fuel consumption metrics, and online computations.We demonstrate the proposed control framework in both hardware-in-the-loop simulations and, for the first time, on-road experiments in a perfectly real-world driving condition (with other human drivers and with real-time communication to traffic lights). Demonstration results (of both HIL and on-road experiments) are reported, followed by qualitative and quantitative analysis.

This paper summarizes and extends our previous work in Refs. [45] and [46]. The mathematical foundations and implementation setup are inherited from our previous work and we consolidated cost functions, constraint settings, and algorithms. Importantly, this paper reports the results of perfectly real-world driving tests with the presence of other human drivers (whose behaviors are considered one of the major unknown factors). In other words, this paper practically validates the potential of vehicle-to-infrastructure connectivity for enhancing the energy efficiency of PHEV, which can be used as a valuable reference for future research. We also provide comparisons between simulation and experimental results, indicating the value of simulations in autonomous driving researches.

The paper is organized in the following manner: Section 2 presents mathematical formulations of Eco-driving controller, followed by Sec. 4 that formalizes safety controls. Section 5 illustrates an implementation setup for the controller both in HIL simulations and on-road experiments. Section 6 reports demonstration results. The paper concludes with a summary in Sec. 7.

## 2 Control Structure and Vehicle Model

### 2.1 Control Structure.

The main objective of this work is to design an ecological adaptive cruise controller (ECO-ACC) that prevents collisions, obeys traffic signals, and minimizes energy consumption and travel time by cruising through the green phases of the various intersections.

Figure 2 presents the two components of ECO-ACC: (i) *Eco-driving controller*, which optimizes a speed reference trajectory from the current location to the next few hundred meters, aimed at minimizing the energy based on both real-time and probabilistic information on SPaT. The Eco-driving controller essentially assumes free-flow conditions. (ii) *Adaptive Cruise Controller (ACC)*, which computes the wheel torque required to follow the speed reference, yet guarantees safety, i.e., collision avoidance and traffic signal compliance. The ACC recognizes the real-time traffic around the vehicle and robustly secures frontal collision avoidance.

This time scale separation also makes intuitive sense to tame the computational complexity of the overall control task.

### 2.2 Vehicle and Powertrain Model.

*k*,

*a*(

*k*) is expressed via Newton's second law of motion

where the input is a wheel torque $Tw(k)$ and the model parameters are vehicle mass *m*, wheel radius *R _{w}*, gravitational acceleration

*g*, road grade

*θ*, air density

*ρ*, the front cross-sectional area

*A*, rolling resistance coefficient

*C*, and air drag coefficient

_{r}*C*.

_{d}*r*is a transmission gear ratio, $Tsft$ is a shaft torque before the transmission, and

_{gb}*T*

_{brk}is a mechanical braking torque. The battery state-of-charge (SOC) dynamics reads

where *P _{b}* is a terminal battery power, $Voc$ is an open-circuit voltage,

*R*is an internal resistance, and

_{b}*Q*is a battery pack capacity. Details on PHEV powertrain models can be found in Ref. [47].

_{b}## 3 Eco-Driving Control: Speed Reference Optimization

### 3.1 Objective.

where *s* is a tuning parameter, and $Pelec$ is an electrochemical battery power which is computed as $Pelec=Voc\xb7Ib$ where *I _{b}* is a terminal current of a battery. We leverage a classic equivalent consumption minimization strategy (ECMS) controller [48,49] as the production powertrain controller implemented in the vehicle and assume that the ECMS parameter is given and fixed at each SOC level, i.e., the tuning parameter

*s*in Eq. (4) is deterministic.

To precisely evaluate the powertrain cost, we need the battery SOC and engine switching dynamics [50,51] in addition to the vehicle dynamics (11). However, using dynamic programming (DP), the problem becomes computationally intractable due to the Bellman's curse-of-dimensionality. Thus, we make two approximations to remedy the curse of dimensionality: **[AP1]** We treat SOC as a fixed parameter over the receding horizon, instead of a dynamic state. Because (i) the SOC does not change significantly over a short distance, e.g., few hundred meters, in urban driving scenarios, and (ii) the optimization finds new solutions every few seconds, during which the SOC is reset to its measured value. **[AP2]** We neglect the additional electric and fuel power costs caused by engine switching dynamics over the receding horizon. This approximation is made because we assume that the engine status does not switch frequently over the short distance.

The approximations enable precomputing the powertrain cost function (4) for all possible combinations of speed *v* and wheel torque *T _{w}* at any SOC level. Eventually, we obtain the empirical model $gc\u22c6$ that maps $(v,Tw,SOC)$ to a single numeric cost value. Figure 4 shows an example of the obtained empirical cost map (on the left) for the SOC level, 0.92. There are two highlights in the power cost map: (i) Unlike the wheel torque cost map (right plot in Fig. 4), the power cost map can be negative due to battery charging from regenerative braking. (ii) Certain wheel torque and velocity combinations result in particularly large power costs because the engine is turned on to satisfy the torque demand, and the engine power cost is expensive when the PHEV is in charge-depleting mode (i.e., the SOC level is high).

*d*(from the origin), the objective function with precomputed powertrain cost map $gc\u22c6$ over a receding horizon

*d*reads

_{H}with the weight *λ*. The second term, i.e., $\Delta sv(k)$, denotes travel time. Recall, the wheel torque $Tw(k)$ at each step *k* is our control variable and the allocation between engine and motor torque [48,49] is not considered since the empirical powertrain cost map $gc\u22c6$ is resulted by solving the allocation problem.

#### 3.1.1 Terminal Cost Beyond Control Horizon.

*d*) as

_{f}where *h*(*i*) denotes an instantaneous cost function at step *i* in Eq. (5). However, due to the limited connectivity range and the variability of traffic signals, we limit the (receding) control horizon to a few hundred meters ahead, i.e., we can only evaluate the first term in Eq. (6) in real-time. Consequently, the objective (5) is nearsighted, which may result in suboptimal performance. To mitigate the suboptimality, we leverage a sample mean to assess the terminal cost (the second term in Eq. (6)) over a variety of traffic signals with which we solved the problem (20) through simulations a priori.

with the number of sample *M* and *j*th SPaT scenario *σ _{j}*. Recall that $min\u2211i=d+dH+1dfh(i;\sigma j)$ is a former optimal solution obtained under scenario

*j*, which are then used as a prior knowledge.

where *τ _{H}* is a total travel time within the receding horizon, $tfD$ is a desired travel time over the receding horizon, and $v\u0302avg$ is an empirical average speed over the remaining route.

### 3.2 Constraints

#### 3.2.1 System Dynamics.

*v*(

*k*) and travel time

*t*(

*k*) as states at position $k\Delta s$

^{3}and follow:

for $k\u2208{0,\u2026,N\u22121}$, with the position step size $\Delta s$^{4}. we denote $v(k+1)=fv(k)$ and $t(k+1)=ft(k)$ for convenience. It is important to note that the dynamics are difference equations in space, not time, inspired by Refs. [23] and [52]. Space-based dynamics benefits from not having to know of a terminal travel time a priori when it is used in optimizations. A preset upper bound of travel time is imposed. The space-based dynamics can cause the edge case with zero speed. Therefore, for our experiments, we cramped the zero speed to small but nonzero value to avoid a numerical issue.

#### 3.2.2 State and Control Bounds.

for all $k\u2208{d,\u2026,d+dH}$. The bounds are generally set with a given min and max. Note that the lower bound of wheel torque $Twmin$ is set to the sum of max braking torque and regenerative braking torque for PHEVs.

#### 3.2.3 Traffic Signal Obedience.

We set the constraints to obey the traffic signals, i.e., stop at red and move at green. It is important to note that we receive SPaT information from the upcoming intersection; however, we only have historical data from the other intersections within the communication range.

With SPaT information, we examine red waves within a signal cycle, which are then formulated to an infeasible set^{5} of travel time. Figure 5 illustrates the signal waves with a fixed cycle length (the sum of red, green, and yellow light length). If the travel time state is within the infeasible set, the ego vehicle must stop at the intersection. In contrast, the ego vehicle can cross the intersection within the feasible set of the travel time state (at either green or yellow light). At the yellow light, we set the controller to stop and wait for the green light in the next cycle, if the ego vehicle has sufficient time to slow down to the stop line.

We formalize the infeasible set **IS** of states $x(k)=[v(k),t(k)]\u22a4$, for step $k\u2208{d,\u2026,d+dH}$, that satisfies logical conditions in the following two cases.

*Case 1:*if an intersection is located at step

*k*+

*1 and it is the first upcoming intersection from the current location*

*d*

*Case 2:*if an intersection is located at step

*k*+

*1 and it is not the first upcoming intersection*

where *s _{p}* is a signal phase,

*s*is a signal timing (remaining time), $\u2113c(n)$ is a cycle length at intersection

_{t}*n*, $\u2113\u0302r(n)$ is an estimated red light duration, $\u2113c,O(n)$ is a time shift of the signal cycle initiation, and $R(\xb7)$ is the modulo operator. Given the current travel time and cycle length, the modulo operator locates a clock time within the signal cycle. The clock time is then mapped to a corresponding signal phase if the duration of each signal phase is known. For example, in Fig. 5, the modulo locates the clock time within the red wave, which is formalized as Eq. (17) with an estimated red light duration. Similarly, with a deterministic SPaT in Eq. (17), the red waves are identified at each signal phase.

Since we only have historical SPaT data from the intersections except for the upcoming one, we estimate the red light duration $\u2113\u0302r(n)$ as *η*th percentile in the distribution of red light duration.

#### 3.2.4 Clearance Delay at Intersections Due to Traffic.

**IS**in Eqs. (16) and (17) in a way that $\alpha (n)$ increases the volume of

**IS**(as the effective red light duration technically increases a total red light duration within a traffic signal cycle). For example, for

**case 1**, at red light, i.e.,

*s*= red, the infeasible set with the effective red light duration reads

_{p}where $\eta \u2208[0,1]$ is a desired reliability and $F\u22121(1\u2212\eta )$ denotes the inverse cumulative distribution function (CDF) of $\alpha (n)$. The above reformulation is applied to the other instances of signal phases. We highlight that the SPaT information is received in real-time and is available at the beginning of each horizon. Given (i) the signal cycle length and (ii) the distribution function of *α* at each intersection *n*, the infeasible set is fully characterized with the chance constraint in Eq. (19) at the beginning of the horizon.

### 3.3 Complete Optimization Problem.

We apply DP to solve the above optimization problem, given the current states and SPaT information from the next traffic light. Algorithm 1 summarizes the process of computing the optimal policy map of wheel torques $Tw\u22c6$, i.e., $Tw\u22c6:(d,v,t)\u21a6Tw\u22c6$. A speed reference profile is then computed via Algorithm 2 using the policy map $Tw\u22c6$. It is important to note that the optimization through Algorithm 1 may take up to a couple of seconds, however, the Eco-driving controller sends a speed reference at the current state at every 0.2 (sec) through Algorithm 2. The Eco-driving controller repeats solving the optimization problem until the vehicle arrives at the destination, i.e., $d\u2264df$.

In Algorithm 1, *d _{I}* is a set of traffic light locations, ($nv\xd7nt$) is the grid size of (

*v*,

*t*), the operator $(\xb7)+$ takes a positive element in $(\xb7)$, and

*β*is the weight of the slack variable

*γ*defined in Sec. 3.1.

Input:$d,t,dI,dH,\u2113c,\u2113\u0302r,sp,st$ |

Output:$Tw\u22c6\u2208R(dH\xd7nv\xd7nt)$ |

Init: Compute relative distance to traffic lights within the distance horizon $d\u0303I=(dI\u2212d)+\u2208[0,dH]$ |

Set the terminal cost |

$J\u0302[d+dH+1,df]+\beta \gamma 2$ |

1 for$k=dH\u22121\u21920$do |

2 Solve Bellman's equation for all feasible states |

$\u2200(vi,tj)\u2208{(v(k),t(k))|(v(k),t(k))\u2209IS},$ |

3 $Vk(vi,tj)=minTw{g(vi,tj)+Vk+1(f(vi,tj,Tw))}$ |

4 Get the minimizers |

$[Tw\u22c6]i,j\u2190minimizer\u2009of\u2009Vk(vi,tj)$ |

5 end |

Input:$d,t,dI,dH,\u2113c,\u2113\u0302r,sp,st$ |

Output:$Tw\u22c6\u2208R(dH\xd7nv\xd7nt)$ |

Init: Compute relative distance to traffic lights within the distance horizon $d\u0303I=(dI\u2212d)+\u2208[0,dH]$ |

Set the terminal cost |

$J\u0302[d+dH+1,df]+\beta \gamma 2$ |

1 for$k=dH\u22121\u21920$do |

2 Solve Bellman's equation for all feasible states |

$\u2200(vi,tj)\u2208{(v(k),t(k))|(v(k),t(k))\u2209IS},$ |

3 $Vk(vi,tj)=minTw{g(vi,tj)+Vk+1(f(vi,tj,Tw))}$ |

4 Get the minimizers |

$[Tw\u22c6]i,j\u2190minimizer\u2009of\u2009Vk(vi,tj)$ |

5 end |

Input: $d,t,v,Tw\u22c6\u2208R(dH\xd7nv\xd7nt)$ |

Output:$v\u22c6\u2208RdH$ |

Init: $v(k)=v,t(k)=t$ |

1 for$k=d\u2192d+dH$do |

2 Get the optimal wheel torque at |

$v(k),t(k)Tw(k)=Tw\u22c6(k,v(k),t(k))$ |

3 Get longitudinal acceleration through Eq. (1) $a(k)\u2190$(1)$|Tw(k),v(k)$ |

4 Propagate speed profile through Eq. (11) |

$v\u22c6(k+1)\u2190v(k)+a(k)\Delta sv(k)$ |

5 end |

Input: $d,t,v,Tw\u22c6\u2208R(dH\xd7nv\xd7nt)$ |

Output:$v\u22c6\u2208RdH$ |

Init: $v(k)=v,t(k)=t$ |

1 for$k=d\u2192d+dH$do |

2 Get the optimal wheel torque at |

$v(k),t(k)Tw(k)=Tw\u22c6(k,v(k),t(k))$ |

3 Get longitudinal acceleration through Eq. (1) $a(k)\u2190$(1)$|Tw(k),v(k)$ |

4 Propagate speed profile through Eq. (11) |

$v\u22c6(k+1)\u2190v(k)+a(k)\Delta sv(k)$ |

5 end |

## 4 Adaptive Cruise Control: Collision Avoidance

This section discusses the proposed ACC depicted in Fig. 2. The objective of our ACC is twofold: (i) Track the speed reference computed by the Eco-driving controller and (ii) Enforce vehicle safety, such as collision avoidance with a leading vehicle, and nonviolation of traffic light laws. We use a robust model predictive control framework, based on the work [53].

### 4.1 System Dynamics.

where we assume that the road is flat at all times. Moreover, we denote by $adecmaxandtstopmax$ the maximum deceleration which the vehicle is capable of at any time and the maximum time required for the vehicle to come to a full stop from any initial velocity, respectively. They can be obtained by $adecmax=TwminmRw\u2212gCrand\u2009tstopmax=\u2212vmaxadecmax$

### 4.2 Safety Constraints.

where $spup(\tau )$ is a phase of the upcoming traffic light at time-step $\tau $ and $\varphi (\tau )$ is a slack variable, $\varphi (\tau )\u22650$. The constraint (23) ensures a collision avoidance by keeping the minimum stopping distance $dmin$ larger than the distance to the front vehicle $df(\tau )$ at time-step $\tau $. The constraint (24) ensures the ego vehicle stop at the red light by keeping the distance to the traffic light larger than zero. We assume that the yellow signal is long enough for the vehicle to come to a full stop with maximum deceleration. This assumption with the soft constraint in Eq. (25) ensures that the vehicle is either capable of the full stop before the traffic light or passes the light when it turns to red from yellow. The constraint (26) keeps the vehicle velocity $v(\tau )$ is lower and upper bounded by minimum and maximum velocity, $[vmin,vmax]$. The maximum velocity $vmax$ is set to the maximum speed limit on the road.

### 4.3 Complete Optimization Problem.

where index $(\u2113|\tau )$ indicates prediction at time $\u2113$ based on measurements and predictions at time $\tau .Np$ is the prediction horizon and $vref$ is an speed reference obtained from the Eco-driving controller or the driver. The cost function $J$ serves multi-objectives: a penalty for deviating from $vref$(27*a*), a penalty for input torques (27*b*), a penalty for jerk (27*c*), and a penalty for violating the soft yellow light constraint (27*d*). The weights for those penalties are denoted by $Wv,\u2009Wu,\u2009W\Delta u$, and $W\varphi $, respectively; a higher weight on the reference tracking $Wv$ yields a higher energy efficiency, which then may result in a jerky behavior. The constraint (27*e*) bounds the input, the wheel torque $Tw(\u2113|\tau )$, within $Twminand\u2009Twmax$. The polytopic constraint (27*f*) enforces the terminal state to lie inside the *robust control invariant* sets defined in Ref. [53] for recursive feasibility of the controller and, therefore, persistent safety of the system.

By solving (27) at time $\tau $, we obtain the optimal input trajectory and apply the first input to the system during the time interval $[\tau ,\tau +1)$. At the next time-step $\tau +1$, (27) with new state measurements is solved over a shifted horizon, yielding a *receding* horizon control strategy. In this study, we assume the front vehicle abruptly stops for robust safety. However, note that variants of prediction methods can be applied for enhanced energy efficiency [13].

## 5 Implementation Setup

This section presents a testing route and implementation setup for hardware-in-the-loop simulations and on-road experiments. Recall that both simulations and on-road experiments are essential before deploying automated vehicles. Simulations help to verify the proposed mathematical framework for various complex traffic scenarios. In simulations, we can reproduce the same traffic scenarios, e.g., same traffic signal schedules and driving routes, to perform a comparative analysis between different values of hyperparameters in controller designs. It is also possible to design specific traffic scenarios where specific functionalities are tested. That said, a simulated environment cannot fully represent real-world driving, e.g., random behaviors of other human drivers or sensor noises. Given the needs of both simulations and experiments, we develop an implementation setup of ECO-ACC that can be generically applied to both.

### 5.1 Driving Route.

We consider Live Oak Avenue in Arcadia, CA, as the testing route. The route, depicted in Fig. 6, is 2.6 km long and has eight signalized intersections. This route is across a commercial area that expects high traffic during commute hours and medium traffic during lunch hours. Not many pedestrians cross the street and the average speed of the vehicles is roughly 30 (mph). The route is almost flat with zero degrees of slope.

### 5.2 Real-Time Applicability.

The Eco-driving controller implements two concurring tasks. One task, every $\u223c$1.5 (s), updates continuously the DP solution solving problem (20), from the current state until the end of the trip. The other task, every 200 (ms), outputs a speed reference for the ACC; this is obtained querying, with the current state, the optimal control policy computed by the most recent DP run. The Eco-driving controller is implemented in robot operating system and the computations are performed calling matlab; we utilize the matlab parallel computing toolbox [54] to assign the update of the DP solution to one worker and the update of the speed reference to another worker. The ACC is implemented solving the nonlinear optimization problem (27) with NPSOL [55].

### 5.3 Hardware-in-the-Loop Simulation Setup.

Our HIL setup consists of four main components communicating over a controller area network (CAN bus), as depicted in Fig. 7: (i) the subject vehicle, a PHEV, placed on a dynamometer; (ii) a desktop computer, running the simulator of the environment surrounding the vehicle; (iii) a dSPACE micro-auto-box II, running the acc software; (iv) an Adlink Matrix-embedded PC, running the eco-driving control software. The basic specifications of the above components are provided in Table 1. Readers are referred to Ref. [42] for more details. Note that the PHEV can be replaced by mathematical vehicle and powertrain dynamics embedded in the traffic simulator for repeated and copious simulations.

Item | Specifications |
---|---|

Desktop | Intel^{®} Core™ i 7-7700KK CPU at 4.20 Hz with NVIDIA GEForce GTX 1080 |

Matrix embedded PC-Adlink | MXC-6101D/M4G with Intel Core i7-620 LE 2.0 GHz processor |

dSpace micro-auto-box | IBM PowerPC 750FX processor, 800 MHz |

Plug-in hybrid electric vehicle | 8.89 kWh of battery capacity |

Item | Specifications |
---|---|

Desktop | Intel^{®} Core™ i 7-7700KK CPU at 4.20 Hz with NVIDIA GEForce GTX 1080 |

Matrix embedded PC-Adlink | MXC-6101D/M4G with Intel Core i7-620 LE 2.0 GHz processor |

dSpace micro-auto-box | IBM PowerPC 750FX processor, 800 MHz |

Plug-in hybrid electric vehicle | 8.89 kWh of battery capacity |

#### 5.3.1 Environment Model.

The environment model represents all components related to real-world traffic that interacts with the vehicle on-road. Namely, the environment includes the road (e.g., intersections and traffic networks) geometry, other vehicles (e.g., positions and behaviors) driving on the road, as well as traffic signal schedules (e.g., SPaT). The environment is constructed by two software: pre-scan [56] and ptvvissim [57].

pre-scan constructs a traffic network and road geometry. Then, given the network and geometry, ptvvissim^{6} determines a traffic flow/density and other vehicles' behavior, such as longitudinal and lateral controls, which are then simulated by pre-scan in a loop. Finally, vehicle and powertrain dynamics is simulated by matlabsimulink, which is embedded in the pre-scan environment. Especially, powertrain dynamics that evaluates energy consumption is validated using real-world trip information [51].

We utilize historical traffic data measured and collected by Sensys Network over July 2019. The traffic data include SPaT, inbound/outbound vehicle counts^{7}, as well as aggregate traffic flows at each intersection. There are three use cases of the traffic data in the environment model: (i) pre-scan simulates a traffic signal scenario composed of {cycle length, red light duration, time shift of the signal cycle initiation} at each intersection. (ii) Vissim initializes an inflow and outflow rate at each intersection. (iii) We compute an empirical probability mass function (PMF), which is then used to parameterize the chance constraints (19).

Figure 8 shows the PMF and CDF of time delays at the seventh-intersection, for example, at 6 pm, the mean delay is 1.96 (sec) with a standard deviation of 1.033 (sec).

### 5.4 On-Road Experiment Setup.

The controller hardware for the on-road experiment is identical with the controller part (lower part) of the HIL simulation setup in Fig. 7 while the simulation environment (upper part of Fig. 7) is replaced by the real-world. Additionally, to measure an intervehicle distance to a front vehicle, our test vehicle is equipped with radar and camera sensors. To enable real-time communication between our test vehicle and approaching traffic lights and offer signal phase and timing (SPaT), our vehicle and the traffic lights (pictured in Fig. 9) are equipped with radiocommunication modules (Cohda MK5, Cohda Wireless Pt.y Ltd. in Wayville, Australia and Siemens RSU, Munich, Germany, respectively) and follow dedicated short-range communications (DSRC) protocols. Additionally, our test vehicle uses its GPS data to compute the distance to traffic lights in real-time. For high precision measurement, our test vehicle is instrumented with a high accuracy fuel flowmeter, and high accuracy current sensors (ETAS DAQ) to measure the high voltage battery current, the motor current, the starter/generator current, and the current for auxiliaries.

## 6 Results

In this section, we first present simulation results to verify the proposed ECO-ACC design. The verification includes examining the benefit of incorporating equivalent fuel into Eco-driving controller, the impact of a limited communication range on energy efficiency, and energy savings. Then, in September 2019, we conducted on-road experiments to validate the proposed controller with the presence of other human drivers on road. We also discuss the quality of traffic information and compare the results between simulations and experiments. Note that we focus on the charge-depleting mode (using battery pack as a primary energy source) of PHEV in both simulations and experiments.

### 6.1 Baseline: Adaptive Cruise Controller With a Fixed Speed Reference.

The baseline controller is set to the adaptive cruise controller in 4 with a constant speed reference. Namely, the speed reference is not optimized for the baseline controller, but fixed as maximum speed limit. We call the baseline “ACC-Only” for convenience.

### 6.2 Verification Through Simulations.

#### 6.2.1 Benefit of Incorporating Powertrain Dynamics to Speed Reference Optimization.

We first focus on investigating the benefits of incorporating powertrain dynamics into the Eco-driving controller. We compare two different controllers that implement each cost map illustrated in Fig. 4. The rest of the simulation environments, such as a SPaT schedule and traffic flow at each intersection, are identical for fair and exclusive comparative analysis. Figure 10 presents speed and SOC trajectories for the two controllers. The engine did not operate for both cases, so we only analyze SOC trajectories to compare energy consumption. The controller that uses the power cost map formulated with powertrain information generates velocity reference profiles to maximize the battery charging from regenerative braking considering the powertrain efficiency, as shown in Fig. 10. As a result, the proposed controller spends less battery energy, improving energy performance by 9% in miles-per-gallon equivalent (MPGe).

#### 6.2.2 Receding Horizon versus Global Horizon.

Next, we examine the significance of the length of the control horizon. In particular, we explore how much energy we lose with a receding horizon against a global horizon. With the global horizon, we suppose that the SPaT information is deterministic and known a priori, and thus we obtain a globally optimal speed profile over the route. With the receding horizon, however, we obtain a locally optimal speed profile limited to the receding horizon, without perfectly evaluating the cost beyond the horizon. We set the receding horizon to 400 (m), which is an arbitrary limit of the DSRC range.

Figure 11 presents the speed trajectories of ECO-ACC from the origin to the destination, with the global horizon and receding horizon, respectively. With the global horizon, the Eco-driving controller perfectly projects the trajectory that cruises through green waves, and the vehicle does not stop at any intersection. With the receding horizon, however, the Eco-driving controller is only able to partially evaluate green waves of the upcoming intersection, which results in more volatile behaviors in accelerations and braking and stops at a couple of intersections. In consequence, the MPGe reduces 14.97% with the receding horizon against the global horizon. Despite this loss of optimality, this is already a significant improvement compared to ACC with a constant speed reference. The details are presented later in this section.

#### 6.2.3 Energy Savings and Travel Time.

We quantitatively verify the energy savings of ECO-ACC under a variety of traffic signal schedules and traffic flows. We leverage the empirical PDFs of each signal duration conditioned on the hour of the day to generate each driving scenario (the empirical PDFs are obtained with a month of SPaT data collected throughout the testing route). Figure 12 shows that ECO-ACC secures 27.31% energy savings on average against ACC-Only throughout the different times of the day. However, it is notable that ECO-ACC has 15.41% more travel time on average against ACC-Only (with the constant speed reference).

Several papers examined a contrast relation between travel time and energy efficiency [59]. That is, additional travel time can improve energy efficiency and vice versa. A control engineer can decide the desired balance, based on sensitivity analysis for combined cost with different weights on travel time and energy efficiency. However, tuning hyperparameters typically is a time-consuming process, requiring multiple iterations of quantitative analysis. We hence present a simulation-based (without additional hardware) sensitivity analysis for the balance between travel time and wheel energy (wheel torque squared), summarized in Fig. 13. The stars represent the performance of the ECO-ACC and ACC-Only controllers in the HIL simulations, conducted in the same conditions of traffic lights; we observe similar gaps in energy and travel time between the two controllers over two extreme traffic scenarios, which indicates that the improvement of Ecological driving style is somewhat consistent regardless of traffic conditions. The red dots indicate the performance of the ECO-ACC controller in simulations with mathematical PHEV model, under the identical scenarios tested with real PHEV; with different values of $\lambda $ in Eq. (5). It is seen that the energy consumption tends to increase as $\lambda $ (i.e., the penalty on the total travel time) increases. Interestingly, at $\lambda =150$, the performance of ECO-ACC matches between simulations using real PHEV and using the mathematical model with a small offset—which indicates the potential of using mathematical models for reproducible simulations in both timely and cost-efficient manner. We notice that the red dots are somewhat clustered into two groups, indicating a “jump” for a small variation of $\lambda $ (from $\lambda =65\u2009to\u2009\lambda =70$); this is due to discrete-time windows of green waves.

### 6.3 Validation Through On-Road Experiments.

Finally, we report the on-road experiment results. We conducted the real-world testing (pictured in Fig. 14) in September 2019, on Live Oak Avenue in Arcadia, CA. The objectives of the on-road experiment are to: (i) test implementation setups under real driving settings and (ii) validate ECO-ACC performances in energy savings compared to ACC-Only. The demonstrations were performed over different times of the day where traffic flow varies from free-flow to dense. We focused on charge-depleting mode during demonstrations. Two vehicles (of the same vehicle model) drive the route simultaneously with roughly 10 s of a time gap in start time (which is enough for other vehicles to cut in). This way, two controllers (ECO-ACC and ACC-Only) are affected by the same traffic (or, with a minor discrepancy). In some cases, we observed one of the two vehicles was stuck at the red light while the other passed at the end of the green light. The test ceased if a front vehicle is too close or the vehicle accelerated too fast, which makes the passengers nervous and uncomfortable. As a result, we collected a total of 17 runs both eastbound and westbound (each run indicates the two vehicles driving from one end to the other end). The results only include full runs which were not interrupted by a human driver.

Figure 15 shows the speed profile of ECO-ACC in comparison with ACC-Only from the demonstration at 9:00 am where the traffic is moderate. The ECO-ACC tends to accelerate and decelerate smoothly, and consequently, there was more headway with the preceding vehicle. The room motivates an adjacent vehicle to cut in, yielding a fluctuating trajectory of the ego vehicle as seen over the speed profile in Fig. 15. Still, the range of fluctuations of ECO-ACC is lower than that of ACC-Only, which decelerates significantly at intersections notably around 120$\u223c$130 s to stop at the red light.

Figure 16 illustrates the histogram of MPGe and arrival time (i.e., total travel time) of ECO-ACC and ACC-only in the same form of Fig. 12. Interestingly, the results from the demonstration are consistent with HIL simulations in Fig. 12. That is, on average, eco-driving controller on top of the ACC controller yields 30.98% improvement in MPGe at the cost of 8.51% additional travel time. We point out that a mismatch of magnitudes exists both in MPGe and travel time between HIL simulation and on-road experiments. This is because there is a mismatch in vehicle dynamics and powertrain dynamics between the mathematical models we used in HILs and the real vehicles in demonstrations. Even though both simulations and demonstration are based on the charge-depleting mode, we observed occasional engine-on events in simulations as opposed to no engine usages during demonstrations. Nevertheless, it is important to highlight that the relative savings are consistently significant both in HIL simulations and demonstrations. In other words, the proposed simulation setup is still effective in capturing the energy improvement of the Eco-driving controller, which can facilitate rigorous developments of conceptual ideas prior to on-road demonstrations. Furthermore, this is an essential finding, for the first time, that practically measures the potentials of ecological motion planning for “autonomous driving” with vehicle-to-infrastructure connectivity.

Lastly, we examine the safety of ECO-ACC. Figure 17 shows the probability mass function of intervehicle gaps between the ego vehicle and a leading vehicle when exists. It shows that at any time of experiments, the safety distance was secured against a leading vehicle. The minimum distance (2.10 (m)) was observed when a vehicle suddenly cut in front of the ego vehicle. Over 75% of the time, the ego vehicle had 10 (m) or higher gaps at front, i.e., the optimal speed reference was not interrupted by the leading vehicle over 75% of the time.

## 7 Conclusion and Future Work

In this paper, we examine the mathematical and structural framework for ecological adaptive cruise controller (ECO-ACC) to enable automated longitudinal control with traffic signals. Under a two-layer structure, the upper layer plans a speed reference profile based on both real-time and historical signal phase and timing (SPaT) information. The output speed reference leverages optimal combinations of MPGe and travel time. The lower layer guarantees safety by avoiding collisions to front vehicles and by complying with traffic signals (red, green, and yellow). The proposed ECO-ACC addresses several practical challenges, including limited vehicle-to-infrastructure communication range, uncertain vehicle queue, complex PHEV powertrain dynamics, and rapid computations. We demonstrate the effectiveness of ECO-ACC on the real road in Arcadia, CA. The route includes eight signalized intersections with other human drivers who are ignorant to the test. The demonstration results indicate that, on average, ECO-ACC expects around 30% of improvement in MPGE (even for a high-end energy-efficient vehicle, PHEV, by its structure) at the cost of 8% of additional travel time, which is equivalent to a few tens of seconds. The future works may include: rigorous testing with variants of traffic routes and driving conditions as well as with charge sustaining mode (where the engine is switched to on/off frequently).

## Acknowledgment

This paper is an extension of work presented at the American Control Conference, Philadelphia, in 2019, and the 58th IEEE Conference on Decision and Control, Florida, in 2019.

The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

The authors would also like to thank Hyundai America Technical Center, Inc. for providing us with the vehicle and a testing facility, and Sensys Networks for granting access to the traffic data used in this paper.

## Funding Data

Advanced Resaearch Projects Agency-Energy (ARPA-E), U.S. Department of Energy (Award Number DE-AR0000791; Funder ID: 10.13039/100009224).

## Footnotes

Position $k\Delta s$ is equivalent to step *k*.

Throughout the paper, the position step size is 1 m, i.e., $\Delta s=1$.

We form an infeasible set (red waves) instead of a feasible set (green waves) for coherence with an effective red light duration that is discussed in Sec. 3.2.4.

The Vissim model takes the route inflows and outflows as inputs. At the intersections, the vehicles generated by the Vissim model can either turn or continue along the Live Oak Avenue, according to a probabilistic turn policy; such policy is also parameterized by the recorded aggregate traffic volume and turn counts data [42]. Because no vehicle-to-vehicle communication is assumed, the behavior of the surrounding vehicles, e.g., decelerations or lane changes, is unpredictable for the subject vehicle. Such uncertainty is dealt with by the ACC system.

Measured on the actual road by vehicle detectors.