CT Study of Minimum Collision Avoidance Distance for Electric Vehicles with Four Wheel Independent Driving and Active Front and Rear Steering D

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CT-4-69 Study of inimum Collision Avoidance Distance for Electric Vehicles with Four Wheel Independent Driving and Active Front and Rear Steering Daisuke Sawamura, Hiroshi Fujimoto (The University of

1 CT-4-69 Study of inimum Collision Avoidance Distance for Electric Vehicles with Four Wheel Independent Driving and Active Front and Rear Steering Daisuke Sawamura, Hiroshi Fujimoto (The University of Tokyo) Abstract In this paper, automatic collision avoidance is studied, where it is formulated as an optimal control problem. Furthermore, the problem is designed as minimization of the longitudinal distance for avoiding the collision. The optimal force inputs are obtained by the vehicle initial velocities of longitudinal and lateral, as well as the lateral distance to avoid the obstacle. Then, the inputs are distributed as the forces distributed to the four tires. Simulations and experiments are carried out to verify the effectiveness of the osed approach.,,,, (electric vehicle, four wheel independent driving, active front and rear steering, collsion avoidance, optimal control ). (Electric Vehicle:EV), 3 () EV () (3) EV, (4) (6) (5),,, (6) 4,,,, (6) 4, (3)., Fig.. FPEV-Kanon FPEV-Kanon FPEV-Kanon Table. Vehicle ass Vehicle Specification. 869 kg Wheel base l f.999 m Wheel base l r.7 m Gravity height h g.5 m Tire radius r.3 m Vehicle inertia I 67 kgm Tread width d f = d r.3 m FPEV-Kanon, ±5 Nm, ±34 Nm, ±.35 rad, ±.5 rad (a), δ i,, () (5),F xall,f yall,n z,n t, z,f xij,f yij,d i,l i /6

2 (a) Vehicle model. (b) Friction circle. Fig.. Vehicle model. Fig Avoidance trajectory., i (f, r), j (l, r) F xall = F xfl + F xfr + F xrl + F xrr () F yall = F yfl + F yfr + F yrl + F yrr () N z = d f (F xfl F xfr ) d r (F xrl F xrr) (3) N t = l f (F yfl + F yfr ) l r (F yrl + F yrr ) (4) z = N z + N t (5), (7), Y i,, V, β, γ, δ i, C i, C f F yfj Y f = + T f s (β + l f V γ δ f ) (6) C r F yrj Y r = + T r s (β l f V γ δ r) (7),, T i F zij,, l i, ρ i, h g, a x, a y, sgn (7) F zfj = l r l g ax h g + sgn(j)ρ h g ra y (8) l d j F zrj = l f l g + a x h g + sgn(j)ρ r a y h g (9) l d j j = l(r), sgn(j) = () 3 F xij F yij F zij Fxij + F yij µf zij () (b) (7) η ij η ij := F xij + F yij µf zij F xij + F yi µf zii () η ij (8) (3), 3. (6) 3, (6) 4 (6), v X, v Y Y e,,, X e F opt (t) 3, XY t X(t), Y (t), (),(3) [X() Ẋ() Y () Ẏ ()]T = [ v X ] T () [Y (t e ) Ẏ (t e)] T = [Y e ] T (3), F X + F Y F max (4), X e(t) F opt(t) (6),, ν, ν, t e v X ν (ν t e+ν ) +t e ν ν ν Q= ν +ν (+ν ) 3 v Y ν v Y t e+ ν (ν t e +ν ) +t e ν ν +ν ν ( ν ) 3ν ν (+ν ) (+ν ) 5 + ν Q= (+ν ) 3 Q Y e + {(+ν )(ν ν t e) 3ν } (ν t e+ν ) +t e = (+ν ) Q=ln (+ν )t e ν ν + (ν t e +ν ) +te +ν ν ν + ν +ν v X, v Y, Y e,,, (5) ν, ν, t e, F opt (t) (5) /6

3 Fig Yaw-rate Control System F opt (t) = [F Xopt (t) F Y opt (t)] T = F max t+t e ( t+t e ) +{ν ( t+t e )+ν } ν t+ν t e+ν ( t+t e ) +{ν ( t+t e )+ν } (6) F opt(), F opt() =, rad/s, X e X e = +v Xt e {(+ν )t e 3ν ν } (ν t e+ν ) +t e (+ν ) 3ν ν ν (+ν ) + ν(ν ) ( + ν ) Q (7) 5 (4), = ηµg η η, X e, η,,,, η 4. 3 F opt (t) 4 (9), 4 ( ),, (),(3) 5 Y (t) = Y e t 3 5 Y e t Y e t 5 (8) t 3 e t 4 e F ymax (9) 3 Y e t e = 3 ηµg () t e η, (),(4), N t = [ ] [ ] [ ] Fyf Fyall = () F yr l f l r N t t 5 e 4 ( ),, (),(3) [ Fxl F xr ] = [ (d f +d r) d f +d r ] [ Fxall N z ] () z = N t = N z 4 3 (3) N z, ˆN t, z, ˆN d, () (5) F xall F yall z = l f l r d f d f dr d r F yf F yr F xfl F xfr F xrl F xrr (3), [F xall F yall z ] T b, A, [F yf F yr F xfl F xfr F xrl F xrr ] T x µ, J J = (µη ij) i=f,r j=l,r = x T W x ( W = diag F + F zfl zfr ), F + F, zrl zrr F, F, F, (4) F zfl zfr zrl zrr, W F zij (8),(9) a x, a y J x opt = W A T (AW A T ) b (5), η ijmax.,.5,.3 η X e 5. 5, ρ f = ρ r =.5 µ =.8, C f =, C f = 36, (7),(8) T f = T r =.585 3,, v X =3 km/h,v Y = km/h,y e = m, γ = (P ), N in γ I ns - rad/s,yo - rad/s () F yj (PI ) PI (6),(7) - rad/s 3/6

4 avoidable distance X e [m] Y [m] conv conv maximum (a) Simulation. 5 avoidable distance X e [m] conv conv maximum (b) Experiment. η ijmax Fig. 5. Avoindance distance for each η ijmax.. conv conv 5 5 X [m] (a) Simulation. Y [m] conv conv 5 5 X [m] (b) Experiment. 6 (η ijmax =.5). Fig. 6. Avoindance trajectory(η ijmax =.5). 5, η ijmax =.5 η 7,8,9 7,8,9 (b) (c) (d), 7,8,9 (f), (6), 7,8,9 (h).5, km/h,, F (t),γ = 4 t e, 6,,,, (b) (f),, (c), PI,, (e) N t N z z η ijmax 5, 6 5(a) η ijmax η 5(b) 5(a) η ijmax =.,.5,.3 η,, (Y e =,.97 m,.9 m,.94 m),, 3 cm, X e η ijmax η ijmax =.5 X e 6.48 m, 3.6 m, 3.7 m X e 9.48 %,.57 %,, Y e X e, η ijmax, X e 7., 4,,, NEDO ( ID 5A487d) A :6496 Y. Hori: Future Vehicle Driven by Electricity and Control Research on Four Wheel otored: UOT Electric arch II, IEEE Trans. IE, Vol. 5, No. 5, pp (4) S. Sato and H. Fujimoto: Pitching Control ethod of Electric Vehicle with Braking Torque Estimation, IEEJ, JIASC, pp. 4 44, 7 (in Japanese) 3 N. Ando, H. Fujimoto Yaw rate control for electric vehicle with active front/rear steering and driving/braking force distribution of rear wheels, in Proc. the th IEEE International Workshop on Advanced otion Control, pp () 4,,,,, No.44-3, PP.-4(3) 5. Galvani, F. Biral, B. Nguyen and H. Fujimoto: Four Wheel Autonomous Steering for Improving Safety inemergency Colision Avoidance anoeuvres, The 3th International Workshop on Advanced otion Control, pp (4) 6 Y. Hattori, E. Ono and S. Hosoe An Optimum Vehicle Trajectory Control for Obstacle Avoidance with the Shortest Longitudinal Traveling Distance, Vol.43, No., pp.47 54(7)(in Japanese) 7, (3) 4/6

5 5 δf.4. Fy Fy 5. FXopt,FYopt [N] 5 5 Fyf 4 δr Fx Fyf 3 Fyr 5 Fyr Fx z ,,z [Nm] (e) oment 図 7 シミュレーション結果 (従来法, ηijmax =.5) Fig. 7. Simulation results(conv, ηijmax =.5). 5 δf.4 Fx FXopt,FYopt [N] Fyr 4 5 Fyr..8. Fyf 3 Fy 5 Fyf 4 δr. Fy Fx 5.5 z ,,z [Nm] (e) oment 図 8 シミュレーション結果 (従来法, ηijmax =.5) Fig. 8. Simulation results(conv, ηijmax =.5) Fyf 3 Fyr 5 Fyr. 4 r 5 5 Fyf δ. Fy Fy FXopt,FYopt [N] δf.4 Fx Fx (a) Optimal force z (e) oment ,,z [Nm] 図 9 シミュレーション結果 (提案法, ηijmax =.5) Fig. 9. Simulation results(, ηijmax =.5) 8 西原修, 平岡敏洋, 熊本博光独立操舵車両における横力と制駆動力の最適配分: タイヤ負荷の inimax 最適化, 日本機械学会論文集 C 編, Vol. 7, No.74, pp (6) 9 青木良文, 堀洋一電気自動車における車体すべり角オブザーバのロバスト化と実車データによる検証, 電気学会論文誌Ｄ, Vol.5, No.5, pp (5) 5/6

6 ( η ijmax X e) Table. Experiment results(avoindance distance for each η ijmax ). η ijmax conv [m] conv [m] [m] v.s. conv [%] v.s. conv [%]. 7.7 ( η =.74) 4.8 ( η =.68) 4.7 ( η =.7) ( η =.) 3.6 ( η =.) 3.7 ( η =.9) ( η =.43).77 ( η =.34).5 ( η =.46) 8.5. F Xopt,F Yopt [N],,z [Nm] Fx Fx Fy Fy z δ f δ f δ r δ r Fyf Fyf Fyr Fyr (e) oment (, η ijmax =.5) Fig.. Experiment results(conv, η ijmax =.5) F Xopt,F Yopt [N],,z [Nm] Fx Fx Fy Fy z δ f δ f δ r δ r Fyf Fyf Fyr Fyr (e) oment (, η ijmax =.5) Fig.. Experiment results(conv, η ijmax =.5) F Xopt,F Yopt [N],,z [Nm] Fx Fx Fy Fy (a) Optimal force. z δ f δ f δ r δ r Fyf Fyf Fyr Fyr (e) oment (, η ijmax =.5) Fig.. Experiment results(, η ijmax =.5) /6

IIC Proposal of Range Extension Control System by Drive and Regeneration Distribution Based on Efficiency Characteristic of Motors for Electric

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