Intersection Vehicle Cooperative Eco-Driving in the Context of Partially Connected Vehicle Environment

Transcription

1 Intersection Vehicle Cooperative Eco-Driving in the Context of Partially Connected Vehicle Environment M.A.S. Kamal, S. Taguchi and T. Yoshimura Abstract Vehicles with communication functionality are appearing on the roads and transition towards a fully connected vehicle environment will be gradual. Infra-vehicle communication can play a major role in promoting traffic performance in a partially connected vehicle environment. This paper addresses such a real traffic context to present a vehicle control system for eco-driving based on intersection vehicle cooperation. More specifically, the proposed system measures the state of the preceding vehicle by the on-board sensors, and receives information from upcoming intersection signal that exists within the communication range. Next, based on the predicted behavior of the preceding vehicle in a look forward horizon and traffic signal timing, the optimal acceleration of the vehicle is generated in a model predictive control framework. The velocity of the vehicle is dynamically tuned to reduce or avoid idling in red signals either by speeding up or slowing down early, considering constraint imposed by any unconnected preceding vehicles. The proposed eco-driving system is evaluated through microscopic simulation. I. INTRODUCTION Despite wide use of advanced vehicular technologies and traffic management systems, traffic congestion and cost of extra fuel remain crucial issues in the most developed countries. It is a demand of the times to shift the road transportation into a new paradigm with cooperativeautonomous mobility that brings the furthest possible benefits and comfort in every respect to the billions of automobile users worldwide. As expected, vehicles with communication functionality are appearing on the roads. Such vehicles can transmit own information and receives information of other vehicles (V2V) or infrastructure (I2V) within the limited communication range of few hundred meters. At low penetration of such connected vehicles, apparently there is almost no benefit of using V2V communication. A fully connected vehicle environment might be a matter of a few decades, when all the unconnected vehicles will expire and new vehicles with mandatory communication functionality replace those in the natural course of time. However, large efforts from researchers are seen for the fully connected vehicle environment with various cooperative and efficient driving applications. Only few of them address microscopic strategies in driving in the partially connected environment. Although, probability to have direct cooperation between two vehicles is little in low penetration of equipped vehicles, infrastructure with communication functionality can play an important role for improving traffic performance in sensitive M.A.S. Kamal, S. Taguchi, and T. Yoshimura are with System & Electronics Engineering Department I, Toyota Central R&D Labs., Inc., 41-1, Yokomichi, Nagakute, Aichi , Japan. Corresponding author, maskamal@ieee.org areas on roads vulnerable to traffic congestion or accidents, e.g., at intersection, merging area, sag, tunnel. Specifically, intersection-vehicle cooperation can improve performance of both the individual vehicles and intersection, which is addressed in this paper. On urban road-networks, often a signal turns into red when a car is already close to the intersection, where it has to stop with aggressive braking resulting wastage of energy. In addition, idling time at the red signal influences both the fuel consumption and network occupancy of individual vehicles. Traffic responsive optimization of signal timing at intersection can improve intersection performance to some extent but its implementation is costly. As an ultimate solution, recently a few methods have been proposed for signal free coordination or autonomous operation of intersection for smooth traffic flows [2],[1]. However, such system requires not only a fully connected environment but also all vehicles equipped with fully autonomous driving technology. Obviously, realization of such systems is a distant goal of intelligent transportation systems (ITS) at this stage. Beside the traffic signal optimization through traffic responsive or with any kind of signal control technologies, intersection-vehicle cooperation may improve the traffic performance further. Some eco-driving systems use the current signal state for fuel efficient driving on the urban roads, e.g., [3], [4]. However, aggressive braking is inevitable when the red signal appears while the vehicle is already close to the intersection. If the signal timing is known in advance, aggressive braking due to sudden red signal appearance can be avoided easily to improve the driving performance [5]. Recently, a number of methods have been proposed for the optimal driving utilizing traffic signal timing on the given route. Fuel consumption efficiency of a vehicle approaching a single signalized intersection is addressed in [6] with a realistic assumption that SPAT information may be available through I2V communication when the vehicle is close to the intersection. Their focus is on determining desired speed profile based on microscopic fuel consumption of the vehicle without considering much about the influence of the preceding vehicles. Utilizing signal-phase-timing (SPAT) information, a predictive cruise control algorithm is proposed to get through a series of intersections without stopping [7] [8]. A graph discretizing approach along with velocity pruning algorithm is used to obtain energy-optimal velocity of an electric vehicle using a complete knowledge of SPAT in the network [9]. In the most approaches, an ideal environment is considered where the future SPAT information of the entire route are fixed and given in advance.

2 If the distance between two intersections is large and/or red signal period (or cycle length) is comparatively short, these predictive cruise control systems provide tremendous improvement in travel time in the case of free flow. Assumption that SPAT information is available in advance for the entire routes contradicts the traffic responsive signal systems, where the signal timing is regularly tuned depending on the traffic volume. None of these existing methods considers the dynamics of the preceding vehicles in deciding the desired trajectories. Specifically in Japan, urban road networks are often congested where speeding freedom is very limited, distance between intersections can be less than m, and signal cycles are as high as from 9 sec to 15 sec. Therefore, a more realistic driving method needs to be developed. This paper presents a driving system utilizing signal changing time of an intersection and considering the state of a preceding vehicle in a model predictive control (MPC) framework. Introducing a potential function in the performance index, the velocity of the vehicle is dynamically tuned to minimize idling in red signal either by speeding up or slowing down early. The proposed driving system differs from the existing ones in the following aspects as illustrated in Fig. 1. Firstly, it is assumed that the traffic signal timing is broadcasted by the intersection control unit, which is available to only the equipped vehicles within the communication range (usually -3 m from the intersection). If such information is not available, the proposed system drives the vehicle considering only the current signal status. Secondly, the driving system anticipates the state of the preceding vehicle, which may or may not be connected. These considerations make the proposed driving system more realistic and applicable to the partially connected vehicle environment. The proposed driving system has been simulated numerically in a microscopic traffic simulator. The speeding behavior and performance of the vehicles are observed in typical roads with multiple intersections and compared with the traditional driving of unconnected vehicles. II. ECO-DRIVING UTILIZING SIGNAL INFORMATION A partially connected vehicle environment is considered, where only a fraction of traffic has Dedicated Short-Range Communication (DSRC) connectivity. Such connected vehicles may receive the SPAT information broadcasted by the intersection when they are within the communication range, e.g., about -3 m. Depending on the current status and remaining duration of traffic lights, the vehicle has to adjust its velocity dynamically for maximizing its performance through safe driving, i.e., by avoiding any signal violation and regulating a safe distance from the preceding vehicle. The vehicles in the preceding traffic may or may not be connected and driven traditionally. Subject to the constraint imposed by the preceding vehicle, following ecodriving behavior can be realized when the vehicle approaches an intersection. If the signal is going to be red, speed up to a certain level to cross the intersection without signal violation Fig. 1. Schematic of the host vehicle control problem for eco-driving in a partially connected vehicle environment. Signal information through I2V and preceding Vehicle s information are available to the controller of the host. or slowly approach the intersection by passing out the red period, whichever maximize the performance. If the signal is going to be green, cross the intersection after the end of red signal by adjusting the velocity for the optimal performance. A. Control Problem Formulation Considering the above desired driving behavior, a vehicle control problem is formulated to drive a single vehicle, which is also termed as the host vehicle (HV or H) hereinafter for simplicity. It is assumed that the HV measures the state of the immediate preceding vehicle (hereinafter P1) and receives state information of some other connected vehicles, if they exist within the communication range Fig. 1. It is assumed that the intersection broadcasts the details of the traffic signal timing, e.g., current status of traffic lights and remaining duration. Here it is assumed that the other vehicles are driven traditionally according to some car following models by imitating human driving behavior, and their driving system is termed as the traditional driving system () for simplicity. It is assumed that all the vehicles have the identical shape and length. The longitudinal motion dynamics of any vehicle i on the straight and flat road can be expressed in the discrete time framework indexed by t as x i (t +1) = x i (t)+v i (t)δτ +.5u i (t)δτ 2, (1) v i (t +1) = v i (t)+u i (t)δτ, where x, v and u are position, velocity and acceleration of the vehicle, respectively, and Δτ is the size of the discrete step. Let vector s i =[x i,v i ] T denotes the state variables. Only the motion of the HV, denoted by suffix i = h, is controlled by calculating its suitable input (acceleration) u h. A number of constraints are defined considering the safety, comfort and regulation relevant to a road network. The control input of the host vehicle u h is assumed to be bounded u h U:= [u min,u max ]. (2) The velocity of the HV v h is bounded by v h χ := [,v max ]. (3) The minimum gap from the preceding vehicle in any situations is given by the constraint x p x h R + t v h, (4) where t is the minimum time headway, and R is the minimum gap of between the vehicles at stand still condition.

3 following model f a, e.g., intelligent driver model, Gipps model. In general, consider the case of vehicle P1 in Fig. 2. Its acceleration can be given by a p1 (t) =f a (Δx p2 (t),v p1 (t), Δv p1 (t)), (8) Fig. 2. Illustration of acceleration estimation of vehicle P1 using its preceding traffic and red signal at the next intersection. B. Traffic Signal Timing The intersection unit independently controls the traffic signal which is not under the scope of this vehicle control system. The cycle time, split time and offset time are assumed to be fixed within the cycle. In this I2V communication framework, it is assumed that the current state and the next signal transition time is broadcasted to the vehicles nearby. Let λ(t) =(τ g (t),τ r (t),x J (t)) denotes the beginning time of the green and red period, and the position of the next intersection, respectively, which are assumed to be available to the vehicle. Let derive binary variable [θ(t) =1] [τ r (t) t], i.e., θ(t) =if the current signal is red (τ r (t) t). Considering the red signal stopping line x J (t), a constraint is defined as x h (t) x J (t)+θ(t)r e, (5) where R e is an infinitely large distance, which is activated when signal is not red. If the the remaining duration of green signal is known in advance, the vehicle is allowed to cross the intersection within the duration. Although constraint (5) is sufficient to make stopping decision during the red or yellow signal appearance, aggressive braking for a stop is sometime inevitable, specifically when the vehicle is near the critical distance. To avoid any aggressive braking and taking smooth decision, a desired condition is defined as follows. Suppose it is provided that the red signal will begin at τ r (t) > t and end at τ g (t). Binary variables δ 1 (t) and δ 2 (t) satisfying following conditions are defined [δ 1 (t) =1] [x h (τ r (t)) x J (t)], (6) [δ 2 (t) =1] [x h (τ g (t)) x J (t)]. Variable δ 1 (t) =1states that the vehicle has not crossed the intersection at the beginning of the red signal and variable δ 2 (t) = 1 states that the vehicle has already crossed the intersection at the end of the red signal. Therefore, the desired conditions associated with signal violation can be given by δ 1 (t)+δ 2 (t) =1. (7) Note that constraint (3) ensures nonnegative minimum velocity, hence δ 1 (t)+δ 2 (t) =never happens, and δ 1 (t)+ δ 2 (t) =2means the vehicle crosses the intersection during the red period. C. Prediction of the Preceding Vehicle The acceleration of a vehicle in the preceding traffic, which is not under control, can be estimated using a car where Δx p2 = x p2 x p1 and Δv p1 = x p1 x p2 are the relative distance and relative velocity. However, if information of vehicle P2 is absent, car following model (8) cannot be used for estimating acceleration of P1. In such case, following approximation is considered instead { ap1 (t 1) v a p1 (t) = p1 (t) χ (9) otherwise. It states that vehicle P1 continues at the same acceleration as of last step unless it reaches a maximum value or stop completely. It is assumed that P1 is driven by a human driver who may also see the red signal in advance and consider it in deciding the control input. Assume that the same car following model f a is used to determine the acceleration due to influence of red signal, which is given by b p1 (t) =f a (Δx J (t),v p1 (t),v p1 (t)), (1) where Δx J is the distance to the intersection. Considering the influence of both, the acceleration of the P1 is obtained as u p1 (t) =min(a p1 (t),b p1 (t)). (11) D. Optimization Problem An optimization problem with T step finite horizon is formulated. For this purpose, the red period is redefined within the prediction horizon, and requirement (7) is converted into a potential (penalty) function in continuous form as follows L J (t) =w J (δ1(t)+δ c 2(t) c 1), (12) ( where δ1(t) c = 1+e α(x J(t) x h ( τ r (t))) ) 1, and δ c 2 (t) = ( 1+e α(x J(t) x h ( τ g (t))) ) 1 are the continuous function corresponding to the discrete conditions (6). Coefficient α defines the shape of the sigmoidal functions, and the red period within the horizon is denoted by τ r (t) = max{t, τ r (t)} and τ g (t) =min{τ g (t),t+ T }. With a weight w J in (12), L J (t) w J defines a penalty if the predicted states of the vehicle violate the red signal in the horizon. Finally, with (1)-(5) suppose that at time step t the state of the host vehicle is given by s h (t), and estimated state of the preceding vehicle is provided by S p1 =(s p1 (t),...,s p1 (t + T )) in the horizon T. Find a state-feedback controller u h (k), k [t, t+t ] minimizing the following cost function: J(s h (t),u h ( ),S p (t),λ(t)) = L J (t)+ t+t ( wv (v h (k) v d ) 2 + w u u 2 h(k) ). (13) k=t The first term in (13) with a weight w v states the cost of deviation from the desired velocity, and minimization of this term improve both the travel time fuel efficiency. The

4 second term in (13) with a weight w u describes the cost of acceleration (deceleration) to be minimized for both the driving comfort and fuel efficiency. Note that the last term is only activated when the red period enters in the horizon t to t + T. This cost will be dominating with a large w J, its minimization means either decelerate slowly or speed up (beyond v d ) for red avoidance. At each time t, the states of vehicles are measured, information of traffic signal and other vehicles are received, if they are available via I2V/V2V. Next, the future states of the preceding vehicle in the horizon is estimated. Using these information, the optimization problem is solved to obtain control input of the host vehicle u h (t),...,u h (t + T ). Control input corresponding to the current time u h (t) is executed and the process is repeated in the model predictive control framework. III. SIMULATION RESULTS The proposed eco-driving system () based on intersection-vehicle cooperation is evaluated through microscopic traffic simulation. In the simulator, traffic flows are realized using the car following model IDM (intelligent driver model) [1] with the lane change model MOBIL (minimizing overall braking induced by lane change) [11]. Typical parameters of both IDM and MOBIL are used for controlling the vehicles. The fuel consumption of the vehicles are estimated using the model based on velocity and acceleration which was proposed in [12]. The parameters and the preferences are set as v max =18m/s, u max =4m/s 2, u min = 6 m/s 2, t =1. sec, v d =15.27 m/s (55 kph), R e = 5, w v =3, w u =5, w J = 1, α=.15. The prediction horizon of 25 sec is used, and discrete time framework is based on the step size Δτ =.5 sec. At first, the proposed eco-driving system () is compared with the traditional driving system () for driving a vehicle approaching an isolated intersection without the presence of a preceding vehicle in the vicinity. The speeding behavior and driving performance of the vehicle are observed on the single lane road of 1. km with an intersection at.5 km. Fig. 3 (a) and (b) show two cases of relative arrival of the vehicle with respect to the signal cycle. Each shows velocity, cumulative fuel consumption and time of the vehicle under control with respect to its position on the road. In the distance-time graphs, the red period is marked by a red bar. In Fig. 3 (a), the vehicle approaches a red signal that later turns into green. In traditional driving only the current state of traffic light is considered, the vehicle stops at the red signal by decelerating at some desired rate, idles for a while and then crosses the intersection. In contrary, the vehicle under the uses the information of the remaining period of current signal, and reduces its velocity early to avoid a full stop at the intersection. The corresponding cumulative fuel consumption and travel time show that the proposed driving system out performs the traditional driving in both indices. In Fig. 3 (b), the vehicle approaches a green signal that later turns into yellow and then red. In traditional driving, the vehicle has to stop critically with aggressive braking due to sudden appearance of the red signal and idle almost entire red period. In contrary, the vehicle under uses information of the remaining period of current signal, and smoothly speeds up to avoid the red signal at the intersection. The corresponding cumulative fuel consumption and travel time shows that the proposed driving system significantly out performs the traditional driving in both indices. Although desired velocity of 55 kph is used in the optimization, by the influence of potential function the raises the velocity as high as.9 kph and in order to avoid the red signal. However, if such increase in velocity were not sufficient, the vehicle would choose to decelerate very smoothly similar to the case Fig. 3 (a). Next, the evaluation is conducted on a single lane road consists of multiple intersections. The traffic lights are set synchronously at 9 sec cycle with sec red and 5 sec green periods (including 4 sec amber period). In a high traffic volume, flowing behavior of all vehicles are observed for a period 5 sec. At first all vehicles are driven traditionally, i.e., without using signal timing in advance. Figure 4 (a) plots trajectories of all vehicles. The grids on the vertical axis show the position of the intersection stopping line and grids on the horizontal axis shows the green-red duration in the observed period. As usual, vehicles under the run at steady velocity and decelerate for a stop at red signal when it is near the intersection, and in the most cases, they idle at the red signals. Figure 4 (a) shows the case where some vehicles (one in every tenth vehicle) are driven by the proposed by utilizing the broadcasted signal timing information from the intersection when they are within the communication range. The trajectories of those vehicles are shown by thick green curves in the graph. These vehicles predict the preceding traffic and use the advance signal timing in deriving the control inputs. In the most cases these vehicles avoid a complete stop at red signal by early velocity adjustments. Interestingly, by their influences the vehicle closely behind them unconsciously avoid idling time and consequently improved their performance. Finally, the overall performance of the vehicles under proposed driving system is compared. Improvement of fuel economy and travel time are shown in Table I. More specifically, individually vehicles with the green curves in 4 (a) are compared when they are traditionally driven as given in 4 (b). These vehicles improved their fuel economy by 6.4% and travel time by 4.7% by utilizing the traffic signal and taking anticipative action. The overall traffic (mixed vehicles shown in 4 (a)) improved their fuel economy about 2.% and travel time about 2.8% compared to the case of traffic in 4 (b). Whenever a vehicle under the slowly stops at the red signal, any close traditional vehicles behind are forced to follow it. Consequently, they also improve their performance. Therefore, even at low penetration of connected vehicles, they always have a positive impacts on traffic flows if such signal information is available from the intersection. However, on double-lane roads, the traditional vehicles may injudiciously change the lane due to a slow vehicle and their performances are not improved at the same level. It is found that on the double lane roads with

5 7 7 Velocity (kph) 5 3 Velocity (kph) Fuel (ml) Fuel (ml) Time (sec) 8 Time (sec) (a) (b) Fig. 3. Behavior of the controlled vehicle under the proposed eco-driving system () and traditional driving system (). (a) The vehicle approaches a red signal that later changes into green. (b) The vehicle approaches a green signal that later changes into red. Each case shows comparison of velocity, cumulative fuel consumption and travel time (including the red period) for traveling 1 km road including an intersection at.5 km. the same penetration rate, the vehicles improved fuel economy by 4.5% and travel time by 2%. Performance of the overall traffic improved as follows: fuel economy by.73% and travel time by +.92%. The reason of travel time deterioration of the proposed on multi-lane roads is investigated further. The host vehicle under the slowly approaches the red signal and creates a longer gap. Since it is general tendency of drivers to overtake a slow vehicle on multi-lane roads, the vehicles on the other lane exploit the situation and cut-in and the vehicle behind also change the lane due to slow preceding vehicle. Consequently, the vehicle fall behind and requires a bit longer time to complete the travel. However, such lane changes may reduce with higher penetration of the vehicles or by notification to the traditionally driven vehicles. Further investigation will be done in the future. IV. CONCLUSION In this paper an intersection vehicle cooperative ecodriving system is proposed for efficient driving of vehicles on urban roads in a partially connected vehicle environment. The proposed eco-driving system decides to decelerate or TABLE I PERFORMANCE IMPROVEMENT WITH 1% OF VEHICLES IN TRAFFIC ON SIGNAL LANE AND DOUBLE LANE ROADS. vehicles All vehicles Single Lane Fuel economy: +6.4% Fuel economy: +2.% Road Travel time: +4.7% Travel time: +2.8% Doulbe Lane Fuel economy: +4.5% Fuel economy: +.73% Road Travel time: -2.% Travel time: +.92% speed up for avoiding red signal when signal timing is provided in advance considering the dynamical presence of the preceding vehicle. Despite discrete signal change events, the influence of traffic signal is approximated using a continuous function and used in the performance index that makes the optimization implementable in real time. Numerical simulation reveals that the vehicles with the proposed eco-driving system have improved the fuel economy and travel efficiency significantly compared with the traditional driving. By the influences of the eco-driven vehicles with low penetration, the traditionally driven vehicles also improved their performance considerably.

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