Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011
Ecological Driving Based on Preceding Vehicle Prediction Using MPC M.A.S. Kamal ∗ M. Mukai ∗∗ J. Murata ∗∗ T. Kawabe ∗∗ ∗
Fukuoka Industry, Science, and Technology Foundation, 3-8-33, Momochihama, Sawara-ku, Fukuoka, Japan, (e-mail:
[email protected]). ∗∗ Faculty of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, Japan,(e-mail: {mukai, murata, kawabe}@ees.kyushu-u.ac.jp) Abstract: This paper presents an ecological (eco) driving system based on prediction of the preceding vehicle using model predictive control. At any measured road-traffic states it computes the optimal vehicle control input using the models of the vehicle dynamics and fuel consumption. The prediction model the preceding vehicle is formulated based on experimentally obtained driving data. The proposed system is evaluated for driving on urban roads containing traffic control signals at the intersections using the microscopic transport simulator AIMSUN. Significant improvement in fuel efficiency by introducing the model of the preceding vehicle has been confirmed from the simulation results. Keywords: Ecological driving, intelligent transportation systems, model predictive control. 1. INTRODUCTION Emissions of the pollutant gases from a vehicle is directly related to the amount of fuel consumed in it. Whereas, the amount of fuel consumption in a vehicle is related to various physical factors such as type and size of the engine and its power-train, structure of the vehicle against aerodynamic drag, road surface conditions. Beside these physical factors fuel consumption is also influenced by driving styles, see Mierlo (2004). A recent experiment conducted on urban roadways revealed that due to variation in driving styles fuel consumption varies significantly among the drivers, see Taniguchi (2008). Generally, fuel efficiency is improved if a vehicle runs at a steady speed avoiding excessive acceleration and braking, see FORD (2003), Team (2005). Therefore, a fuel-efficient or ecological strategy would be to anticipate what is happening ahead and drive the vehicle with smooth acceleration, cruise at the optimal velocity, and decelerate slowly at stops. For the optimum fuel efficiency, a driver has to anticipate the road traffic situations properly and pose perfect knowledge of engine dynamics of his car, which is hardly attainable by a human driver. Therefore, the driver can be technologically assisted to drive in such optimal fuel efficient style. Driver assistance in various ways for eco-driving has emerged recently. Speculative features of eco-driving are available in the form of driving tips, FORD (2003). Some recently manufactured cars have an indicator that shows green ‘ECO’ mark to a driver when it consumes little or no fuel. A driver would find his driving as ecological only when he maintains a steady velocity at a reasonable level or brakes the car. Some car service providers launched an off-board eco-driving support service for some users in which, after driving record is sent to a telemetric data center for off-line analysis, advice is sent to the driver Copyright by the International Federation of Automatic Control (IFAC)
for improving his driving style in the next time. Based on past performance they have proposed an on-board assistance system to motivate the driver for eco-driving by showing his comparative driving efficiency, his position in fuel composition ranking, etc, see Satou et al (2009). Another approach of assisting a driver uses information of traffic signal, jams, road gradient and distance between cars, and the advice is given in a very rough form, such as ‘keep driving’ or ‘reduce pressure on pedal’, depending on motivation of the driver, Ichihara et al (2009). However, existing approaches to eco-driving assistance are very superficial, they do not provide exact information such as the level of velocity or acceleration required for long term fuel efficient driving by analyzing current vehicle-road-traffic situation and its trend. Recently, a new concept of an Ecological Driver Assistance System (EDAS) has been proposed, see Kamal et al (2010a). Using current road-traffic information the EDAS anticipates future states of vehicles using their simplified dynamic models and calculates the optimum vehicle control input to assist the driver on a flat road. A more comprehensive approach of eco-driving has been presented in Kamal et al (2010b). The influences of resistances and traction forces are included in the dynamic model of the vehicle, and fuel consumption is estimated based on engine efficiency characteristics. Whereas a very simplified model of the preceding vehicle is used, which does not reflect with its real stopping behavior at the red signal. Therefore in such cases, imperfect prediction of the preceding vehicle causes the host vehicle deviate from the optimum energy efficient track. This paper presents an enhanced vehicle control system for eco-driving that can be used for the realization of an EDAS. Based on driving data obtained by experiments
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on an urban road, an enhanced prediction model of the preceding vehicle is formulated to estimate its acceleration or deceleration at any driving conditions. Model predictive control method is used to compute the optimum vehicle control input with a given performance index that includes the costs for not being fuel efficient and unsafe driving. The proposed system is simulated on a crowded urban road in AIMSUN microscopic transport simulator. The proposed system is found to be more fuel efficient than the conventional driving and the simple eco-driving presented previously. Finally, the influence of the eco-driving on the following vehicle is also observed. 2. ECO-VEHICLE CONTROL SYSTEM 2.1 Model of Vehicle Dynamics A simplified model for longitudinal motion control of a host vehicle is formulated considering the presence of a preceding vehicle. The effect of traffic signal is taken into account indirectly through the prediction model of the preceding vehicle. It is assumed that the state equation of the non-linear vehicle control system at any instant t can be represented as follow x(t) ˙ = f (x(t), u(t), q(t)),
(1)
where, x = [xh , vh , xp , vp ]T denotes state vector representing location and speed of the host vehicle (xh and vh ), and location and speed of the preceding vehicle (xp and vp ), respectively, and u is the control input, and q is the time varying parameter representing acceleration of the preceding vehicle. The velocity of the host vehicle at t is subjected to the total forces acting on it, which can be expressed as as follow dvh (t) (2) = FhT (t) − FhR (t), M dt where, M , FhT and FhR are the equivalent mass of the vehicle including its rotating parts, the traction force, and the sum of all motion resistance forces, respectively. The resistance forces include aerodynamic drag, rolling resistance and gradient forces as follow 1 FhR = CD ρa Av vh2 + μM gcos(θ(xh )) + M gsin(θ(xh )), (3) 2 where, CD , ρa , Av , μ, and θ(xh ) are the drag coefficient, the air density, the frontal area of the vehicle, the rolling resistance coefficient and the road gradient angle as the function of location xh , respectively. The traction force is related with the mass of the vehicle and control input as FhT = M uh . The only control input u = uh , related to the traction force of the host, is bounded by an inequality constraint as umin ≤ uh ≤ umax to meet the physical limits of the actuators (the accelerator and brake). The road gradient angle θ(xh ) is usually very small, therefore for computational simplicity it can be approximated as sin(θ(xh )) ≈ θ(xh ), and cos(θ(xh )) ≈ 1.0. 2.2 Prediction of the Preceding Vehicle The movement of the host vehicle is greatly influenced by the presence of an adjacent preceding vehicle. It is
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Fig. 1. Three distinct scenarios of the HV, the PV, and the signal assumed that the preceding vehicle is not influenced by the host vehicle, and its position xp (t), velocity vp (t), and acceleration ap (t) can be measured at real time t. The acceleration (or deceleration, if it is negative) ap (t) depends on the situation of the surrounding road-traffic and driving behavior of the preceding vehicle. Therefore, it is necessary to predict ap (t) in the respective situations on the road for controlling the host vehicle efficiently. To accomplish the modeling of the preceding vehicle for its prediction, various situations are analyzed. Figure 1 shows three distinct scenarios of the preceding vehicle, the host vehicle, and the traffic signal ahead. Figure 1 (a) shows the case in which the traffic signal is green, and there may or may not be some other vehicles in the front of the preceding vehicle. It is assumed that the preceding vehicle would continue moving with the same acceleration until it stops or exceeds a maximum velocity Vm , and it would never move backward. Therefore, at t1 , the acceleration of the preceding vehicle in such situations at t2 = t1 + Δt is predicted as follow {0 < vp (t2 ) < Vm } ap (t1 ), (4) ap (t2 ) = 0, {otherwise} In the case of an idling preceding vehicle at the red signal, Fig.1(b), it is assumed that it would continue idling for a while. If there is no preceding vehicle between the host vehicle and stopping point at the red signal, it is assumed that a dummy vehicle is idling there. In these cases equation (4) can also be applied. Therefore, the signalling system is completely introduced in the modeling without any change in the problem formulation. The time dependent parameter q(t) of (1) is related as (5) q(t) = ap (t). The case shown in Fig.1(c), where the preceding vehicle is approaching a red signal, equation (4) cannot be applied, since the vehicle must decelerate to stop at the end of the section. This is a special case, and it is necessary to construct a prediction model of the the preceding vehicle how it approaches and stops at the signal. To accomplish this, experimental driving data are analyzed. Driving scenarios of three drivers of different skills are recorded experimentally on the national route 129 in Kanagawa prefecture, Japan. On the test drives, each driver stopped their car several times at the red signals. The stopping velocities of the vehicle at various intersections are shown in Fig.2 with respect to the stopping distance l, where the car is moving towards the red signal at l = 0. A typical average velocity curve is formed using the 30 stopping
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patterns and shown by the thick curve in the graph. This average curve is approximated as the braking velocity curve vb∗ (l) by the polynomial of the stopping distance l as follow vb∗ (l) = 5.635 × 10−10 l5 − 3.446 × 10−7 l4 + (6) 7.925 × 10−5 l3 − 8.519 × 10−3 l2 + 0.4805.
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Similarly, for a vehicle with a velocity vb (l) = vb∗ (l) stopping after the same distance L0 , its approximate braking rate ab (l) can be given as ab (l) ≈
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When a vehicle with a velocity v(l) > vb∗ (l), it must stop at the distance l with a higher braking rate than the rate given in (7). Similarly, when a vehicle with a velocity v(l) < vb∗ (l), it may stop at the distance l with a lower braking rate. The assumption that a vehicle stops at the same distance regardless of the velocity leads to the general expression of braking rate ab (l) as follows. For a vehicle at a certain velocity vb∗ and braking rate of a∗b , if its projected distance for a complete stop is L0 , then the magnitude of its current braking rate (7) can be approximately given as
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Substituting the value of L0 from (9) to (10), the approximate braking rate of any vehicle can be obtained as 2 v(l) ∗ . (11) ab (l) ≈ ab (l) vb∗ (l) The above formulation provides a relationship of the braking rate with respect to the both velocity and stopping distance. Figure 3 shows various stopping patterns vpb (l) in the v − l space using (11) predicted at different initial velocities v and stopping distances l. The shapes are very similar to the patterns obtained from the experimental data which were not so smooth due to the influence of other vehicles on the road. In this study, (11) is used to predict the stopping behavior of the preceding vehicle when it approaches a red signal ahead. Therefore, in this case the time dependent parameter q of (1) is obtained as q(t) = ab (l(t))
(12)
Considering the above details of the host vehicle and the preceding vehicle, the state equation (1) of the targeted system can be rewritten as
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Fig. 3. Stopping patterns predicted at various points in the space of the velocity and stopping distance ⎡ ⎤ vh 1 ⎢ ⎥ 2 ⎢ ⎥ f (x, u, q) = ⎢ − 2M CD ρa Av vh − μg − gθ(xh ) + uh ⎥ (13) ⎣ ⎦ vp q where, q is selected either from (4) or from (12) depending on the context described. 2.3 Fuel Consumption Estimation Efficiency of a vehicle at any driving conditions depends on the torque and rotational speed of the engine as illustrated in JSAE (1990). Exact derivation of the fuel consumption equation could be very complex, which is not the main objective here. Instead, an approximate and differentiable function of the velocity and acceleration is sufficient to develop the algorithm for ecological driving.
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An engine torque-speed-efficiency characteristics curves of a typical vehicle equipped with continuously variable transmission was constructed in such a way that the estimated fuel consumption on 10-15 mode matches the catalogue mileage of 17.20 [km/l], see Kamal et al (2011). Fuel consumption data for sufficient sampled values of the velocity and acceleration are obtained from the engine efficiency characteristics map, and the fuel consumption rate in [ml/s] is approximated using a polynomial function as fV = fCruise + fAccel (14) = b0 + b1 v + b2 v 2 + b3 v 3 + a ˆ(c0 + c1 v + c2 v 2 ), where, a ˆ = aV + aθ is the sum of the apparent acceleration of the vehicle aV and acceleration required internally to counteract decelerating force due to the road slope (aθ = gsinθ(x1 ))). The fuel consumption rate at a steady velocity is represented by fCruise , and the additional consumption due to the presence of acceleration is given by fAccel . It is assumed that if the vehicle input uh ≤ 0, no fuel is consumed in the engine. Details of the formation of the above fuel consumption model are described in Kamal et al (2011). 2.4 Model Predictive Control In this proposed model predictive vehicle control, at any time, the system measures the states and derives a set of optimum control inputs required for a safe and efficient travel in the prediction horizon. An optimization algorithm is used to compute the control inputs from a set of initial values obtained or guessed in a suitable way at each sampling interval. The inequality constraint relating to the control input is redefined in the form of equality constraint using a dummy input ud as (15) C(x, u, q) = (u2h + u2d − u21max )/2 = 0. The prediction horizon T is set at a suitable value keeping analogy with anticipation of human driver. A long horizon would be meaningless since the traffic movement has a lot of variations. Since there is no desired state at the end of the horizon, subject to (13) and (15), the performance index is chosen to have following form t+T L(x(τ ), u(τ ), q(τ ))dτ, (16) min J = u
t
clearance from the preceding vehicle, which is multiplied by a varying weight w3 . At each step in the prediction horizon, these weights represent their relative contextual merits or eligibility in the subjective situations. The weight w3 is dynamically calculated as w3 = re−α(herr ) , where the headway error herr is calculated using the current headway (xp −xh )/vh and desired headway hd . The weight w3 ensures a large penalty at the closing preceding car, and negligible penalty when the preceding car is far enough. Even the weight w3 is calculated using a function of states, it is used as a constant or coefficient in the cost function to avoid further complexity in computation. The other weights are kept at some suitable values. The Hamiltonian function is formed using (13), (15) and (17), as follow H(x, λ, u, ψ, q) = L(x, u, q) + λT f (x, u, q) + ψ T C(x, u, q), (18) where, the vector λ denotes co-states, and ψ denotes Lagrange multiplier associated with the constraint. Using the given performance index (16), for a prediction horizon T discretized into N steps of size δ, from virtual time t = nδ to t = nδ + T , the instant and future ve hicle control inputs {unδ (t )}tt =nδ+T are optimized. Con=nδ tinuation and generalized minimum residual (C/GMRES) method is used to generate the sequence of control inputs, see Ohtsuka (2004). Since this method has less computational burden than such iterative methods as Newton’s method, it can be executed in real time for realization of an on-board EDAS. Detailed description of the C/GMRES method including its convergence and computational stability can be found in Ohtsuka (2004). At each sampling opt t =nδ+T (t )}t =nδ , for the time, a set of optimum actions, {unδ instant and future time is available after the optimization. Only the input corresponds to the current time is used to control the vehicle up to the next sampling instant, (19) unδ (t) = unδ (nδ), nδ ≤ t ≤ (n + 1)δ. At each simulation step, the immediate input calculated by this way is fed to control the host vehicle, and the whole process is repeated throughout the driving course, except at idling time. Repeating the whole process and renewing the control input at each sampling time is required to overcome the influence of varying traffic and modeling error in the computation.
where,
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+ w1 a ˆ + w2 (vh − Vr )
+ w3 (hd vh − xh + xp )2 , (17) where, the reference speed Vr is the speed limit imposed on the road section, and hd represents a safe headway while following a preceding vehicle. The cost function L consists of four terms. The first term, multiplied by a weight of w0 , represents the cruising fuel economy (fuel [ml] over distance [m]). The second term with a weight of w1 indicates that the acceleration and braking cost should be minimized. The third term recommends to follow the speed limit imposed on the road section and its influence depends on weight w2 . The last term is to ensure a safe L = w0
The proposed eco-driving system has been simulated by choosing suitable values of the parameters as u1max = 1.80 [m/s2 ], Vr = 13.89 [m/s], hd = 1.8 [sec], and Vm = 15.0 [m/s]. Fuel consumption parameters are approximated as b0 = 0.1569, b1 = 0.0245, b2 = −7.415x10−4 , b3 = 5.975x10−5 , c0 = 0.07224, c1 = 0.09681, c2 = 0.001075. The weights are set at w0 = 110.0, w1 = 7.70, w2 = 0.30, and the parameters of w3 is set at r = 0.016 and α = 2.954. The prediction horizon of T = 50 [s] is split into N = 100 steps of size δ = 0.5 [s]. The car following model implemented in AIMSUN is based on Gipps model, see AIMSUN (2006), Gipps (1981). An extension of AIMSUN simulator was created through
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Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011
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Fig. 5. Conventional driving, (a) the signal, and velocities of the PV, HV and FV, (b) ranges, and (c) the HV input application program interface (API) to collect traffic data and control a vehicle from the outside of AIMSUN for evaluating the developed system.
Figure 5(a) shows the status of the traffic signal (Green, Red, Yellow) and the velocities of the PV, HV, and FV while they run according to the conventional driving. Fig.5(b) and (c) show corresponding inter-vehicle ranges
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An image of the road-traffic network created in AIMSUN is shown in Fig.4, where S1, ..., S14 denote road sections, and PV, HV, and FV indicate the preceding, the host, and the following vehicle, respectively. The single lane route of about 4.1 km consists of 14 sections, and the junctions are connected by traffic control signals, which are synchronously set at 90 seconds cycle including 52 second for green and 2 seconds for yellow signal. The network is set for a traffic density of about 600 vehicles per hour. The roads have a speed limit of 50 [km/h]. The traffic parameters are set stochastically to create a pseudo realistic traffic environment. A vehicle just entered in the first section S1 is selected as the host vehicle, and then it is controlled through API until it exits the last section S14 after traveling the route of about 4.1 km. For the purpose of comparison, the same vehicle with the same initial conditions is controlled by the proposed EcoDriving system, Simple Eco-Driving without the stopping model of the preceding vehicle Kamal et al (2010b), and Conventional Driving based on Gipps model Gipps (1981) (the default method in AIMSUN), separately.
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Fig. 7. The proposed Eco-Driving with stopping model of the PV (a) the signal, and velocities of the PV, HV and FV, (b) ranges, and (c) the HV input and the control input to the host vehicle, respectively. It can be observed that the HV speeds up rapidly to the desired velocity, and stops at the red signal with aggressive braking. Figure 6 shows the same while the HV is controlled by the Simple Eco-Driving method without using the stopping model of the preceding vehicle. Although
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Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011
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The prediction model of the vehicle has been formulated using experimental driving data. The proposed system is simulated on typical urban roads in AIMSUN traffic simulator. The vehicle with the proposed eco-driving is found to be the most efficient in comparison with the vehicles driven by both the conventional and the simple eco-driving methods. By the influence of an eco-driving vehicle the fuel consumption of the following vehicle is also improved significantly. The proposed system can be used to develop an on board EDAS through further technological advancement in intelligent transportation systems.
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ACKNOWLEDGEMENTS
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The authors would like to thank NISSAN MOTOR CO., LTD. for providing experimental driving data and valuable comments on this development.
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REFERENCES
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㪜㪺㫆㪛㫉㫀㫍㫀㫅㪾
㩿㪞㫀㫇㫇㫊㩷㫄㫆㪻㪼㫃㪀
㩿㫎㫀㫋㪿㫆㫌㫋㩷㪪㪤㪀
㩿㪧㫉㫆㫇㫆㫊㪼㪻㪀
㪚㫆㫅㫋㫉㫆㫃㩷㪤㪼㫋㪿㫆㪻㩷㫆㪽㩷㫋㪿㪼㩷㪟㫆㫊㫋㩷㪭㪼㪿㫀㪺㫃㪼
(b)
Fig. 8. Comparative fuel consumption of (a) the host vehicle (b) the following vehicle it accelerates more slowly than the HV driven by the conventional method, it does not anticipate the stopping of the PV, which results aggressive braking at the red signals. Figure 7 shows the same driving scenarios while the HV is controlled by the proposed Eco-Driving method with the stopping model of the PV. It accelerates more slowly than the HV driven by the conventional method, and anticipates the stopping behavior of the preceding vehicle. Therefore, the HV stops at the red signal smoothly by avoiding aggressive braking which ensures reuse of the kinetic energy of the vehicle. The fuel consumed by the HV in three driving methods are compared in Fig.8(a). The proposed Eco-driving HV (with the stopping model of the PV) has saved 13.4% fuel consumption in comparison with the conventional HV. Introducing the stopping model of the PV, its fuel consumption has been improved by 3.7% in comparison with the Simple Eco-Driving HV. In Eco-Driving the HV is controlled in such a way that it can avoid aggressive acceleration and braking. Therefore, the following vehicle has to avoid aggressive driving as well. The influence of the Eco-Driving on the consumption of the following vehicle (FV) has also been investigated in Fig.8(b) for different methods of HV. In these cases the FV is controlled by AIMSUN using a typical conventional method. By the influence of the Eco-Driving HV the consumption of the FV has also been reduced significantly. 4. CONCLUSIONS An eco-driving system based on prediction of the preceding vehicle using model predictive control has been presented.
AIMSUN. (2006). AIMSUN NG User’s Manual. Version 5.1.4 Dec 2006, http://www.aimsun.com/. FORD-WERKE. Ford eco-driving. Schneller schalten, weiter kommen. Cologne. Gipps, P.G. (1981). A behavioural car following model for computer simulation, Trans. Res. Board, vol. 15-B, no. 5, pp. 403-414. Ichihara, T., Kumano, S., Yamaguchi, D., Sato, Y., and Suda, Y. (2009). Driver Assistance System for EcoDriving. in the Proc. of 16th ITS World Congress, Paper ID 3415. Kamal, M.A.S., Mukai, M., Murata, J., and Kawabe, T. (2010a). Ecological Driver Assistance System Using Model Based Anticipation of Vehicle-Road-Traffic Information. in IET Journal of Intelligent Transportation Systems, vol. 4(4), pp. 244-251. Kamal, M.A.S., Mukai, M., Murata, J., and Kawabe, T. (2010b) On Board Eco-Driving System for Varying Road-Traffic Environments Using Model Predictive Control. in proc. of the IEEE MSC2010, pp.1636-1641. Kamal, M.A.S., Mukai, M., Murata, J., and Kawabe,T. (2011). Ecological Vehicle Control on Roads with UpDown Slopes. accepted in the IEEE Transactions on Intelligent Transportation Systems. Ohtsuka, T., (2004). A Continuation/GMRES Method for Fast Computation of Nonlinear Receding Horizon Control. Automatica, Vol. 40, No. 4, pp. 563-574. Society of Automotive Engineers Japan. (1990). Handbook of Automobile Technology. Vol.1, Ch.1, pp.13-16. (in Japanese). Taniguchi, M. (2008). Eco-driving and Fuel Economy of Passenger Cars. in Proc. of Annual Meeting of IEE Japan, pp. S21(5-8),2008. Team Minus 6%. 10 items of eco-driving performance. http://www.team-6.jp/ Satou, K., Shitamatsu, R., Sugimoto, M., and Kamata, E. (2009). Development of an On-board Eco-driving Support System. Nissan Technical Review , No.65(20099) . (in Japanese) Mierlo, J.V., Maggetto, G., Burgwal, E. V., and Gense, R. (2004). Driving style and traffic measures - influence on vehicle emissions and fuel consumption. Proc. of the I MECH E Part D Journal of Automobile Engineering, volume 218(1), 43-50.
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