Eco-driving Optimization Based on Dynamic Programming and Vehicle Connectivity in a Real-World Scenario

1. Introduction

With climate change threatening the future of our environment and society, implementing immediate and effective strategies to curb Greenhouse Gas (GHG) emissions is the need of the hour. The transportation sector is one of the guiltiest parties, accounting for 35% of the worldwide energy consumption [1]. Road vehicles, especially passenger cars and road freight transport vehicles, account for 86% of the global share [2].

Along with GHG emissions, road congestion is a current problem for transport policy at all levels. According to Joint Research Centre (JRC), the cost of road congestion in Europe is estimated to be over €110 billion a year [3]. Not to mention the dramatic effects that traffic has on the increased air pollution [4] and environmental noise [5]. Despite allowing competing flows of traffic to safely cross busy intersections, traffic signals lead to increased congestion in urban areas.

In this framework, global regulatory targets and customer demand are pushing the automotive industry to develop vehicles with improved fuel economy to curb GHG emissions [6]. On the other hand, integrated with the feasible technical solutions aimed at improving the efficiency of current propulsion systems [7], the adoption of Connected and Automated Vehicles (CAVs) could lead, in the next decade, to a major technological revolution in the mobility sector. The benefits of mass adoption of CAVs can range from enhanced road safety [8], improved traffic handling [9], and reduced fuel consumption [10]. Moreover, creating systems in which information and communication technologies can be easily exchanged, namely Intelligent Transportation Systems (ITS) [11], can also have a beneficial effect on reducing congestion in urban areas. Connected vehicles, featuring Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) technologies [12], can have access to the Signal Phase and Timing (SPaT) of traffic lights. This information can be directly transmitted to vehicles through a Dedicated Short Range Communications (DSRC) technology [13] or may become available by the traffic control center through cellular and Wi-Fi networks, namely Cellular Vehicle-to-Everything (C-V2X) [14]. The C-V2X potentiality could be further boosted by a possible coupling with the new 5G mobile network [15] or a joint use of DSRC and C-V2X communications [16]. Alternatively, several studies have demonstrated that SPaT information may be inferred via on-board cameras [16] and via crowdsourcing [17].

Traditional approaches focused more on signal control methods to enhance traffic flow at signalized intersections, such as signal timing optimization [9], or actuated signals application in real-world traffic [18] that could allow to smooth traffic oscillations and decrease vehicle waiting times at intersections. However, with the recent advances in ITS technology, it is also possible to focus on vehicle control, i.e., using V2V and V2I communications to develop eco-driving algorithms. Authors in [19] demonstrated how upcoming traffic signal information can be used by a vehicle’s adaptive cruise control system to reduce idle time at traffic lights and fuel consumption, while [20] introduced a novel software for detecting and predicting the SPaT to enable a Green Light Optimal Speed Advisory (GLOSA) system: i.e., a speed corrector to avoid unnecessary halts at traffic lights. [21] takes into account also the performance degradation of the GLOSA system due to queuing effects and actual tracking driver errors, while [22] introduces the uncertainties of SPaT information due to varying patterns of traffic lights. In the literature, several other applications of eco-driving optimization have been shown: [23] proposes an algorithm to jointly adjust vehicle speeds at intersections and signal timings, while [24] proposes a dynamic eco-driving system for signalized corridors based on an arterial velocity planning algorithm. [24] also assesses the effect of different penetration rates of their algorithm through a sensitivity analysis. Finally, [25] assesses the benefits of incorporating near-term technologies in a predictive management strategy.

From the powertrain control point of view, the increasing adoption of connected vehicles can allow for simultaneously optimizing powertrain control and velocity profile. Several studies have explored methods for optimizing the vehicle velocity profile for Battery Electric Vehicles (BEVs) as well as for Internal Combustion Engine Vehicles (ICEVs). In [26], Dynamic Programming (DP) is used to optimize the velocity of a BEV, while in [27] the fuel consumption reduction of a DP-based algorithm is assessed on a heavy-duty ICEV. However, Hybrid Electric Vehicles (HEVs) and plug-in Hybrid Electric Vehicles (pHEVs) can benefit the most from embedding them in an ITS, since the information from the surrounding environment can be used to optimize their control strategies [28] [29]. Vehicle-to-Everything (V2X) communication along with cloud computing adoption [30] may enable a change of paradigm of the energy management problem: from an instantaneous optimization to globally minimizing it over the entire driver route [31]. In many studies, DP is used for obtaining the optimal solution, but the heavy computation burden of this strategy has made its use largely limited to obtaining an offline performance benchmark. Suitable simplifications to the problem can make the DP real-time implementable, as shown in [32], or the optimization problem can be solved in a remote and/or distributed cloud computing environment [33]. Alternatively, in [34], the optimal solutions provided by DP are used to train Recurrent Neural Networks (RNNs) in improving the energy management of a pHEV.

In this framework, this work aims to assess the benefits that the introduction of V2V and V2I communication, integrated with cloud computing, can have in a real-world route in terms of energy and time savings. The reference scenario is a pre-defined Real Driving Emissions (RDE) compliant route [35], while the simulation scenarios are generated by assuming two different levels of penetration of V2X technologies. DP is used to solve the associated energy minimization problem, where the optimization framework includes information coming from the surrounding environment, e.g., traffic lights state, speed limits, distance to travel, etc. The simulations show that introducing a smart infrastructure along with optimizing the vehicle speed in a real-world urban route can potentially reduce the required energy by 54% while shortening the travel time by 38%. The results of the proposed analysis must be considered as a benchmark since the simulations are carried out for a simplified urban traffic network with vehicles in almost free flow, i.e., no direct constraints related to preceding vehicles. However, it can be conceptually extended to the case of multiple vehicles equipped with the proposed algorithm.

The rest of the paper is organized as follows. In Section 2 the simulation scenarios are introduced along with the description of the virtual test rig used for the simulations. Then, the eco-driving optimization problem is formulated in Section 3. In Section 4, the results of the optimization algorithm are shown in the two different scenarios. In Section 5, conclusions are summarized and further studies are provided.

2. Case Study

2.1. Simulation Scenarios

Energy consumption significantly depends on the route characteristics. In this work, in order to fully collect the variability coming from real-world mission profiles, an RDE-compliant route [35] is chosen as a starting point. The RDE driving cycle is considered as the Reference Scenario, without connectivity. As already described, CAVs technology is largely based on the exchange of different types of data between vehicles (V2V) and with the infrastructure (V2I). Two data types may be differentiated: time-invariant and time-variant ones. Time-invariant data, i.e., road network architecture, road elevation, road slope, road speed limits, speed bumps, etc., can be accessed via a Geographic Information System (GIS) server [36]. On the other hand, time-variant data, i.e., traffic information, road closings, SPaT, etc., could be available only thanks to V2X communication. In this study, it is assumed that both time-invariant and time-variant data can be available through cellular/Wi-Fi networks to the vehicle and that the optimization problem can be solved in a cloud domain. In this framework, the optimal velocity profile can be sent to the driver in the vehicle domain. Starting from the RDE route, Scenario #1 and Scenario #2 were created.

2.1.1. Reference Scenario

The Reference Scenario represents a typical real-world mission profile. It is an RDE-compliant route [35] conducted on public roads in the surroundings of the Italian city of Turin. The route, shown in Figure 1, lasted approximately 92 minutes and was 96 kilometers long. The vehicle position was obtained from Portable Emissions Measurement System (PEMS) and combined with a topographic map. In the simulation environment, the speed profile and the vehicle stop of the Reference Scenario are imposed.

2.1.2. Scenario #1

Scenario #1 was designed to assess the benefits that a global optimization can have on the vehicle speed in a real-world mission profile, still respecting all the full stops imposed by traffic and/or infrastructure. It was generated starting from the Reference Scenario and introducing an intersection regulated by a stop sign every time the vehicle comes to a full stop. As detailed in Figure 2, a vehicle speed window was created where the optimizer is allowed to range. The window’s upper and lower boundaries were thought to merge the effects of speed limits and mild traffic conditions in a realistic scenario. Starting from the speed of the Reference Scenario, the upper and lower boundaries are obtained by applying a moving average over a section of 500 meters +- 20 km/h, respectively. It should be noted that the upper boundary never exceeds 135 km/h, and both the upper and lower ones merge to zero whenever a full stop sign is introduced. As depicted in Figure 3, for Scenario #1 it is assumed that the optimizer can have full access to all the time-invariant data and to traffic information.

2.1.3. Scenario #2

Scenario #2 was designed to assess the benefits that the introduction of a smart infrastructure can have on Scenario #1. It was generated starting from Scenario #1 and converting all the stop signs into traffic lights. When designing traffic lights, the quality of the urban realm should be taken into account. According to [37], for urban areas, short cycle lengths of 60–90 seconds are ideal. Moreover, supposing a minor intersection at each traffic light, a 3:2 ratio is suggested for the amount of green time to improve pedestrian compliance and decrease congestion on surrounding streets. Following these guidelines, in this work, the traffic lights were modeled through square waves with a period and a duty cycle of 1 minute and 60%, respectively (the high period corresponds to the green phase). For the sake of simplicity, only red and green phases were considered, while variability was introduced by randomly assigning the initial phase. The speed boundaries coming from Scenario #1 were modified allowing a time-dependent upper boundary in correspondence with the traffic lights, i.e., the upper boundary assumes the moving average value when the traffic light has a green phase. As depicted in Figure 4, it is assumed that SPaT are deterministic and given; thus, the optimizer can have a-priori access to both time-invariant and time-variant data via V2I communication.

2.2. Vehicle Model

The RDE used as the reference scenario was obtained by collecting data from the PEMS mounted on a Mercedes E300de [38]. This vehicle is a state-of-the-art diesel pHEV available in the European market. Figure 5 schematically shows the powertrain layout and Table 1 summarizes the main vehicle and powertrain characteristics. It features a P2 architecture where a Euro 6d-temp 1950 cc diesel engine is integrated into a 90 kW Electric Machine (EM). Both the ICE and the EM are connected, through a Torque Converter and a 9-speed Automatic Transmission, to the rear axle. The vehicle was extensively investigated through an experimental campaign, followed by the validation of a virtual test rig against the experimental data, as explained in [39]. In this work, a simplified version of the vehicle model, relying on a backward kinematic model [40] developed in a MATLAB environment was used. Moreover, since this work presents a powertrain agnostic optimization (i.e., adaptable for each type of vehicle, e.g., ICEV, HEV, pHEV, BEV), the minimization is performed on the energy.

3. Eco-Driving Optimization

In this section, the algorithm for eco-driving is introduced. It takes advantage of V2X communications and is designed for a simplified urban traffic network with vehicles in free flow, i.e., no direct constraints related to preceding vehicles. V2X information can be used to improve the energy efficiency of a vehicle at two different levels:

• Route optimization: choosing the optimal route;
• Eco-driving: optimize the vehicle speed over the defined route.

This work focuses only on the second stage, i.e., eco-driving. The eco-driving problem can be formalized as an optimal control problem, where the optimizer can access both the vehicle’s GPS coordinates (e.g., total trip length, road grade, and speed limits) and V2X information (e.g., SPaT, traffic conditions). Since the position of all the route features varies in a time-based perspective but remains fixed in a distance-based one, it is beneficial to express the model equations in distance-based coordinates: distance (instead of time) becomes the independent variable.

3.1. Optimal Control Problem

In the following, a formulation of the eco-driving problem in distance-based coordinates is proposed:

$$J=\mathsf{\Phi }(x\left(d_f\right),d_f)+{\int }_{d_0}^{d_f}L(x\left(d\right),u\left(d\right),d)dd$$

(1)

Where J is the cost function, $x\in {\mathbb{R}}^n$ is the vector of the state variable, $u\in {\mathbb{R}}^m$ is the vector of the control variables, d is the distance variable, $L\left(x\right(d),u(d),d)$ is the instantaneous cost function, and $\mathsf{\Phi }(x\left(d_f\right),d_f)$ is the terminal cost. The cost function is minimized by choosing, in the distance interval $[d_0,d_f]$ the optimal control law $u\left(d\right):[d_0,d_f]\in {\mathbb{R}}^m$ that leads to the minimization of the cost function. The cost function defined in Equation (1) is subject to the following constraints:

$$\left\{\begin{array}{c}G\left(x\right(d),d)\le 0\hfill \\ x\left(d\right)\in X\left(d\right)\hfill \\ u\left(d\right)\in U\left(d\right)\hfill \end{array}\right.\forall d\in [d_0,d_f]$$

(2)

Where $G\left(x\right(d),d)\le 0$ denotes a generic instantaneous constraint, while $U\left(d\right)$ and $X\left(d\right)$ are the admissible control and state ranges. Since the main objective of the optimization is to minimize the required energy along with the travel time, the cost function was defined according to the following:

$$J={\int }_{d_0}^{d_f}\beta \frac{e_{fd}(x\left(d\right),u\left(d\right),d)}{E_{fd}}+(1-\beta )\frac{t\left(x\right(d),u(d),d)}{T}dd$$

(3)

Where $e_{fd}$ and t denote, respectively the energy and time demand at the single distance step, while $E_{fd}$ and T denote, respectively, the energy and time demand along the entire cycle. $\beta$ is a calibration factor that can be used to trade-off between the vehicle energy demand and the traveling time. The constraints for the specific problem concern the physical limitations of the actuators (maximum deliverable power) and of the road infrastructure, e.g., speed limits and traffic lights stop. Moreover, limits regarding the maximum acceleration and deceleration values were imposed to enhance the driver’s comfort in the vehicle. As described in Table 2, in Scenario #1 the vehicle speed is the only state variable and vehicle acceleration is the only control one. As for Scenario #2, since the SPaT is time-dependent, the time must be added as a state variable increasing the computational burden. Dynamic Programming (DP) [41] was used by the Authors to solve the constrained optimal control problem. The open-source MATLAB code developed at ETH-Zurich [42] was used for solving the optimal control problem.

3.2. Variable State Search Grid

DP was first introduced by R. Bellman in 1957 and is based on the concept of breaking up sequential decision problems into a finite number of manageable problems wherein the combination of their solutions leads to the global optimal solution of the entire problem. As already reported in [43], the Achilles heel of discrete DP is the “curse of dimensionality”: in n-dimensional state and m-dimensional control spaces, the number of discrete grid points rises exponentially with the dimensions of n and m [44]. Different techniques could be adopted to reduce the computational time required for finding the most energy-efficient path [45]. In order to reduce the computational time, in this work, a variable state search grid was introduced. As shown in Figure 6, this artifice is particularly relevant for Scenario #2 (two control variables) allowing a reduction in the computational time of more than 95%. The computational times here shown refer to a workstation with the following specifications: Intel(R) Xeon(R) CPU E5-2680 v3 @ 2.50GHz, 64 GB RAM. Figure 7 shows the definition of the variable grid in the urban section. The variable speed grid was defined according to the upper and lower boundaries, supposing that the vehicle can never exceed those limits. The variable time grid was defined allowing the optimizer to sufficiently vary around a predicted time of arrival, where V2X and GPS information plays a key role in providing a time arrival estimation. constraints about the maximum available power are introduced.

4. Results

In this section, the improvements in terms of energy consumption and travel time for Scenario #1 and Scenario #2 are shown. Section 4.1 and Section 4.2 show the results for the case with factor $\beta =0.5$ (see 3, i.e., the same weight is given to energy and travel time in the cost function. Section 4.3, instead, shows a sensitivity analysis on the weighting factor $\beta$. For Scenario #1, the vehicle speed was optimized over the entire selected route in order to assess the performance of the optimization algorithm under different conditions, i.e., urban, rural, and motorway. Instead, since most of the traffic lights are present in the first section of the urban profile the results for Scenario #2 will be shown only for this section. The achievable reduction in terms of time and energy reduction will be shown in the entire driving cycle and only in the selected urban profile for Scenario #1 and Scenario #2, respectively.

4.1. Scenario #1

In this section, the optimization algorithm is applied to Scenario #1. This is aimed at assessing the benefits that optimizing the vehicle speed can have in a real-world mission profile, still respecting all the full stops imposed by traffic or infrastructure. Figure 8 shows the optimized vehicle speed for Scenario #1 (blue line) compared to the Reference Scenario (black dotted line). It seems that the optimizer chooses an almost constant speed only in the rural section. In fact, in the urban and rural sections, the vehicle speed tends to follow as much as possible the lower and upper boundaries, respectively. Figure 9 shows a zoom on the urban section. As expected, Scenario #1 presents smoother accelerations and decelerations if compared to the Reference Scenario, although always respecting the full stops imposed by the infrastructure.

Figure 10 shows the achievable reductions in terms of travel time and energy for Scenario #1 considering the entire route (see Figure 8). Nearly 30% of energy reduction can be obtained while decreasing the travel time by almost 10%. These results are achievable while still respecting all the full stops required by the infrastructure analogously to the Reference Scenario. Note also that regenerative braking is not considered in this analysis, so all the energy required for braking is considered lost.

4.2. Scenario #2

Since the a-priori knowledge of traffic lights SPaT can have major benefits chiefly in an urban environment, the optimization performed by the proposed optimizer will be shown only in these conditions. As already described, Scenario #2 perfectly reproduces Scenario #1 but replaces all the traffic stops with traffic lights. Figure 11 shows the vehicle position as a function of the time axis along with all the traffic light phases. The optimizer chooses the best speed trajectory in order to cross all the intersections at a green light. As evident from Figure 12, since the SPaT of the traffic lights is communicated to the optimizer, the vehicle speed is corrected over the entire route to never cross an intersection at a red light. Differently from Scenario #1 (see Figure 9), where the vehicle speed often laid on the upper boundary when the vehicle was not at an intersection, for Scenario #2 an almost constant speed is preferred. The simulations show that a stop sign (or in general a full stop of the vehicle) is detrimental to both the travel time and the energy required. In fact, the deceleration and acceleration phases preceding and following the full stop of a vehicle cause a major reason for energy loss that should be avoided.

As shown in Figure 13, the introduction of smart infrastructure in the simulated scenario leads to a significant reduction both in terms of travel time and energy. In an urban environment, the energy required by the vehicle can be reduced by half while decreasing the travel time by more than 35%. These findings quantify the maximum achievable reductions in energy and travel time in a framework of connected vehicles able to exploit V2X information in a smart infrastructure.

4.3. Sensitivity Analysis

The sensitivity analysis on the weighting factor was performed to assess the impact that the variation of the relative weights in the cost function can have on the results. In Case 1 ($\beta =0.2$) travel time is prioritized at the expense of energy. In Case 2 ($\beta =0.5$) the same weight is given to travel time and energy (results shown in Section 4.1 and 4.2). In Case 3 ($\beta =0.8$) energy is prioritized at the expense of travel time. Figure 14 shows the Pareto front between energy and travel time for both Scenarios #1 and #2 when varying the value of the weighting factor. Focusing on Scenario #1 (blue marks), for all three cases, the energy consumed to perform the cycle is lower than the Reference Scenario one, mainly due to smoother accelerations and increased cruise traveling time. However, for Case 3 (blue diamond), the excessively conservative driving style, despite decreasing by half the required energy, leads to an increase in travel time if compared to the Reference Scenario. Focusing on Scenario #2 (red marks), Figure 14 reveals that the introduction of a smart infrastructure (such as connected traffic lights) can further improve the trade-off between required energy and total travel time. Moreover, Figure 14 shows that the variation of the weighting factor in Scenario #2 leads to a much more restrained variation in the trade-off energy/time. Prioritizing time does not jeopardize the benefits in terms of energy and vice versa.

5. Conclusions

Over the next decade, Connected and Autonomous Vehicles (CAV) technologies are expected to become ever more commonly available on new vehicles. Although their ultimate goal is to improve safety and convenience for customers, they can provide significant information about the planned driver route and the surrounding environment. The knowledge of this information can improve the energy efficiency of a vehicle while reducing, at the same time, travel time. In this framework, this work assessed the benefits that the introduction of Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication, integrated with cloud computing, can have in a real-world profile in terms of energy and time savings. The Reference Scenario is a pre-defined Real Driving Emissions (RDE) compliant route, while the simulation scenarios were generated by assuming two different levels of penetration of V2X technologies. The associated energy minimization problem was formulated and solved by means of a global optimization algorithm, i.e., Dynamic Programming (DP). The optimization framework included information coming from the surrounding environment, e.g., traffic lights state, speed limits, distance to travel, etc. Energy reduction benefits are dependent on several factors: route characteristics, traffic conditions, driver behavior, etc. For the route evaluated in this paper, numerical results showed that, in an urban context, introducing a smart infrastructure along with optimizing the vehicle speed in a real-world route can potentially reduce the required energy by 54% while shortening the travel time by 38%. The results of the proposed analysis must be considered as a benchmark since the simulations were carried out for a simplified urban traffic network with vehicles in almost free flow, i.e., no direct constraints related to preceding vehicles. However, it can be conceptually extended to the case of multiple vehicles equipped with the proposed algorithm. Finally, a sensitivity analysis was performed on the bi-objective optimization cost function to find a set of Pareto optimal solutions, between energy and travel time minimization. Future work will be aimed at testing the proposed algorithm on different powertrain topologies (i.e., BEV, ICE, PHEV) and assessing the impact that a real-time traffic simulator can have on the results.