Bench Test of Minimum Time Autonomous Driving for Electric Vehicle Based on Optimization of Velocity Profile Considering Energy Constraint

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1 Bench Test of Minimum Time Autonomous Driving for Electric ehicle Based on Optimization of elocity Profile Considering Energy Constraint Yuta Ikezawa Hiroshi Fujimoto Daisuke Kawano Yuichi Goto Misaki Tsuchimoto Koji Sato The University of Tokyo --, Kashiwanoha, Kashiwa, Chiba, Japan Phone: National Traffic Safety and Environment Laboratory 7--7, Jindaijihigashimachi, Chofu, Tokyo, 8- Japan Phone: Ono Sokki Co., Ltd. -9-, Shin-Yokohama, Kohoku-ku, Yokohama, Kanagawa, -87 Japan Phone: I NTRODUCTION Due to the increasing concerns on environmental and energy problems, many kinds of research have been conducted in the last decade. As one of the countermeasures for this problem, the electric vehicle (E) has attracted great attention due to its environment-friendly characteristics. Although E is environmentally friendly, many kinds of research for improving efficiency have been conducted, for example, designing high efficiency motors [], and new types of power train []. On the other hand, some research solve the energy problem by improving traffic flow by using Intelligent Transport Systems (ITS) []. Traffic flow is improved by platooning running using the information of the front and rear vehicles [] and by introducing virtual traffic lights []. As ITS develop, all vehicles will be automatically controlled. In the era of autonomous driving, vehicle velocity control has been considered for energy efficiency. Therefore maximization of miles-per-charge with time constraint and minimization of the traveling time with energy constraint are possible. The former is useful in saving remaining energy during commuting. The latter is useful in arriving at the destination as soon as possible when going home. The authors research group has proposed the Range Extension Autonomous Driving (READ) system, which extends miles-per-charge by optimizing the velocity profile on the assumption that the stop FPE-Kanon Wheel velocity [km/h] (a) Front motor. Fig.. Torque [Nm] I. Fig.. Torque [Nm] Abstract Recently, Intelligent Transport Systems (ITS) technology have been intensively studied to solve environmental and energy problems by improving traffic flow. Along with the development of ITS and autonomous driving technologies, vehicle velocity control has to be considered for energy efficiency. In this paper, a minimum time autonomous driving (MTAD) system, which minimizes the traveling time considering energy constraint for an electric vehicle (E), is proposed. The proposed method minimizes the traveling time by optimizing the velocity profile and front and rear driving-braking force distribution. The effectiveness of the proposed method is verified by simulations and bench tests Wheel velocity [km/h] (b) Rear motor. Efficiency maps of front and rear motors. point and gradient information are acquired from ITS [6], [7]. However, thus far the minimization of the traveling time considering energy constraint has not been examined. In this paper, the Minimum Time Autonomous Driving (MTAD) system, which minimizes the traveling time with energy constraint is proposed for autonomous driving vehicles. This method introduces the optimal velocity profile by modeling vehicle motion and consumption power and solving an optimal control problem. The effectiveness of the proposed method is verified by simulations and bench tests. II. E XPERIMENTAL EHICLE AND EHICLE M ODEL In this section, experimental vehicle is introduced. In addition, vehicle motion and consumption power are modeled.

2 Tab. I. EHICLE SPECIFICATION. ehicle mass M 8 kg Wheelbase l.7 m Distance from the center of gravity l f :. m to the front and rear axlea l f,l r l r :.7 m Gravity height h g. m Front wheel inertia J ωf. kg m Tab. II. A. Experimental ehicle Rear wheel inertia J ω r.6 kg m Wheel radius r. m SPECIFICATION OF IN-WHEEL MOTORS. Front Rear Manufacturer TOYO DENKI SEIZO K.K. Type Direct Drive System Rated torque Nm 7 Nm Maximum torque Nm Nm Rated power 6. kw. kw Maximum power. kw.7 kw Rated speed 8 rpm rpm Maximum speed rpm rpm In this research, an original electric vehicle FPE- Kanon, manufactured by the authors research group, is used. Fig. shows the experimental vehicle. This vehicle has four outer-rotor type in-wheel motors. Therefore each wheel can be independently controlled, and driving-braking force distribution among all the wheels is possible. Fig. shows the efficiency maps of the front and rear in-wheel motors. Table I and Table II show the specifications of the vehicle and the in-wheel motors, respectively. B. ehicle Model In this section, a four-wheel driven vehicle is modeled. As only straight driving is considered, the torques of the right and left motors are equal. The equations of wheel rotation and vehicle dynamics are given as J ωj ω j = T j rf j, () M = F all sgn( )F DR ( ), () F all = F j, () where J ωj is the wheel inertia, ω j is the wheel angular velocity, T j is the motor torque, r is the wheel radius, F j is the drivingbraking force of each wheel, M is the vehicle mass, is the vehicle velocity, F DR is the driving resistance, F all is the total driving-braking force, and sgn is the sign function. The subscript j represents f or r (f stands for front and r does for rear). The driving resistance F DR is defined as F DR ( ) = µ Mg + b + ρc da, () where µ is the coefficient of rolling friction, b is the factor which is proportional to, ρ is the air density, C d is the drag coefficient, and A is the frontal projected area. Next, the slip ratio λ j is described as λ j = ωj max( ωj,, ϵ), () where ωj = rω j is the wheel speed and ϵ is a small constant to avoid zero division. It is known that the slip ratio λ is related with the coefficient of friction µ [8]. In the region λ <<, µ is nearly proportional to λ. Letting the driving stiffness D s be the slope of the curve, the driving force of each wheel F j is given as F j = µ j N j D s N j λ j, (6) where N j is the normal force of each wheel. During driving at and F all, N f and N r are respectively calculated as N f (, F all ) = [ lr l Mg h ] g l F all sgn( )F DR ( )}, (7) N r (, F all ) = [ lf l Mg + h ] g l F all sgn( )F DR ( )}, (8) where l f and l r are respectively the distance from the center of gravity to front and rear axle, l is the wheelbase, and h g is the gravity height. During straight driving, the required driving-braking force can be distributed to each wheel. Since the motors of the E assumed in this research can be independently controlled, a degree of freedom of the driving-braking force distribution exists. By introducing front and rear driving-braking force distribution ratio k, driving-braking forces can be formulated based on F all using the distribution ratio k as follows: F j = γ j(k)f all, (9) k (j = f) γ j (k) =. () k (j = r) The distribution ratio k varies between and. k = means the vehicle is a front driven system, and k = means the vehicle is a rear driven system. C. Inverter Input Power Model Neglecting the mechanical loss of the motor and inverter loss, inverter input power P in is described as [9] P in = P out + P c + P i, () where P out is the sum of the mechanical outputs of each motor, P c is the sum of the copper losses of each motor, and P i is the sum of the iron losses of each motor. Suppose that the torque caused by the wheel inertia and slip ratio λ j are small enough. Therefore P out is calculated as P out = ω j T j F all ( ) γ j (k)f all + D γ j (k).() s N j (, F all ) Suppose that the magnet torque is much larger than the reluctance torque and that the q-axis current is much greater than the d-axis current. In the modeling of the copper loss P c, the iron loss resistance is neglected for simplicity. Then, the sum of the copper losses P c is given as P c = R j i qj r F all R j K tj γ j (k), ()

3 where R j is the armature winding resistance of the motor, i qj is the q-axis current, and K tj is the torque coefficient of the motor. Next, the iron loss is modeled. Suppose that the magnet torque is much larger than the reluctance torque and that the q-axis current is much greater than the d-axis current. Suppose that the d-axis armature reaction is much smaller than the speed electromotive force caused by the permanent magnet and that the slip ratio λ j is small enough. Sum of the iron loss P i is expressed as P i = = r v odj + v oqj R cj ω ej (L dj i odj + Ψ j ) + (L qj i oqj ) } R cj (rlqj ) γ j (k)f all + Ψ } j P nj R cj K tj,() where v odj and v oqj are respectively the d and q-axis induced voltages, R cj is the equivalent iron loss resistance, ω ej is the electrical angular velocity of each motor, L dj is d-axis inductance, L qj is the q-axis inductance, i odj and i oqj are respectively the differences between the d and q-axis currents and the d and q-axis components of the iron loss current, P nj is the number of pole pairs, and Ψ j is the interlinkage magnetic flux. The equivalent iron loss resistance R cj is described as R cj (ω ej ) = + R cj R cj ω ej. () In (), the first and second terms of right hand side are respectively the eddy current loss and the hysteresis loss. Therefore the inverter input power P in is expressed as a function of, F all, and k as follows: P in (, F all, k) = P out (, F all, k) + P c (F all, k) +P i (, F all, k). (6) III. MINIMUM TIME AUTONOMOUS DRIING In this paper, the case where the vehicle velocity changes from (t ) = to (t f ) = f with a fixed travel distance, energy, speed, and driving-braking force constraints is considered. This method optimizes the vehicle velocity profile and the front and rear driving-braking force distribution ratio, which minimize the traveling time. Therefore, the objective function and constraint conditions are expressed as min. t t = tf t dt, (7) tf P in (x(t), u(t))dt W lim, (8) s.t. W in (t) = t F all (t) F lim, (9) (t) lim, () ẋ = f(x(t), u(t)) ( = M (F ) all sgn( )F DR ( )), () (t) χ(x(t )) = x(t ) x = ( ) (t ) =, () X(t ) X ψ(x(t f )) = x(t f ) x ( f ) (tf ) = f =, () X(t f ) X f where W lim is the energy constraint, F lim is the drivingbraking force constraint, lim is the speed constraint, x(t) = ( (t) X(t)) T, and u(t) = (F all (t) k(t)) T. In this paper, the steepest descent method is used to introduce the optimal velocity profile. The following penalty functions are added to the integrand to apply (9) and () []. r (F P (t) = lim F all (t) ) (F lim <F all (t)),() (F lim F all (t)) r ( P (t) = lim (t) ) ( lim < (t)), () ( lim (t)) where r and r are penalty coefficient. I. A. Comparison Condition SIMULATION In this paper, the following three velocity profile generation methods are considered. Consider the velocity profile given as + a x t (t < t < t ) (t) = lim (t < t < t ), (6) lim a x t (t < t < t f ) where a x = lim( f + ) f lim, (7) X t lim (t f t ) X t = X f X, (8) t = t + lim a x, (9) t = t f lim f a x. () The conventional method is velocity profile expressed as (6) which minimizes the traveling time t t and satisfies the energy constraint under the condition that k =.. Optimize the vehicle velocity trajectory with energy constraint to minimize the traveling time under the condition that k =.. Optimize the vehicle velocity trajectory with energy constraint to minimize the traveling time under the condition that k = k opt. k opt is the optimal driving-braking force distribution ratio which minimizes the inverter input power P in. Since P in (k) is a quadratic function of k, k opt satisfies P in / k k=kopt =. Therefore, k opt is derived as a function of and F all as = k opt (, F all ) ( ) D s N f (,F all ) + r R f K tf + Lqf R cf (ω ef ) Ψ f D s N j(,f all ) +r R j K tj + R cj(ω ej) ( Lqj Ψ j ). ()

4 Tab. III. EXPERIMENTAL CONDITIONS. f X f X F max max W lim case A km/h km/h 8 m N 6 km/h kws case B km/h km/h 8 m N 6 km/h kws B. Simulations Tab. I. TRAELING TIME. Traveling time [s] case A case B Simulations are conducted under the conditions shown in Table III. Figs. and show the simulation results. To analyze the simulation results, mechanical output P out is separated into the power stored as kinetic energy of the vehicle mass P M, the sum of the power stored as the rotational energy of each wheel P J, the loss caused by the driving resistance P R, and the sum of the losses caused by the slip of each wheel P S as follows: P out = P M + P J + P R + P S, () P M = d ( ) dt M, () P J = ( ) d dt J ω j ω j, () P R = F DR, () P S = F all λ j γ j (k) = (P M + P R ) λ j γ j (k). (6) The integrated values of these values are described as W X = tf t P X (x(t), u(t))dt, (7) where the subscript X represents M, J, R, S, c, and i. Table I shows the traveling time of each condition. Compared with the conventional method, the proposed methods and respectively reduce the traveling time by. % and.6 % in the case A, and reduce the traveling time by.9 % and.7 % in the case B. ) case A (W lim = kws): Fig. (a) shows the vehicle velocity. Proposed method reduces the traveling time by increasing acceleration when the vehicle runs at a low speed, even though the maximum velocity is lower than the conventional method. Therefore proposed method suppresses the iron loss P i and the loss caused by driving resistance P R as shown in Figs. (e) and (g). On the other hand, according to Fig. (f), the copper loss P c becomes large than that of conventional method when the vehicle runs at a low speed because the maximum value of total driving-braking force F all is larger than the conventional method. As a result, the percentage of the copper loss W c to the consumption energy W in becomes larger than the conventional method. Proposed method can suppress the motor loss because the driving-braking force distribution ratio is optimized. Therefore a larger driving-braking force than the proposed method can be generated with smaller copper loss P c and iron loss P i. The maximum speed can become higher than proposed method because proposed method can increase the mechanical outputw out by reducing the copper loss W c and the iron loss W i. Therefore the proposed method reduces the traveling time by.8 % compared with proposed method. According to Fig. (h), energy lost through slip W s becomes larger than that of proposed method because slip ratio of front wheel λ f becomes larger than that of proposed method. ) case B (W lim = kws): Fig. shows simulation results. The velocity profile shows the same tendency as case A in both proposed method and. The reduction effect on the traveling time is smaller than case A because the time spent running at the speed limit became larger than case A in both proposed method and. On the other hand, proposed method reduces the traveling time by.7 %. Therefore the reduction effect on the traveling time caused by optimizing driving-braking force distribution ratio k of proposed method and that of proposed method makes no difference.. EXPERIMENTS A. Real Car Simulation Bench Experiments are conducted under the same conditions as the simulations. In the experiment, the Real Car Simulation Bench (RC-S) [] which Ono Sokki Co., Ltd. possesses is used. The drive shaft of a driving wheel is directly connected to dynamo via wheel bearing device. Experiments with various road conditions are possible by changing the vehicle model of the RC-S. In addition, the RC-S is suitable for the transition analysis of an E whose power source is a motor because the response speed of the control is faster than that of the chassis dynamo meter which uses roller whose inertia is large. The RC-S is very useful for this research because we don t have to consider the changes of wind, road surface conditions. B. Control System Design This research was carried out on the assumption that the vehicle velocity can be controlled automatically. Fig. shows the vehicle velocity control system to control the vehicle velocity automatically. The input is the vehicle velocity reference, and these controllers generate the total driving-braking force reference Fall. And then, F all is distributed to the front and rear driving-braking force reference Fj. Considering the slip ratio, the front and rear torque reference Tj is given as Tj = rfj + J ω j a x ( + λ j ), (8) r where the second term of the right hand side means the compensation of the inertia of the wheels. In this research, λ j is given as. (a x > ) λ j = (a x = ). (9). (a x < ) The vehicle velocity controller C PI is a PI controller, and it is designed by the pole placement method. The plant of the vehicle velocity controller is expressed as F all = Ms. ()

5 elocity [km/h] (a) elocity Distribution ratio [ ] (d) Distribution ratio k. Loss caused by F DR [kw] 6 8 (e) Loss caused by driving resistance P R. Copper loss [kw] 6 8 (f) Copper loss P c. Iron loss [kw] (g) Iron loss P i. Conv. Pro. Pro. W i W c W S W J W R W M (h) Consumption energy W in. Fig.. Simulation results (case A: W lim = kws). elocity [km/h] (a) elocity Distribution ratio [ ] (d) Distribution ratio k. Loss caused by F DR [kw] 6 8 (e) Loss caused by driving resistance P R. Copper loss [kw] 6 8 (f) Copper loss P c. Iron loss [kw] (g) Iron loss P i. Conv. Pro. Pro. W i W c W S W J W R W M (h) Consumption energy W in. Fig.. Simulation results (case B: W lim = kws). Fig.. s a x M k r (+λ j ) Jωj Driving + C force PI r distribution + F all ehicle speed control system. F j T j ehicle In the experiments, the poles of the vehicle velocity controller are set to - rad/s. C. Experimental Results Figs. 6 and 7 show experimental results. Experiments were conducted 6 times under respective condition. The inverter input power P in was calculated as P in = dc I dcj, () where dc is the measured input power voltage of the inverter and I dcj is the measured input current of the front and rear inverters. The vehicle velocity was calculated by the vehicle model of the RC-S. According to Figs. 6(b) and 7(b), a larger total driving force than that of simulation is generated immediately after

6 elocity [km/h] (a) elocity Conv. Pro. Pro. (d) Consumption energy W in. Fig. 6. Experimental results (case A: W lim = kws). elocity [km/h] (a) elocity Conv. Pro. Pro. (d) Consumption energy W in. Fig. 7. Experimental results (case B: W lim = kws). starting acceleration. The total driving-braking force constraint is satisfied except in the vicinity of t = t. In addition, the total driving force of the conventional method differs from that of the simulation at the point where the acceleration a x is increased in a step state. These differences are caused by a large jerk. Because of these large jerks, the inverter input power differs from that of the simulation. According to Figs. 6(d) and 7(d), the energy constraint is satisfied in all velocity profile generation methods. Compared with the conventional method, proposed method and respectively reduce the traveling time by. % and.6 % in the case A, and reduce the traveling time by.9 % and.7 % in the case B. I. CONCLUSION In this paper, an optimization method of the velocity profile and driving-braking force distribution ratio is proposed as Minimum Time Autonomous Driving (MTAD). The proposed method reduces the traveling time with energy constraint by increasing the acceleration when the vehicle runs at a low speed and by lowering the maximum speed. The effectiveness of the proposed method is verified by simulations and bench tests. The proposed method can only be applied to straight driving. Therefore future work is to introduce a velocity profile which minimizes the traveling time assuming the course which includes straight driving and turning. ACKNOWLEDGMENT This research was partly supported by Industrial Technology Research Grant Program from New Energy and Industrial Technology Development Organization (NEDO) of Japan (number A87d), and by the Ministry of Education, Culture, Sports, Science and Technology grant (number 67 and 696). REFERENCES [] D. Sato and J. Itoh: Loss Minimization Design Using Permeance Method for Interior Permanent Magnet Synchronous Motor, IEEJ Trans. on Industry Applications, ol., No., pp. 8 6 (). [] M. Takeda, N. Motoi, G. Guidi, Y. Tsuruta, and A. Kawamura: Driving Range Extension by Series Chopper Power Train of E with Optimized dc oltage Profile, Proceedings of the 8th Annual Conference of the IEEE Industrial Electronics Society, pp (). [] J. Zhang, F. Y. Wang, K. Wang, W. H. Lin, X. Xu, and C. Chen: Data Driven Intelligent Transportation Systems:A Survey, IEEE Trans. on Intelligent Transportation Systems, ol., No., pp (). [] J. W. Kwon and D. Ghwa: Adaptive Bidirectional Platoon Control Using a Coupled Sliding Mode Control Method, IEEE Trans. on Intelligent Transport Systems, ol., No., pp. 8 (). [] M. Ferreira and P. M. d Orey: On the Impact of irtual Traffic Lights on Carbon Emissions Mitigation, IEEE Trans. on Intelligent Transport Systems, ol., No., pp. 8 9 (). [6] Y. Ikezawa, H. Fujimoto, and Y. Hori: Range Extension Autonomous Driving for Electric ehicles Based on Optimal ehicle elocity Trajectory Generation and Front Rear Driving Braking Force Distribution with Time Constraint, The st IEEJ International Workshop on Sensing, Actuation, and Motion Control, pp. 6 (). [7] H. Yoshida and H. Fujimoto: Range Extension Autonomous Driving for Electric ehicles Based on an Optimal ehicle elocity Trajectory Considering Road Gradient Information, The st IEEJ International Workshop on Sensing, Actuation, and Motion Control, pp. 6 (). [8] H. B. Pacejka and E. Bakker: The Magic Formula Tyre Model, ehicle System Dynamics: International Journal of ehicle Mechanics and Mobility, ol., No., pp. 8 (99). [9] H. Fujimoto and S. Harada: Model Based Range Extension Control System for Electric ehicles With Front and Rear Driving Braking Force Distributions, IEEE Trans. on Industrial Electronics, ol. 6, No., pp. (). [] T. Ohtsuka: Introduction to Nonlinear Optimal Control, CORONA PUBLISHING CO.,LTD. () (in Japanese). [] D. Kawano, Y. Goto, K. Echigo, and K. Sato: Analysis of Behavior of Fuel Consumption and Exhaust Emissions under On road Driving Conditions Using Real Car Simulation Bench (RC S), 9 JSAE Annual Congress (Spring), ol. 9, pp. 9 (9) (in Japanese).