**1. Introduction**

Automated and connected mobility is currently forecasted reshaping public and private transportation over the next few decades [1–4]. Remarkable benefits could be achieved in general through implementing automated mobility, including enhancing passenger comfort, reducing energy consumption for propulsion, enhancing traffic management, and improving road safety, among others [5]. This technological advance demands developing effective and flexible numerical tools for controlling and designing automated vehicles [6–11].

Automated driving, as fostered by the different communication technologies (e.g., vehicle-to-vehicle, vehicle-to-infrastructure, vehicle-to-pedestrian, vehicle-to-grid, vehicleto-device), represents an extension of advanced driver assistance systems (ADASs). Examples for ADASs currently implemented in road vehicles include cruise control (CC), where the vehicle is controlled to travel at constant longitudinal speed over time, and adaptive cruise control (ACC), where the longitudinal speed of the vehicle is controlled to vary over time according to the measured distance from the vehicle ahead. In an ACC driving scenario, the following vehicle (named hereafter as the following vehicle) typically exploits data from the preceding vehicle (named hereafter as the preceding vehicle), which

**Citation:** Anselma, P.G. Optimization-Driven Powertrain-Oriented Adaptive Cruise Control to Improve Energy Saving and Passenger Comfort. *Energies* **2021**, *14*, 2897. https://doi.org/10.3390/ en14102897

Academic Editor: Francis F. Assadian

Received: 13 April 2021 Accepted: 13 May 2021 Published: 17 May 2021

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can be either human-operated or automated. ACC systems use sensors, such as radar, Light Detection and Ranging (LIDAR) or cameras to identify and monitor the preceding vehicle for measuring its current distance and speed difference [12]. Current ACC systems are calibrated to regulate the longitudinal speed of the vehicle to maintain a constant headway from the preceding vehicle [13,14]. Avoidance of front-end collision between the preceding vehicle and the following vehicle can be ensured in this way. However, when propulsion and brake systems are controlled with the exclusive aim of maintaining a constant time-headway (or distance) from the preceding vehicle, it cannot be guaranteed that the ACC-enabled vehicle achieves improved performance in terms of energy economy or passenger comfort as an example [15]. New possibilities and challenges open up in this framework concerning the development of ACC approaches that can vary both the following vehicle's longitudinal speed and distance from the preceding vehicle over time regardless of the longitudinal speed of the preceding vehicle. Improving various predefined performance metrics for the preceding vehicle can be set as a control target for such an enhanced ACC system.

Literature regarding control approaches for the following vehicle's speed exploiting information coming from the preceding vehicle in automated driving can be divided between single-powertrain-based approaches and multiple-powertrain-based approaches. Single-powertrain-based ACC approaches can focus either on conventional vehicles (CVs), hybrid electric vehicles (HEVs) or battery electric vehicles (BEVs) as examples. Concerning CVs powered solely by an internal combustion engine (ICE), Lang et al. [16] in 2013 discussed a control logic aiming to minimize fuel consumption while neglecting gear shifting. He and Orosz [17] in 2017 compared feedback-based and rolling horizon optimal control-based as cooperative cruise control approaches minimizing fuel consumption. The same authors extended a fuel-optimal longitudinal speed controller to the case of heavy-duty trucks exploiting information coming from multiple vehicles ahead through vehicle-to-vehicle (V2V) communication [18]. As concerns HEVs, a recurrent research topic involves developing velocity predictors that can improve the energy management strategy of the following vehicle through the information coming from the preceding vehicle. Different categories of longitudinal speed regulation logics have been developed in the literature (e.g., heuristic, instantaneous optimization, machine learning), and various HEV powertrain layouts have been considered, such as power-split [19], parallel P0 [20], parallel P2 [21] and series-parallel P1P4 [22] as an example. Regarding BEVs, the author of this paper proposed an optimal off-line velocity controller based on dynamic programming (DP) capable of minimizing the energy consumption of the following vehicle [23]. Recently, Koch et al. [24] focused on battery-electric buses and implemented DP while assuming ideal V2I communication and a dedicated traveling road lane to generate energy-efficient driving profiles. The same authors recently proposed an algorithm validated using DP that allows the simultaneous optimization of speed profile and powertrain operation to compare different BEV powertrain architectures [25].

Regarding multiple-powertrain-based control approaches for the following vehicle in car-following scenarios, in 2018, Tate et al. [26] considered different automated driving scenarios by generating the related vehicle speed profiles with a heuristic approach according to engineering experience. Both a CV and a BEV layout were retained, and considerable reductions in greenhouse gas emissions were suggested, especially in the BEV case, thanks to implementing car-following automated driving. Plum et al. [27] in 2018 investigated a CV, an HEV and a BEV powertrain layout while considering a model predictive acceleration controller that exploited information coming from traffic light schedules and the preceding vehicle. The HEV powertrain layout was demonstrated, achieving a greater portion of up to 27.7% energy savings. Nevertheless, the controller was specifically calibrated for a limited number of predefined inner-city driving conditions. Recently, Spano et al. [28] considered a CV and an HEV and estimated the fuel consumption reduction capability at different levels of automated driving using a heuristic approach.

In general, reviewed ACC approaches for enhancing energy-saving of automated road vehicles in car-following scenarios are usually developed and calibrated ad hoc for specific powertrain configurations in terms of architecture and component sizes. Extending the reviewed approaches to reduce the energy consumption of vehicles embedding different powertrain types and component sizes might, in turn, require thorough and time-consuming re-calibration procedures. To the best of the author's knowledge, developing a control approach for the longitudinal speed of automated vehicles in car-following scenarios that can easily adapt to foster energy-saving of different powertrain layouts and component sizes still represents an open research question. To overcome the highlighted research gap, this paper aims to present a new multiobjective optimization-driven ACC algorithm that can easily estimate energy savings and passenger comfort improvements for various powertrain categories when traveling as a following vehicle in car-following scenarios. The proposed ACC approach relies on DP as a widely employed off-line control algorithm capable of identifying the optimal global solution for the considered control problem [29]. Energy consumption minimization and passenger comfort enhancement are considered as conflicting optimization targets for the proposed car-following controller. The ease of adaptability of the discussed approach is suggested through its efficient implementation retaining a CV powertrain, a BEV powertrain, a single-motor parallel HEV powertrain and a dual-motor power-split HEV powertrain. In all the presented cases, only the objective function considered in DP needs to be adapted to the given powertrain category, yet the proposed workflows can be straightforwardly applied considering different component sizes for each propulsion system category. Our results demonstrate the potential of the proposed approach for effectively and easily determining optimization-driven speed profiles over time for the following vehicle in car-following scenarios. Engineers may adopt the proposed optimization-driven ACC approach to evaluate the performance of corresponding real-time ACC approaches and to improve powertrain design methodologies considering enhanced ACC driving. The remainder of this paper is as follows: the considered vehicle powertrain layouts and the related modeling approach are first illustrated. The mathematical formulation of the car-following driving problem is then discussed, and the proposed algorithm is presented. Results are presented over different driving conditions, and conclusions are given.

#### **2. Vehicle Powertrains**

This section aims at describing the considered vehicle powertrain architectures. The adopted numerical modeling approaches find discussion as well. In this paper, a CV powertrain layout, a BEV powertrain layout, a parallel P2 HEV (P2 HEV) powertrain layout and a power-split HEV (PS HEV) powertrain layout are retained. The corresponding schematic diagrams are illustrated in Figure 1, while detailed discussion for each powertrain architecture is reported in the follow-up of this section.

#### *2.1. CV Powertrain*

For the CV powertrain layout illustrated in Figure 1a, the vehicle is propelled by an ICE alone. An automated manual transmission (AMT) is embedded capable of shifting gear according to the ICE speed and the torque request coming from the driver following a dedicated control logic. In general, a quasi-static modeling approach is implemented here in deriving speeds and torques of power components directly from the vehicle speed profile over time for the considered drive cycle [30]. The torque requested by the driver at the driven wheels *Twheels* can particularly be evaluated following Equation (1) [31]:

$$T\_{\text{whech}} = \left(F\_{\text{roll}} + F\_{\text{nisc}} + F\_{\text{aero}} + m\_{\text{veh}\_{\text{eq}}} \cdot \ddot{\mathbf{x}}\right) \cdot r\_{\text{dyn}} \tag{1}$$

where *Faero*, *Fmisc* and *Froll* represent resistive load elements corresponding to the aerodynamic drag, miscellaneous elements, such as road slope and side forces as an example, and rolling resistance, respectively. .. *x* is the vehicle acceleration, while *rdyn* and *mveheq* , respectively represent the wheel's dynamic radius and the vehicle mass, including the equivalent mass of the rotational elements. Subsequently, the rotational speed *ωICE* and the requested ICE torque *TICE* can be computed as a function of the gear engaged *j* following Equations (2) and (3), respectively [32]:

$$
\omega\_{ICE} = \frac{\dot{\mathbf{x}}}{r\_{dyn}} \cdot \pi\_{diff} \cdot \pi\_{AMT}(\dot{f}) \tag{2}
$$

$$T\_{ICE} = \frac{T\_{\text{uvlecls}}}{\pi\_{diff} \cdot \pi\_{AMT}(j) \cdot \eta\_{TR}^{\text{sig}n(T\_{\text{uvlels}})}} \tag{3}$$

where . *x* is the vehicle speed in meters per second, *τdi f f* and *τAMT* represent gear ratios for the differential and the instantaneous gear *j* engaged in the AMT, respectively. *ηTR* is the efficiency of the transmission system, and it is powered to the sign of the torque at the wheels to account for both vehicle accelerating and braking cases.

**Figure 1.** Schematic diagrams of the retained vehicle powertrain architectures, including (**a**) conventional vehicle (CV) powertrain; (**b**) battery electric vehicle (BEV) powertrain; (**c**) parallel P2 hybrid electric vehicle (P2 HEV) powertrain; (**d**) power-split hybrid electric vehicle (PS HEV) powertrain.

Once *ωICE* and *TICE* are determined, the instantaneous rate of fuel consumption can be determined by interpolating in a two-dimensional lookup table with speed and torque of the ICE as independent variables. As concerns selecting the gear in the AMT, a common approach implemented here refers to determining the engaged gear number according to a pre-calibrated two-dimensional lookup table with vehicle speed and driver torque demand as an independent variable [33].
