## Abstract

Connected and automated vehicles (CAVs), particularly those with a hybrid electric powertrain, have the potential to significantly improve vehicle energy savings in real-world driving conditions. In particular, the ecodriving problem seeks to design optimal speed and power usage profiles based on available information from connectivity and advanced mapping features to minimize the fuel consumption over an itinerary. This paper presents a hierarchical multilayer model predictive control (MPC) approach for improving the fuel economy of a 48 V mild-hybrid powertrain in a connected vehicle environment. Approximate dynamic programing (DP) is used to solve the receding horizon optimal control problem, whose terminal cost is approximated with the base policy obtained from the long-term optimization. The controller was tested virtually (with deterministic and Monte Carlo simulation) across multiple real-world routes, demonstrating energy savings of more than 20%. The controller was then deployed on a test vehicle equipped with a rapid prototyping embedded controller. In-vehicle testing confirm the energy savings obtained in simulation and demonstrate the real-time ability of the controller.

## 1 Introduction

Connected and automated vehicles (CAVs) have the potential to increase safety, driving comfort, as well as fuel economy, by exploiting look-ahead driving information available via advanced navigation systems, vehicle-to-vehicle, and vehicle-to-infrastructure (V2I) communication [1–3]. Intuitively, with these connectivity technologies, a controller can plan a speed trajectory that minimizes unnecessary acceleration and braking events, thereby improving driver comfort and fuel-efficiency [4]. Meanwhile, powertrain electrification can increase the vehicle fuel (or energy) efficiency, by including battery packs and electric motors as alternative energy storage and power generation devices, respectively [5]. While combining these two technologies could further compound their efficiency improvements, they present a greater challenge from a planning and control perspective [6].

Ecodriving, defined in literature as the control of vehicle velocity for minimizing the fuel or energy consumption over an itinerary, is gaining prominence [7]. Based on the powertrain configuration considered in each application, the methods developed for determining the optimized velocity profile can vary, depending on whether the powertrain is equipped with a single power source [8–10] or a hybrid electric drivetrain [11,12]. The latter involves modeling multiple power sources and devising optimal control algorithms that can split the power demand in a synergistic manner to efficiently utilize the electric energy stored in the battery. Most of the existing literature consider the ecodriving problem in a decentralized fashion, i.e., the speed trajectory optimization and powertrain control are performed sequentially, and then integrated within a hierarchical control structure [13]. Based on overall system efficiency and calibration effort considerations, this paper explores an alternative approach, where the speed trajectory and powertrain torque split are jointly optimized.

Incorporation of V2I information enables the processing and use of signal phase and timing (SPaT) information in real-time for performing eco-approach and departure (eco-AND) at signalized intersections. Eco-AND refers to velocity control for increasing the likelihood to pass through a signalized intersection during a green window. Studies from literature have shown that such maneuvers can improve the overall fuel-efficiency [14–16]. When eco-AND is combined with ecodriving, the added complexity means that the controller may not always be able to compute a speed trajectory without violating traffic rules (i.e., optimization constraints) [17]. This warrants a unified optimization framework combining ecodriving and eco-AND that can improve the fuel-efficiency and ensure constraint satisfaction in a broad range of driving scenarios, while remaining computationally tractable on embedded control hardware platforms.

The objective of the work is to conduct energy optimization of an individual vehicle (noncooperative case). The vehicle is however intended to operate in an environment with traffic and infrastructure (communicating and noncommunicating). This paper focuses on the development of a hierarchical multilayer ecodriving controller based on model predictive control (MPC), that jointly optimizes the vehicle speed and battery state of charge (SoC). The proposed control framework is a novel alternative to state-of-the-art [3,13], in that the problem of velocity optimization and energy management is solved as a centralized optimization problem.

To account for route uncertainty and limited V2I communication range, and to mitigate the intensive onboard computation, the optimization routine is split into a long-term and short-term optimal control problem as per the availability of the look-ahead information. The long-term optimization is performed over the entire route with the look-ahead information such as speed limits and position of stop signs available from an advanced navigation system. To account for variability in route conditions such as variable speed limits and SPaT information, the full-route optimization is cast as a receding horizon optimal control problem and evaluated periodically in real-time via MPC over a short horizon. While MPC has been widely used in real-time control applications [18], a key challenge still remains in its implementation—the definition of an appropriate terminal cost and/or terminal state constraints for performance and stability [19]. Using principles from approximate dynamic programing (DP), specifically the rollout algorithm, this paper provides a novel methodology for appropriately selecting the terminal cost of the MPC.

The proposed solution method yields optimal closed-loop strategies that are robust against external disturbances and has its theoretical foundations in the traditional DP [20–22]. This hierarchical optimization framework is well-suited for in-vehicle implementation, where advanced mapping systems can provide long-term route information and vehicle-to-everything (V2X) technologies can update this information in the short-term. Further, this work proposes a systematic and comprehensive verification framework for virtual and experimental evaluation of fuel savings from the CAV optimization algorithms. Simulations and track testing results validate the developed rollout algorithm-based optimization framework making it suitable for real-time applications containing environmental disturbances and modeling uncertainties.

## 2 Model of Parallel Mild-Hybrid Electric Vehicle

The P0 mild-hybrid electric vehicle (mHEV) architecture studied in this work is illustrated in Ref. [23]. A belted starter generator (BSG) is connected to the crankshaft of a $1.8\u2009L$ turbocharged gasoline engine equipped with dynamic skip fire, DSF [24,25], and a $48\u2009V$ battery pack.

A forward-looking vehicle simulator was developed in matlab–simulink to evaluate fuel consumption and compare different control strategies over prescribed routes. The inputs to the plant model in Fig. 1 are the desired BSG torque ($Tbsg,tdes$) and desired engine torque ($Teng,tdes$), which are obtained from a simplified model of the software in the electronic control module (ECM). This contains a baseline torque split strategy and essential functions that convert the driver's input (pedal positions) to commands, which are fed to the powertrain components. Note that in the descriptions of the equations that follow, the arguments of certain terms may be suppressed for brevity.

### 2.1 Vehicle Dynamics.

where *v _{t}* is the velocity of the vehicle,

*M*is the effective mass of the vehicle (including driveline rotational inertia and the total payload), $Tout,t$ is the net output torque, $Fbrk,t$ is the braking force,

*R*is the rolling radius of the wheel, and $Froad,t$ is the road-load, which is defined as the force imparted on a vehicle from aerodynamic drag, tire rolling resistance, and road grade.

_{w}### 2.2 Powertrain.

where $ngr,t$ is the selected gear number, $Teng,t$ is the engine torque, and $\omega eng,t$ is the engine speed.

where $\omega bsg,t$ is the BSG speed, *r*_{belt} is the belt ratio, $Pbsg,t$ is the electrical power required to produce a torque $Tbsg,t$ at speed $\omega bsg,t$, and $\eta bsg,t$ is the BSG efficiency.

where $Voc,t$ is the battery open-circuit voltage, *R*_{0} is an approximation of the battery internal resistance, $Ibatt,t$ is the battery current, *ξ _{t}* is the battery SoC, and

*C*

_{nom}is the nominal capacity of the battery. Further, a calibration term

*I*

_{bias}is introduced as a highly simplified representation of the onboard electrical auxiliary loads.

where $\omega p,t$ is the speed of the torque converter pump, $\omega turb,t$ is the speed of the turbine, $\omega eng,stall$ is the speed at which the engine stalls, *ω*_{idle} is the idle speed (target) of the engine, stop is a flag from the ECM indicating engine shut-off when the vehicle is stationary, $Tturb,t$ is the turbine torque, and $Tpt,t$ is the powertrain torque.

where *r _{f}* is the final drive ratio, $rgr,t$ is the gear ratio, and $Tout,t$ is the transmission output shaft torque.

The model was validated on experimental data [23]. Figure 2 presents results over the Federal Test Procedure (FTP) drive cycle, where the vehicle velocity, battery SoC, and fuel consumption are compared against experimental data. The predicted vehicle velocity, battery SoC, and fuel consumption profiles adequately match the experimental data, with slight mismatches that can be attributed to the simplifications made to the powertrain model.

## 3 Problem Formulation

The objective of the nonlinear dynamic optimization problem, formulated in the spatial domain, is to minimize the fuel consumption of the vehicle over an entire itinerary. A key benefit of a spatial trajectory formulation is that it naturally lends itself to the incorporation of route-related information, such as posted speed limit signs, location of traffic lights, and stop signs, whose positions along the route remain fixed.

where *s* is the discrete position, $xs\u2208X\u2282\mathbb{R}p$ is the state, $us\u2208U\u2282\mathbb{R}q$ is the input or control, and *f _{s}* is a function that describes the state dynamics. In this work, the state variables chosen are the vehicle velocity and the battery SoC: $xs=[vs,\xi s]T$. The engine torque and BSG torque are chosen as the control variables: $us=[Teng,s,Tbsg,s]T$.

The control and the state are constrained, and the constraint function $hs:X\xd7U\u2192\mathbb{R}r$ is expressed as $hs(xs,us)\u22640,\u2200s=1,\u2026,N$, which includes the route speed limits, operating limits of physical actuators and subsystems, constraints for drive comfort, and so on. An admissible control map at position *s* is a map $\mu s:X\u2192U$ such that $h(x,\mu s(x))\u22640,\u2200x\u2208X$. The collection of admissible control maps is denoted by $M:=(\mu 1,\u2026,\mu N)$, which is referred to as the policy of the controller.

where the weight $\gamma \u2208(0,1)$ is a tunable penalty factor that can be used to tradeoff between the amount of fuel consumed and time taken to complete the route; effectively, it constitutes a driving aggressiveness parameter, $m\u02d9f,s$ is the fuel consumption rate, $m\u02d9fnorm$ is a cost normalizing weight, and *t _{s}* is the travel time per step.

## 4 Full-Route Optimization Using Dynamic Programing

*x*and

_{s}*s*, $\mu s*(xs)$ minimizes the right side of Eq. (10) [27]. Here, $Js(xs)$ is interpreted as the optimal cost for the $(N+1\u2212s)$-stage problem starting at state

*x*and position

_{s}*s*, and ending at position

*N*+ 1. For use in Sec. 5, the following assignment is made:

where *V _{s}* is termed the value function, equal to the cost-to-go function at position

*s*.

*N*-step optimization are defined as follows:

*a*

^{min},

*a*

^{max}are the limits imposed on the vehicle acceleration for comfort; $Teng,smin,Teng,smax$ are the state-dependent minimum and maximum torque limits of the engine, respectively; and $Tbsg,smin,Tbsg,smax$ are the state-dependent minimum and maximum BSG torque limits, respectively. To ensure SoC-neutrality over the global optimization, a terminal constraint is applied on the battery SoC: $\xi 1=\xi N+1$. Here, as the dynamic optimization problem is solved by the DP algorithm, the state dynamics introduced in Eqs. (1) and (4) are discretized and transformed to spatial domain

where $\Delta ds$ is the distance over one step (i.e., $\Delta ds=ds+1\u2212ds$, where *d _{s}* is the distance traveled along the route at position

*s*), and $v\xafs(=(vs+vs+1)/2)$ is the average velocity over one step.

## 5 Model Predictive Control Using Rollout Algorithm (Ecodriving)

*N*-steps to $NH\u226aN$ steps, formulated at a position $s=1,\u2026,N\u2212NH+1$ as

where *N _{H}* is the number of steps in the receding horizon. This MPC or look-ahead optimization problem is subject to the same constraints introduced in Eq. (12).

A key challenge in Eq. (14) is the definition of an appropriate terminal cost and/or terminal state constraints that approximate the optimal solution provided by DP in a full-information scenario. Some other methods adopted in the literature for constructing approximations of the value function include local linear approximation [27,28], Monte Carlo-based [29], and Q-learning-based approaches [30–32]. This work introduces a terminal cost (or equivalently, the cost to complete the remaining route) approximation strategy based on the use of approximate dynamic programing, specifically the rollout algorithm.

where the approximation $J\u0303k+NH$ (and as a result $J\u0303s+1$) is the cost-to-go of a known suboptimal policy, termed as the base policy or base heuristic, and $M\u0302*:=(\mu \u0302k*,\u2026,\mu \u0302k+NH\u22121*)$ is the rollout policy. One of the properties that make the rollout algorithm attractive for onboard optimization is the cost improvement property [33], namely, if the base heuristic produces a feasible solution, the rollout algorithm also produces a feasible solution whose cost is no worse than the cost corresponding to the base heuristic (proof in Ref. [27]).

where *V _{k}* is the value function of the full-route DP solution at

*k*, the global position along the route. The rationale behind this is explained using the Bellman principle of optimality equation. Setting the terminal cost in Eq. (15) to the value function of the full-route DP results in Eqs. (10) and (11) for the

*N*-step problem. Solving this system of equations thus yields the optimal cost for the look-ahead optimization problem. This claim is valid in the absence of traffic or other uncertainties en route, i.e., as long as the per stage cost remains the same for both the

_{H}*N*-step and

_{H}*N*-step DP.

*k*along the route, the problem below is solved from local position $k+NH\u22121$ to $k,\u2003\u2200k=1,\u2026,N\u2212NH+1$:

### 5.1 Incorporation of Signal Phase and Timing Information and Eco-Approach and Departure.

Incorporating SPaT information in the ecodriving algorithm can be addressed by adding time as a state variable in the optimization problem formulation [34]. However, this is accompanied by an exponential increase in the computational effort required [35].

In this work, a rule-based approach is developed to increase the likelihood of passing-in-green by using SPaT information broadcast to the vehicle within communication range to determine kinematically feasible vehicle velocity constraints that are then imposed to the MPC routine.

To ensure a feasible solution, the constraints fed to the rollout algorithm are shaped by recursively applying $vs+12=vs2\u22122amin\Delta ds$, from the current speed till the calculated (modified) speed limit is reached. Constraint shaping increases the likelihood with which the vehicle crosses the intersection in the green window while ensuring kinematic feasibility for use in the optimization routine.

## 6 Verification Framework

The process for verification of the vehicle velocity and powertrain optimization strategy is summarized in Fig. 3. The virtual evaluation of the ecodriving case involves the generation of multiple simulation scenarios, where the parameter *γ* in the optimization is varied to determine and quantify the Pareto-optimal fronts among the objectives (total fuel consumption and trip travel time). This evaluation is initially performed by assuming that all the traffic lights along the route are stop signs. The optimizer is benchmarked against a realistic baseline, which is assumed as the same demonstration vehicle. Further, no longitudinal automation is assumed, and for this reason all the simulations were conducted by including a validated enhanced driver model (EDM), a modified car-following model that mimics the behavior of a human driver in presence of speed limits and signalized intersections [36].

Following this initial virtual verification, experimental testing was conducted on a closed test track at the Transportation Research Center (TRC) Inc. in East Liberty, OH, where the ecodriving algorithm was demonstrated through real-time implementation in the demonstration vehicle. To obtain a realistic baseline for benchmarking the results, the vehicle was fitted with a brake and throttle robot (BTR) [37], programed to follow pre-established velocity profiles generated in simulation with the EDM. This deterministic scenario was used to validate the simulation tools on specific scenarios, offering an initial estimate of the fuel-saving potentials of the developed ecodriving algorithm.

Finally, a more comprehensive virtual verification (evaluation of ecodriving algorithm with eco-AND, in Fig. 4) was performed using a Monte Carlo simulation framework, in which the driver aggressiveness and the SPaT information are treated as random variables. From the results of this simulation, in-vehicle verification at TRC was conducted by extracting and testing sample cases from corresponding scenarios selected from the Monte Carlo simulations. Here, SPaT variability, including communication latencies, was realistically emulated during testing. Benchmarking was performed using a BTR that follows the velocity profiles generated in simulation by the EDM, where the decision to approach a signalized intersection is based on the concept of line-of-sight (LoS) [38].

## 7 Virtual Evaluation

### 7.1 Test Route.

Figure 4 shows the features of the representative route over which the optimization routine is tested. This urban route set in Columbus, OH is $7.4\u2009km$ in length and comprises 22 traffic lights and three stop signs.

### 7.2 Evaluation of Ecodriving Algorithm.

Figure 5 shows sample results from the ecodriving algorithm over the urban test route with no traffic, in which all the traffic lights are assumed to be stop signs. The figure compares the MPC ecodriving algorithm against the full-route solution obtained offline via DP. It is evident that the solution of the multi-objective optimization problem (9) yields a γ-dependent Pareto front. Along the Pareto curve, lower values of γ depict an increasingly aggressive driving style, while higher γ values represent more conservative behavior with smoother accelerations and braking maneuvers. For each γ, the vehicle velocity profile was smooth, and the torque split strategy determined by the optimization routine was charge-sustaining in nature. The comparison in Fig. 5 is obtained by imposing identical constraints on the full-route DP optimization and the MPC (ecodriving algorithm), and the value function from the full-route DP solution is applied as the terminal cost of each *N _{H}*-horizon problem. The step sizes of the discretized distance are $10\u2009m$, states are $1.36\u2009m/s,\u20092%$, and engine torque and BSG torque are $13.2\u2009m$ and $4.2\u2009N\u22c5m$, respectively.

### 7.3 Evaluation of Ecodriving Algorithm With Eco-Approach and Departure.

The ecodriving algorithm with eco-AND is evaluated by performing large-scale Monte Carlo simulations over real-world routes in which each traffic light has time-varying SPaT information.

#### 7.3.1 Baseline Case.

The baseline considered is the EDM, a deterministic reference velocity predictor that uses route characteristics to generate velocity profiles representing different levels of driver aggressiveness [36]. The EDM predicts the response of a human driver when operating a vehicle in presence of traffic, stop signs, and traffic lights by using a realistic LoS-based heuristic strategy [38]. For simulations over urban and mixed routes, a LoS of $100\u2009m$ is considered to be reasonable. The velocity reference from the EDM is fed to a tracking controller that generates the necessary inputs to the validated vehicle model described in Sec. 2.

An additional case is now constructed to quantify the fuel-saving potentials of eco-AND. The LoS approach (as introduced in Ref. [38]) is adapted and used in conjunction with the rollout algorithm to interact with traffic signals. Here, the signal phase information is available to the driver only within the LoS, and at any point beyond it, the traffic light is assumed to be a stop sign. It should be noted that unlike eco-AND, the ecodriving with LoS does not receive any timing information from the traffic light.

#### 7.3.2 Variability in Signal Phase and Timing Information.

To recreate the degree of variability typically associated with SPaT at subsequent signalized intersections, a base SPaT sequence is extracted from the traffic simulation program sumo (simulationofurbanmobility) [39]. Starting from this base SPaT, all the traffic lights are offset by the same uniformly random value such that the phase difference between the traffic lights remains constant, i.e., the signals are synchronized. Alternately, this can be interpreted as considering the departure time as a uniform random variable: $tdep\u223cU(0,tcyc)$, where *t*_{dep} is the departure time and *t*_{cyc} is the traffic cycle time, chosen in this study as $90\u2009s$ (fixed).

#### 7.3.3 Monte Carlo Simulations.

Monte Carlo simulations are then performed over the test route by considering the SPaT information as a random variable. Here, 2000 different scenarios are generated by randomly changing the departure time (as described above). The different cases being compared in this simulation study are baseline (EDM with LoS of $100\u2009m$), ecodriving with LoS (no timing information, current phase of each traffic signal is known within a LoS of $100\u2009m$, *N _{H}* = 20), and ecodriving with eco-AND (

*N*= 20). For both the ecodriving cases, three calibrations are considered: $\gamma ={0.4,0.7,0.82}$, to represent an aggressive, normal, and relaxed driving behavior, respectively. Note that the choice of grid discretization used for this evaluation is shown in Table 1. For fair comparison, the baseline EDM for each simulation is calibrated to represent a driver aggressiveness comparable to that value of

_{H}*γ*. In total, 6000 simulations are executed for each case.

Discretized variable | Step size |
---|---|

Distance | $10\u2009m$ |

Velocity | $1.36\u2009m/s$ |

Battery SoC | $2%$ |

Engine torque | $13.2\u2009N\u22c5m$ |

BSG torque | $4.2\u2009N\u22c5m$ |

Discretized variable | Step size |
---|---|

Distance | $10\u2009m$ |

Velocity | $1.36\u2009m/s$ |

Battery SoC | $2%$ |

Engine torque | $13.2\u2009N\u22c5m$ |

BSG torque | $4.2\u2009N\u22c5m$ |

Figure 6 shows the distributions of the fuel consumption for the baseline (inline image), ecodriving with LoS (inline image), and ecodriving with eco-AND (inline image) cases, corresponding to $\gamma ={0.4,0.7,0.82}$. It is to be noted that the travel times obtained for each *γ* remain the same across the three cases being evaluated. A nonparametric probability density function known as the kernel density estimator is used to obtain the fitted distribution for each of the cases shown.

Over the mixed test route, the ecodriving algorithm with eco-AND reduces the fuel consumption of the baseline $48\u2009V$ hybrid by $18%,\u200918%$, and $19%$ corresponding to $\gamma ={0.4,0.7,0.82}$, respectively. Further, there is a significant reduction in the standard deviation of the fuel consumption distribution compared to the baseline. This is a notable result as this means that the ecodriving algorithm equipped with eco-AND can more consistently achieve a fuel consumption close to the mean of the distribution, i.e., the spread of the fuel consumption due to variability in the driver aggressiveness and SPaT information is significantly reduced. Note that the fuel savings from the ecodriving with eco-AND algorithms are not only dependent on the *γ* value and can vary significantly depending on the route features—particularly, the nature of the route (urban or extra-urban or mixed, affecting the average speeds), and number and density of traffic lights and stop signs. For the urban route shown, the high density of traffic lights ($\u22483$ traffic lights/km) and low average speed limit reduce the influence of driver aggressiveness on the fuel consumption, thereby resulting in comparable fuel savings across the three *γ* values.

To quantify the benefits obtained from eco-AND specifically, the results from ecodriving with LoS are compared against that with eco-AND. For the urban route with 22 traffic lights, the eco-AND provides an incremental $6%$ fuel saving over the LoS implementation, with similar mean travel time. Simulations were also performed over other urban and mixed routes, the eco-AND results in $2\u221210%$ additional fuel savings. The reason for the increased benefits from the pass-in-green algorithm over urban routes can be attributed to the higher density of traffic lights.

## 8 In-Vehicle Implementation and Results

The MPC framework was implemented in the demonstration vehicle, a 2016 VW Passat $1.8\u2009L$ with a six-speed automatic transmission and turbocharged gasoline engine, which was retrofitted as a mHEV by installing a BSG and a $48\u2009V$ battery pack. The demonstration vehicle was also equipped with CAV technologies and DSF (shown in Fig. 7(a)). For all baseline testing, the $48\u2009V$ mild-hybrid system is active and DSF is disabled, while for all optimizer testing both the mild-hybrid system and DSF are enabled. The onboard CAV technologies include an advanced GPS module for enhanced navigation, a dedicated short range communication module that enables V2X communication, camera, and radar modules to support adaptive cruise control (ACC) functionality. These CAV technologies enable the ability of full longitudinal control of the vehicle to achieve SAE Level $1+$ functionality (in accordance with SAE J3016).

The real-time ecodriving algorithm (with eco-AND), integrated with V2X communication and ACC, has been implemented using rapid prototyping hardware (dSPACE MicroAutoBox II, or MABx in short) in the test vehicle. Online calibration of control parameters and data logging are performed using dSPACE controldesk software via the host Ethernet interface. A significant result to be noted here is that the implemented optimizer can compute the solution to a 20-step receding horizon optimization problem via the two-state, two-input DP in $\u2248200\u2009ms$ on the MABx.

### 8.1 Experimental Test Setup.

All vehicle tests were performed in a single lane with $0%$ grade on the $7.5\u2009mi$ high-speed test track located at TRC (refer to Fig. 7(b)). The results presented in this section are related to tests run over an urban route, as shown in Fig. 5. For each of the tests conducted, the measured and calculated variables are vehicle speed, battery SoC, cumulative fuel consumed, and travel time. Here, the reader is encouraged to refer to Ref. [40], in which the in-vehicle implementation of the optimizer is compared and verified against the corresponding simulation models over a mixed (urban-highway) route.

#### 8.1.1 Test Setup for Evaluation of Ecodriving Algorithm.

For evaluation of the ecodriving case, three calibrations for the driver aggressiveness parameter are considered: $\gamma ={0.3,0.7,0.75}$. In this scenario, all the traffic lights along the route are assumed to be flashing red, i.e., treated as stop signs. Table 2 summarizes the test setup for the ecodriving test scenario. Note that the horizon length corresponding to *N _{H}* = 20 in this case takes a range of values ($150\u2212750\u2009m$), as the step size of the discretized distance grid is not fixed. This enables the usage of a fine discretization in certain sections of the route and coarser in other sections, allowing the ecodriving algorithm to satisfactorily capture the model dynamics while running in real-time on the MABx.

Variable | Ecodriving | Baseline |
---|---|---|

HEV state | $48\u2009V$ mHEV | $48\u2009V$ mHEV |

DSF state | ON | OFF |

Vehicle mass | $\u22481850\u2009kg$ | $\u22481850\u2009kg$ |

Grade | $0%$ | $0%$ |

Initial SoC | $50%$ | $50%$ |

Controls | Ecodriving control | ECM |

Driver | ACC | BTR |

Variable | Ecodriving | Baseline |
---|---|---|

HEV state | $48\u2009V$ mHEV | $48\u2009V$ mHEV |

DSF state | ON | OFF |

Vehicle mass | $\u22481850\u2009kg$ | $\u22481850\u2009kg$ |

Grade | $0%$ | $0%$ |

Initial SoC | $50%$ | $50%$ |

Controls | Ecodriving control | ECM |

Driver | ACC | BTR |

#### 8.1.2 Test Setup for Evaluation of Ecodriving Algorithm With Eco-Approach and Departure.

In order to evaluate the ecodriving algorithm with eco-AND, a test environment was designed where traffic light SPaT information is broadcast to the optimizer as the vehicle approaches a signalized intersection. To significantly reduce the number of tests and the resulting testing time without compromising the validity of the results, sample cases from the Monte Carlo simulations (Fig. 6) were selected and reconstructed at TRC.

For each tested condition, the values of *γ* and the SPaT scenario were selected to represent a dominant mode of the respective Monte Carlo simulation over that route. In this work, $\gamma =0.7$ is chosen for the reconstructed route as it compactly represents normal driver aggressiveness. The SPaT scenarios are replicated in real-time by broadcasting them on a roadside unit (RSU). For convenience in setup and testing, this RSU is mounted on the rear seat and connected to a supplementary $12\u2009V$ battery as shown in Fig. 8. The V2I communication is emulated via the in-vehicle RSU that broadcasts SPaT and MAP information in accordance with the SAE J2735 standard to the onboard unit mounted on the vehicle.

Note that the travel time recorded for testing the ecodriving with eco-AND case includes the time spent at stop signs and the wait time at red traffic lights along the route. Here, the test setup for evaluation is identical to that for the ecodriving case in Table 2 but for the “controls” category, where the ecodriving algorithm equipped with eco-AND capability is used.

#### 8.1.3 Test Setup for Baseline Evaluation.

To ensure repeatability of the experiments, a BTR is programed and calibrated to follow reference velocity profiles which are generated in simulation using the EDM calibrated to represent a variety of driving styles. This ensures repeatability and controlled variability across baseline tests. The BTR accurately tracks the reference velocity profile by robotic actuation of the accelerator and brake pedals with a human driver only responsible for the steering action. Table 2 summarizes the test setup adopted to evaluate the baseline. Here, note that the processing of the baseline test results differ depending on whether the ecodriving or the ecodriving with eco-AND is being benchmarked. For fair evaluation of the ecodriving case, the travel time recorded excludes the time spent at stops along the route, while for the ecodriving with eco-AND case, the travel time includes the time spent at stop signs as well as the wait time at red traffic lights.

### 8.2 Experimental Results for Ecodriving.

To evaluate the benefits of the ecodriving algorithm over a representative baseline, multiple trips are executed over the same reconstructed urban route for the chosen *γ* values (refer Table 2). The travel times from the ecodriving tests are used to generate the EDM parameter sets with similar (driver) aggressiveness and travel times for each *γ*. The generated EDM velocity profiles are then used as reference inputs to the BTR.

Figure 9(a) compares the vehicle testing results for the baseline (executed using the BTR) against the ecodriving case, for each *γ*. Here, the error bars represent the maximum deviation of the data points from their respective mean and are determined using data from at least five test runs. Over the urban route tested, featuring 23 stops, the ecodriving algorithm with DSF enabled reduces the fuel consumption by over $25%$ (and up to $33%$), relative to the baseline, with comparable travel time.

In Figs. 9(b) and 9(c), a run-to-run comparison of the states (vehicle velocity and battery SoC) and cumulative fuel consumption along the urban route are, respectively, shown for $\gamma =0.7$. A noticeable contrast is observed between the baseline and optimizer tests, with the ecodriving algorithm resulting in $33%$ fuel savings for similar travel time. Here, the DSF-enabled optimizer increases the operation of the engine within the DSF fly-zones and thereby leverages the fuel-saving potential of DSF.

Figure 10 shows the vehicle speed trajectories measured on the demonstration vehicle for the urban route and indicates the different operating modes of the mHEV powertrain for the optimizer and baseline experiments. The operating modes are *engine only*, *E-assist*, *regenerative braking*, *engine-on battery recharge*, *deceleration fuel cutoff*, *DCCO*, and *start–stop*. Here, the engine only mode is self-explanatory. In the E-assist mode, the BSG provides a torque assist to the internal combustion engine. In the regenerative braking or regen mode, the BSG acts as a generator to slow the vehicle down by converting the (excess) kinetic energy from the motion of the wheels to electrical energy, which is then stored in the $48\u2009V$ battery. In the engine-on battery recharge mode, the BSG acts as a generator again, and here the engine produces additional power to supply the required mechanical energy for conversion (to electrical energy). In deceleration fuel cutoff mode, based on certain conditions (such as current gear, engine speed, and so on), no fuel is injected into the engine during deceleration events, while the valves still cyclically open and close. The negative engine brake torque from the pumping losses here contributes to “engine braking,” which is apparent as long as the engine remains mechanically engaged to the transmission. Under braking events in Deceleration Cylinder Cut-Off (DCCO) mode, the fuel can be cut-off, and additionally the intake and exhaust valves can be closed such that the pistons act as air springs, thereby reducing the pumping losses. Finally, a start–stop system automatically shuts down (when the vehicle is stationary) and restarts the engine in the start–stop mode to reduce the time spent in idling.

The results show that the ecodriving algorithm increases the use of the BSG to expand powertrain operation in the E-assist and regen modes. Further, in contrast to the baseline, the optimizer increases the engine only operation while significantly reducing powertrain operation in the highly fuel-inefficient engine-on battery recharge mode. This indicates that the ecodriving algorithm, which utilizes look-ahead information for optimal control, is less conservative than the baseline torque split controls. The fuel savings can be further increased by improving the tracking performance of the ACC to achieve a smoother velocity profile and optimize the use of DCCO.

### 8.3 Experimental Results for Ecodriving With Eco-Approach and Departure.

The specific case (*γ* and SPaT scenario tuple) selected from the Monte Carlo simulations for vehicle testing corresponds to a dominant mode of the statistical distribution. Over the reconstructed urban route considered, the average (over five runs) in-vehicle fuel consumption and travel time are observed to lie within the range of their corresponding distributions. Further, as seen in Table 3, they are closely comparable to their respective mean values from the Monte Carlo simulations (refer to Fig. 6).

Case | Travel time (s) | Fuel consumed (g) |
---|---|---|

Virtual (Monte Carlo simulation) | 712 | 404 |

Experimental tests | 735 | 417 |

Case | Travel time (s) | Fuel consumed (g) |
---|---|---|

Virtual (Monte Carlo simulation) | 712 | 404 |

Experimental tests | 735 | 417 |

The baseline case considered to benchmark the optimizer is constructed such that the driver aggressiveness (i.e., resulting travel time) matches a dominant mode of the statistical distribution obtained through Monte Carlo simulations while being comparable to the mean travel time from the ecodriving with eco-AND testing. Figure 11 compares the in-vehicle test results from the baseline (using the BTR) and the ecodriving with eco-AND cases. The enhanced range (compared to typical human LoS) and information (signal time in addition to the current phase) enabled by V2I technologies is used by the eco-AND feature to provide modified speed constraints to the rollout algorithm-based optimization. While the number of stop-at-red scenarios remains the same in this specific case, the resulting velocity profile is much smoother with fewer acceleration–deceleration events.

The torque split strategies of the baseline and ecodriving with eco-AND cases over the urban route are evaluated by comparing the resulting battery SoC and cumulative fuel consumption trajectories, shown in Fig. 12. A key benefit from the designed ecodriving algorithm with eco-AND is the resulting charge-sustaining torque split strategy. In contrast, the terminal SoC for the baseline case is $40%$ (while its initial SoC was $50%$).

Case | Travel time (s) | Fuel consumed (g) |
---|---|---|

Baseline | 714 | 538 |

Ecodriving with eco-AND | 735 | 417 |

Case | Travel time (s) | Fuel consumed (g) |
---|---|---|

Baseline | 714 | 538 |

Ecodriving with eco-AND | 735 | 417 |

Table 4 summarizes the fuel consumption and travel time obtained by the baseline and the ecodriving algorithm with eco-AND, as obtained from the in-vehicle tests. For the specific route tested here, the optimizer saves over $22%$ in fuel with a marginal increase of $2.9%$ in trip time while ensuring SoC-neutrality over the entire trip.

## 9 Conclusions and Future Work

In this paper, a multilayer hierarchical MPC framework is developed to solve the ecodriving problem for a $48\u2009V$ mild-hybrid powertrain in a connected vehicle environment. The control framework comprises a long-term co-optimization of vehicle speed and SoC performed over the entire route itinerary, and a short-term optimization where the variability in route conditions and/or uncertainty in route information are considered by transforming the full-route optimization into a receding horizon optimal control problem, solved periodically over shorter horizons. The terminal cost for the receding horizon optimization is approximated as the residual cost (or cost to complete the remaining route) from the full-route optimization and solved using approximate dynamic programing, specifically the rollout algorithm.

A comprehensive verification that includes virtual and experimental evaluations on a test vehicle demonstrates the fuel-saving potential of the hierarchical optimization framework. Simulation and track testing data show more than 20% reduction in fuel consumption compared to the baseline. Extensions of the algorithm are part of the ongoing work, including the implementation of the algorithm with the consideration of traffic information via vehicle-to-vehicle and signal phase and timing information via V2I communication.

## Acknowledgment

The authors gratefully acknowledge BorgWarner Inc. (formerly Delphi Technologies) for providing continued technical support and for the insightful discussions.

## Funding Data

U.S. Department of Energy, Advanced Research Projects Agency—Energy (Award No. DE-AR0000794; Funder ID: 10.13039/100000015).

## References

**7**(5), pp. 3759–3773