Proposal of Impedance Control for Electric Vehicles with Wheel Resolver - Application to Hand Assisted Parking and Position Adjustment -

Transcription

1 Poposal of Impedance Contol fo Electic ehicles with Wheel Resolve - Application to Hand Assisted Paking and Position Adjustment - T. Enmei*, H.Fujimoto**, Y. Hoi*** The Univesity of Tokyo --, Kashiwanoha, Kashiwa, Chiba, Japan Phone: enmei@hflab.k.u-tokyo.ac.jp*, fujimoto@hflab.k.u-tokyo.ac.jp**, hoi@hflab.k.u-tokyo.ac.jp*** Abstact Electic vehicles (Es) have an advantage ove intenal combustion vehicles in that the foces applied to the wheel can be estimated fom the wheel velocity and input toque. By exploiting this featue, the authos popose to apply foce contol, which is often used fo industial obots, to Es in ode to achieve much moe human fiendly Es. Many applications of foce contol fo Es ae possible. In this pape, the hand paking assist contol is poposed. The position of the vehicle body is adjusted by the human hand outside vehicles. The high backdivability is achieved by using impedance contol and diving foce contol. Extenal foces applied by human hands and diving foces ae estimated by distubance obseve (DOB). Some assist contol methods ae poposed and the most appopiate one is discussed with simulations by consideing oad suface change and esolution of wheel esolve. Finally, the effectiveness of the poposed method is demonstated by an expeiment. I. Intoduction As the concens of envionmental poblems inceases, Electic ehicles (Es) ae getting attention. Es ae supeio to intenal combustion vehicles not only in the envionmental aspect but also in contollability[]. The esponse of electic motos is much faste than fuel engine, the diving foce on wheels can be estimated[], and it is possible to distibute diving foce within each of the fou E motos. Thee ae many taction contol methods based on these advantages[]. Ou eseach goup also poposed many E contol methods such as slip atio estimation[] and diect diving foce contol method[]. In this eseach, foce contol fo E is poposed. It is based on Es ability to estimate extenal foce, thus ealizing backdivable Es. Reseaches on foce contol ae popula in industial fields so that people and obots can collaboate[], [6]. By applying foce contol to E, vehicles become moe human fiendly. The poposed method is ealized by the use of diving foce contol and impedance contol. Thee can be many applications of foce contol fo Es. In this pape we popose hand assisted paking. Many people ae not good at paking because position adjustment k is vey diffeent fom usual diving. This lack of diving skill sometimes leads to seious accidents. Fig.. Expeimental setup: FPE-Kanon. By applying foce contol to Es, it became possible to adjust vehicle position by human hand. Thee have been many eseaches about paking methods such as automaticpaking[7]. Hand assisted paking is one of the most instinctive method fo humans. The poposed method is convenient in cases which automatic paking cannot cope with. Moeove, impact foce in case of collision can be educed with the aid of impedance contol[8]. In section II, expeimental vehicle models and its contol methods ae intoduced. In section III, some assistance methods ae discussed. By simulations and expeiments, contol pefomance of the poposals ae veified in section I and section. Finally, the conclusion emaks ae in section I. II. Modeling of E and contol methods The expeimental setup and its physical model ae shown in this section. Then, diving foce contol (DFC) and impedance contol ae intoduced. A. Expeimental device Fig. shows the expeimental setup and the concept of this eseach. The vehicle used in this study is FPE- Kanon, manufactued by authos eseach goup. Kanon has fou oute-oto type in-wheel motos and each wheel can be independently contolled. The specifications of the vehicle ae

2 TABLE I ehicle specification. ehicle mass M 8 kg Wheelbase l.7 m Distance fom cente gavity to font axle l f. m Distance fom cente gavity to ea axle l.7 m Gavity height h g. m Font wheel inetia J f. kg m Rea wheel inetia J.6 kg m Wheel adius. m Fiction coefficient µ Slip atio λ T K I s Fig.. Typical µ λ cuve. y T ehicle C Js τs Fig.. Physical model of Electic ehicle. shown on Table I. In this eseach, ea wheels ae used as dive wheel fo assist contol. Because no eduction geas and no gea backlash ae pesent in the units, the motos can dive the wheel diectly. B. Physical Model of E When the cuent contol of moto is fast enough, E mode can be shown as Fig.. Motion equation of wheel and vehicle body can be given as (), (). J i j i j = T i j i j, () M = i j F h. () Hee,,, T,, F h, subscipt i and j epesent wheel angula velocity, vehicle velocity, input toque, diving foce, extenal foce fom hand, font-ea (f, ) and left-ight (l, ) espectively. Diving esistance is ignoed fo simplicity. Slip atio of wheels λ is defined by (). λ = i, j max(,, ϵ). () whee ϵ is a constant used to pevent division by zeo. means wheel speed and is defined as (). =. () When the E is acceleating, is lage than and when deceleating, is smalle than. In this section, we assume the acceleating case and λ is defined as (). λ =. () Fig.. Diving foce contol system. Wheel diving foce can be calculated using fiction coefficient µ and nomal foce N. = µn. (6) Typical elationship between slip atio λ and fiction coefficient µ is shown on Fig.. Magic fomula (7) is well-known appoximate expession of this elation. µ(λ) = D sin(c tan B( E)λ E B tan Bλ), (7) whee B, C, D and E ae non-dimensional constants, usually detemined accoding to fitting. C. Diving Foce Contol Diving foce contol (DFC) was poposed by ou eseach goup[]. The block diagam of DFC is shown on Fig.. DFC is composed of an oute loop contolling, an inne loop egulating wheel angula velocity, and eence geneation pat based on slip atio. µ eaches a maximal value at λ peak and deceases when λ is lage than λ peak as shown on Fig.. Theoe, DFC system should involve slip atio contolle so that maximum diving foce can be obtained. DFC contains slip atio eence geneato based on y and pevents ties fom slipping. y is defined as (8) and has the same dimension as slip atio λ. y =. (8) Incidentally, can be expessed as (9) by using diving stiffness D s and λ. = D s λ. (9)

3 f ext T P C m P M f ext P M Fig.. Typical foce sensoless impedance contol system. C ms F h / C DF F h T ehicle Js (M J )s Fig. 6. Foce assist contol system fo E based on inetia emulation (poposed ). As shown on (9), λ to is the zeo ode plant. Theoe, integato is used fo slip atio contol. By limiting the output of I contolle, y falls within desied ange and tie slipping can be pevented. Diving foce obseve (DFO) is used to estimate foces between wheels and oad. DFO estimates based on () D. Impedance contol = (T J θ). () Impedance contol can change mechanical impedance between obot manipulation and envionment such as stiffness, damping constant and mass. This contol method is often used to implement assist contol o impact foce eduction. Fig. shows the typical impedance contol system based on velocity contol. elocity eence is calculated fom the contact foce and model impedance. Robot velocity is contolled so that the end effecto emulate the model impedance. In Fig., extenal contact foces ae estimated by distubance obseve. III. E hand assisted contol In this section, we popose to apply impedance contol to Es. Impedance contol is a method fo changing contact impedance of obots and is widely used fo industial obots. Howeve, this contol has neve been applied to Es yet. Thee ae vaious applications of foce contol fo E that ae impossible to achieve fo intenal combustion vehicles, such as hand assisted paking. This section discusses how to apply impedance contol to E and methods ae poposed. ms F h C / F h T ehicle (M J )s Fig. 7. Foce assist contol system fo E based on inetia emulation (poposed ). C ms C DF F h T F h / ehicle Js Ms Fig. 8. Foce assist contol system fo E based on inetia emulation (poposed ). A. Simplified DFC fo hand assist paking and extenal foce estimation Expession () shows that it is necessay to contol diving foce in ode to achieve inetia emulation. By contolling, obustness against oad suface change inceases. On the othe hand, the numbe of loops should be minimized to ensue the stability and esponse. Since the velocity of E is limited to low speed egion in assist contol, the wheel slip is vey small. Thus, the diving foce does not each satuation point in assist contol and slip atio eence geneato is not necessay. In ode to incease the system stability, the eence geneation pat is emoved fom DFC fo assist contol. Since F h means extenal foce fom human hands, high esponse is not much impotant fo vehicle speed contol. Fo this eason, wheel angula velocity contol is emoved and a simple stuctue is adopted. When λ is assumed to be zeo, elationship of F h and T is expessed as (). ˆF h = (M J ) T. () Hee, only the tanslational motion is consideed and the input toque F h can be estimated fom (). The fact that F h contains the effect of oad suface change and tavel esistance should be noted.

4 (a) poposed (b) poposed Fig. 9. Simulation esult of F h estimation. (c) poposed [m/s] [m/s] [m/s] (a) poposed (b) poposed Fig.. Simulation esult of. (c) poposed TABLE II Compaison of poposed methods. style of DOB diving foce contol oad suface change quantization noise poposed DOB w good poposed DOB w/o bad poposed DOB w vey good B. Poposal of impedance contol fo Es By incopoating DFC and F h estimation, it becomes possible to apply impedance contol to E. Fig. 6 shows the block diagam of poposed assist contol system (poposed method ). Pop. consists of pats; F h estimation, velocity eence geneation, vehicle speed contol loop, and simplified DFC. By emulating smalle inetia model, assist contol of E is ealized. Resolves ae often used fo wheel angula position detection and its esolution is not so high. Consideing measuement accuacy, poposal adopt as simple stuctue as possible. C. Effect of diving foce contol The necessity of diving foce contol is discussed in this section. Fig. 7 shows the block diagam of assist contol system without DFC (poposal ). By emoving and fom ()-(), () can be obtained. T = (J w M( λ))s. () Because the vehicle speed is low in this system, wheel slip can be ignoed. Assuming λ = in (), () is obtained. This appoximation comes out as a modeling eo. T = (J w M)s. () Fom (), PI contolle is used fo wheel angula contol and pole placement. Since the poposed method has fewe loops and simple stuctue, the system stability is impoved. D. F h estimation method Thee ae ways to obseve F h. One is single DOB embedded in poposal and the othe uses t DOB. In poposed method, in ode to estimate extenal foce F h, vehicle body and wheel plant ae egaded as one and the slip atio is assumed to be. Single DOB method is obust to quantization noise and appopiate fo wheel esolve, whose esolution is not high. Howeve, this method cannot sepaate the effect of oad suface change fom F h. To eliminate the

5 hat (a) Estimated extenal foce ˆF h hat Fd (a) ehicle velocity [m/s] [m/s] (b) ehicle velocity Fig.. Robustness against slip (poposed ). (b) Estimated extenal foce F h Fig.. Robustness against slip (poposed ). assumption that λ =, t DOB must be combined. On the following pages, this method is called poposal. The estimation fomula of poposal ae the following. ˆF h = M ˆ, () ˆ = J T. () Poposed method, at fist, estimates based on input toque and wheel angula velocity. Next, extenal foce F h is estimated using Fˆ d and vehicle speed. Fig. 8 shows the block diagam of poposed method. I. Simulation This section discusses which of poposed method is adequate by the use of numeical simulations. A. Simulations in ideal condition Simulation of hand assist contol fo E is conducted. In the simulation, extenal foce ks on the E plant simulating that human hand pushing vehicle body. The vehicle body is contolled as if the total mass uld become kg even though mass of E body is 8 kg. Contolles ae designed by means of pole placement. Poles of diving foce contolles ae placed on ad/s and those of vehicle speed contolles ae placed on ad/s. Howeve, because diving foce is not contolled in poposed method, only vehicle speed poles ae placed. Fig. 9 and shows the simulation esult of poposed method. Fig. 9 shows the estimated F h and Fig. shows the vehicle speed. F h is estimated coectly to some extent in all figues. The blue and ed lines of Fig. mean the vehicle speed with and without contol. The black line shows the velocity of imaginay vehicle whose mass is kg, taken as eence. Fom the fact that blue line ovelaps the black line, intended contol design is achieved. ehicle moves faste when assist contol is added than the no assistance case, although the same foce is applied. Blue line tacks to black line, meaning that the vehicle speed is contolled as if the E mass is equal to kg. B. Effect of diving foce contol on oad suface change By compaing poposed and on simulations, necessity of DFC is discussed. In addition to fome conditions, oad suface change is lected on these simulation. The fiction coefficient of the oad µ is educed fom.8 to. at sec and its effect is checked. The simulation esults of poposal and ae espectively shown on Fig. and Fig.. Though the oad suface condition have an effect on F h estimation, poposed method ks well. On the othe hand, in poposed method, F h does not convege to value and the assist contol system diveges fom eence. C. Effect of quantization eo The wheel angula velocity is acquied by the esolve. The poposal and ae compaed by a simulation on condition that wheel angle is discetized by esolve. Thee is a lage quantization eo in the estimated F h, leading to deceased

6 pop pop Fig.. Estimation method and quantization noise. contol pefomance. Poposal and ae compaed by simulation consideing quantization eo. The cutoff fequencies of poposal is set to 8 ad/s, and that of poposal is decided so that the noise ipple of both methods become same ode. Fig. shows the estimated F h. Each black, ed, blue line means F h, poposal, and. In ode to achieve same estimation accuacy, the cutoff fequency of poposal must be set to ad/s. It is times lowe than that of poposal.. Expeimental esults In the expeiment, poposed method is consideed. In the expeiment, the ea wheels ae used fo the assist contol and constant input toque equivalent to N is applied, in ode to emulate the F h. Since the slip is small enough to be ignoed, aveage of the angula velocity of ea wheels is used to calculate vehicle speed. Fig. shows the expeimental esult. The blue line in the Fig. (a) shows the smoothed ˆF h and the ed line shows the ˆ of font wheels of the case without contol. Fig. (b) shows the vehicle speed with assist contol. The expeimental esult is simila to Fig. 9 and thus the assist contol is achieved. Thee s geat amount of quantization noise on the estimated foce which makes the velocity eence vibating. ehicle acceleation in the Fig. (b) is slowe than Fig.. The expeimental vehicle speed at sec is only / of simulation. Rolling fictions, tavel esistance and stating toque, which ae not consideed in the simulations, ae the main easons. I. Conclusion In this eseach, foce assist contol fo E is poposed based on inetia emulation and its effectiveness was demonstated by simulations and expeiments. Thanks to this poposed method, back divability of Es can be abitaily chosen and Es can be easily moved by human hand. One main application of this backdivable E is novel humanfiendly paking method. Futhe study contains lateal foce estimation and extenal gavity foce compensation. [m/s] 6 8 Fd_font (a) Estimated extenal foce F h. w/o (b) ehicle velocity. Fig.. Foce assist contol fo E (expeiment). Acknowledgment This eseach was patly suppoted by Industial Technology Reseach Gant Pogam fom New Enegy and Industial Technology Development Oganization (NEDO) of Japan (numbe A87d), the Ministy of Education, Cultue, Spots, Science and Technology gant (numbe 67 and 696). Refeences [] Y. Hoi, Futue vehicle diven by electicity and contol - Reseach on fou-wheel-motoed UOT Electic Mach II, IEEE Tansactions on Industial Electonics, vol., no., pp. 9 96,. [] M. Yoshimua and H. Fujimoto, Diving Toque Contol Method fo Electic ehicle with In-Wheel Motos, IEEJ Tansactions on Industy Applications, vol., no., pp. 7 78,. [] W.-P. Chiang, D. Yin, M. Omae, and H. Shimizu, Integated Slip-Based Toque Contol of Antilock Baking System fo In-Wheel Moto Electic ehicle, IEEJ Jounal of Industy Applications, vol., no., pp. 8 7,. [] K. Fujii and H. Fujimoto, Taction contol based on slip atio estimation without detecting vehicle speed fo electic vehicle, in Fouth Powe Convesion Confeence-NAGOYA, PCC-NAGOYA 7 - Confeence Poceedings, 7, pp [] T. Yoshioka, Stable Foce Contol of Industial Robot Based on Sping Ratio and Instantaneous State Obseve, IEEJ Jounal of Industy Applications, vol., no., pp., 6. [6] N. Motoi, Human Machine Coopeative Gasping / Manipulating System Using Foce based Compliance Contolle with Foce Theshold, IEEJ Jounal of Industy Applications, vol., no., pp. 9 6,. [7] H. Tsung-Hua, L. Jing-Fu, Y. Pen-Ning, L. Wang-Shuan, and H. Jia-Sing, Development of an automatic paking system fo vehicle, ehicle Powe and Populsion Confeence, 8. PPC 8. IEEE, pp. 6, 8. [8] M. R. Dizaji, M. R. H. Yazdi, M. A. Shizi, and Z. Ghaehnazifam, Fuzzy supevisoy assisted impedance contol to educe collision impact, in RSI/ISM Intenational Confeence on Robotics and Mechatonics, ICRoM,, pp