Reduction of Steering Effort in the Event of EPAS Failure using Differential Braking Assisted Steering.
Power assisted steering systems are used in the vast majority of modern vehicles. They apply assistive force to the steering system in order to reduce driver steering effort. Electric Power Assisted Steering (EPAS) has many advantages over the conventional Hydraulic Power Assisted Steering (HPAS), with regard to fuel efficiency, control flexibility, and environmental compatibility . As a result, EPAS is rapidly replacing HPAS in modern-day vehicles. Recent trends towards vehicle electrification and autonomous driving have also facilitated the rapid adoption of EPAS.
Despite the many advantages over HPAS, reliability issues of EPAS are also raising public concerns. Electrical and/or electronic component defects may cause EPAS failure and shutdown. According to NHTSA reports [2, 3, 4], excessive steering effort is demanded from driver in the event of EPAS failure, resulting in dozens of crashes and injuries, and a couple of OEM safety recalls in recent years [5, 6, 7, 8, 9]. Many efforts have focused on developing fault tolerant features for electrical and/or electronic components of EPAS to prevent failures from happening, e.g., [10, 11. 12. 13]. However, there is no work in the open literature or patents addressing safety measures after EPAS shutdown. OEMs have argued that, in the event of EPAS failure, the driver is still capable of controlling the vehicle, since mechanical linkages remain intact and the system merely reverts to manual steering state. However, in reality, steep increase of steering effort may cause driver panic and loss of vehicle control, as in some of the reported crashes . Therefore, it is of immense importance to incorporate protective measures to alleviate driver's steering effort in the event of EPAS failure.
To meet this objective, the primary contribution of this paper is in proposing a backup system for EPAS called Differential Braking Assisted Steering (DBAS), and evaluating it through simulations. As the name implies, DBAS employs differential braking to help reduce driver steering effort upon EPAS failure. DBAS is inspired by Differential Drive Assisted Steering [15. 16. 17]. which utilizes the independent driving torque feature of in-wheel-motor vehicles to alleviate steering effort, with a goal to replace EPAS (or HPAS) in such vehicles. However, unlike Differential Drive Assisted Steering, DBAS makes use of differential braking capabilities which are available in virtually all modern-day vehicles. Furthermore, the purpose of DBAS is to serve as a backup safety system, not to replace EPAS like Differential Drive Assisted Steering.
It is worth mentioning that differential braking has been exploited for various purposes related to vehicle control. A prime example is Electronic Stability Control (ESC), which is now a must-have feature for new vehicles sold in the United States. ESC uses differential braking to counter understeer and oversteer, thus keeping the vehicle stable during steering maneuvers [18.19]. Differential braking has been proposed by Pilutti et al. to correct driver steering input for an unintended road departure system [20,21]. Differential braking has been proven to reduce turning radius in long-wheelbase vehicles . It can also serve as backup for Steer-by-Wire systems when the steering motor fails and the front wheels cannot steer .
The rest of this paper is organized as follows. Section 2 introduces DBAS, together with its control strategy, followed by a presentation of simulation-based case studies carried out in CarSim to evaluate DBAS performance in various realistic safety-critical driving scenarios. In Section 3, a vehicle dynamics model combined with CarSim simulation results are used to demonstrate reasons why DBAS reduces steering effort. Potential side effects of DBAS and possible solutions are also discussed, as a motivation for further study on driver reaction to DBAS as a backup safety strategy. Conclusions and future work are then presented in Section 4.
CONTROL STRATEGY AND PERFORMANCE EVALUATION OF DBAS IN CARSIM
Control Strategy of DBAS
The main objective of DBAS is to reduce driver steering torque in the event of EPAS failure. Since the best case scenario is to reduce steering torque to the same levels as when EPAS functions well, it is natural to choose it as a reference. In DBAS, feedback control is designed to minimize the difference between reference and driver's actual steering torque through differential braking, as illustrated in Figure 1. Measurements of vehicle speed V and lateral acceleration [A.sub.y] from vehicle sensors are used to determine reference steering torque [T.sub.r] from the reference steering torque map. The obtained value of [T.sub.r] is then compared with driver input steering torque [T.sub.sw], resulting in error signal [T.sub.e]. A PI controller operates on [T.sub.e] to produce [T'.sub.e], which is then used to determine the differential braking command [T.sub.b]. The sign of [T'.sub.e] decides whether brakes are to be applied to the left or right wheels of the vehicle. For example, if the driver is making a right turn upon EPAS failure, and the steering torque is larger than the reference, making [T'.sub.e] greater than zero, brakes will be applied to the right wheels. The brake control gains are also speed-dependent. If vehicle speed is higher than a threshold, gain of right front brake KRF will become the only non-zero value in command [T.sub.b], i.e., applying only right front brake. Otherwise, both [K.sub.RF] and [K.sub.RR] will be non-zero (i.e., applying both right front and right rear brakes) in order to amplify the effect of differential braking at lower speeds. Finally, the brake system receives the command [T.sub.b] and actuates the brakes accordingly. The feedback loop between the vehicle (plant) and DBAS controller minimizes the error [T.sub.e] continuously.
The torque map widely used for steering feel design is transformed and put to use for DBAS [1,15]. The reference steering torque map can be created based on a fully functional EPAS through standard tests for vehicle handling evaluation, such as weave test and double lane change test [24,25]. A 2D map, shown in Figure 1. is developed by setting a constant ratio of steering torque to lateral acceleration (e.g., [k.sub.1]) at a certain speed (e.g., [V.sub.1) based on the EPAS-on case (i.e., EPAS is fully functional) as shown in Figure 2. Variable ratio is not considered because steering feel is not the primary concern upon EPAS failure. A flatter slope in on-center zone, though results in less "road feel", makes the difference larger between actual steering torque upon EPAS failure (i.e., the EPAS-off case) and the reference steering torque as soon as driver starts steering, thus quickening system response. Without compromise in system performance, further improvement of reference steering torque map may consider mimicking EPAS torque assist feature. Lateral acceleration is chosen over steering angle as the measure of map due to hardware concerns. According to OEM document , steering angle signal comes from either angle sensor mounted on steering column or motor position sensor within EPAS assist motor. For the latter configuration, measurements of steering angle may become troublesome to get access to upon EPAS failure. Since lateral acceleration is also commonly used in vehicle handling evaluation, it is considered a better choice for DBAS in this paper.
According to DBAS control strategy, measurements of vehicle speed, lateral acceleration, and steering torque, and access to brake system are only required for DBAS to realize its function. In the event of EPAS failure and shutdown, vehicle speed and lateral acceleration sensors and brake system will not be affected. Mnor hardware modification, i.e., an extra signal output cable, is needed to enable the steering torque sensor to output its signal to the DBAS control unit. Therefore, as a backup system, DBAS only requires software upgrades and minor hardware modification.
CarSim Simulation Configuration
CarSim is widely used in the automotive industry for vehicle system-level simulation and analysis. Since CarSim has detailed and accurate vehicle models already built-in, it can be used to evaluate the performance of the proposed DBAS system in simulations. The modeling process of vehicle and steering system in CarSim involves calibration of model parameters for realistic steering torque results. Steering system parameters of an actual passenger vehicle and its steering torque test data for two cases (i.e., with and without EPAS assist) are provided in report , and are used to calibrate parameters in CarSim through simulations of a 30-meter steady state circle test and static steer test. The calibration of CarSim vehicle model using actual system parameters and test data allows more realistic evaluation of DBAS performance in simulations.
The selection of driving scenarios for simulation and DBAS evaluation considers whether they are safety-critical in the event of EPAS failure. Report  listed common steering maneuvers driver may encounter, including 1) static steer; 2) parking lot maneuvers; 3) intersection turns; 4) curvy roads with speed limits at or under 25 mph; 5) curvy roads with speed limits at or under 35 or 45 mph; 6) highway exit ramps; 7) highway driving at or above 60 mph, etc. According to investigation report , steering maneuvers at or under 30 mph may induce excessive steering torque demands upon EPAS failure; test data in  confirms this statement, showing that EPAS usually provides more than 70% of the total steering torque in maneuvers within this speed range. This means that driver needs to apply three times more effort upon EPAS failure. Not every driver has the ability to handle this steep increase well, in which case he/she may lose control of the vehicle. Road designs also have an influence on steering torque applied by driver. For instance, highways or roads with higher speed limits are usually not designed with sharp turns. The designed lateral acceleration levels are usually under 0.2g. Hence steering torque demands are not high even when EPAS fails. Based on this fact, the 5th and 7th scenarios above are excluded. Static steer test is also excluded, since differential braking inherently cannot help reduce steering torque at zero speed. However, since no accidents tend to happen when vehicle is at standstill, the inability of DBAS to handle this scenario is acceptable.
The selected driving scenarios and their parameters are listed in Table I, together with the main purpose of considering each scenario. Note that serpentine driving course, which simulates curvy roads with lower speed limits, is considered here because it has been used before for similar testing of vehicle maneuverability upon HPAS failure . U-turns represent the extreme case of parking lot maneuvers, which usually involve low-speed sharp turns. Driver control in CarSim is set to follow the designed path and speed of each of these driving scenarios. This set of configurations help demonstrate whether DBAS can reduce steering torque and maintain control of the vehicle upon EPAS failure.
CarSim Simulation Results
In this subsection, the driving scenarios listed in Table 1 are simulated, and steering torque results are compared among three cases, namely, EPAS-off, EPAS-on and the proposed DBAS. The trajectory following capability of DBAS is also illustrated.
Highway Exit Ramps
Figure 3(a) shows vehicle trajectory on highway exit ramp. From zoom-in view it can be seen that the driver is able to follow the designed path with a maximum deviation of 0.25 m when DBAS is working, which indicates that the vehicle is stable and sufficiently under control. Figure 3(b) shows the simulation results of steering torque, the primary measure of DBAS performance. When EPAS is on and off, steering torque goes from a steady-state value of 8.45 to 21.43 Nm, respectively. If EPAS fails suddenly, this 150% increase in steering torque could take the driver by surprise and lead to loss of control. However, with DBAS active, steering torque is reduced to the same level as EPAS, thus proving its potential to act as an effective backup system in this scenario.
Serpentine Driving Course
As mentioned in the preceding section, the serpentine driving course (illustrated in Figure 4(a)) has been used in a test to examine whether drivers are capable of controlling the vehicle after total failure of HPAS . Therefore, it is reasonable to apply it to the case of EPAS failure in order to evaluate the performance of DBAS. The serpentine course requires driver to switch steering angle and torque quickly, thus it helps evaluate the transient response and performance of DBAS.
The steering torque results in Figure 4(b) indicate that driver may lose control of the vehicle in the event of EPAS failure, considering the fact that maximum steering torque driver needs to apply goes from 10 to 27 Nm. The steering torque level when DBAS is active is significantly less compared with the EPAS-off case. Although full reduction is not achieved and overshoot emerges in the transient process, the maximum level with DBAS active is still only about 15 Nm. 27 Nm is identified as an endurable steering torque level for all the drivers evaluated in the HPAS test in . This suggests that, even though an increase from 10 Nm to 15 Nm requires some extra effort by driver, it is well within the endurance level of most drivers. On the other hand, the jump from 10 Nm to 27 Nm brings steering torque to the brink of endurance for most drivers.
One of the most common steering maneuvers are intersection turns. According to Ref , a few crashes have happened in this scenario upon EPAS failure because drivers were not able to steer the vehicle as they wished. Therefore, DBAS should handle this situation and avoid excessive steering effort. A 25-ft. radius right turn and 75-ft. radius left turn are selected for demonstration. Different target speeds are assigned to these two scenarios, so that DBAS performance under different vehicle speeds can be evaluated.
Figure 5(a) and (b) show the steering torque results for a right and left turn respectively. Simple moving average with window size of 50 sample data is applied to the steering torque responses for all three cases of the right turn scenario due to system noise generated by CarSim model. For both scenarios, DBAS is shown to reduce steering torque to similar levels as EPAS, freeing driver from excessive effort and potential accident.
Parking Lot U-turns
For parking lot maneuvers, vehicle speed is usually under 10 mph. Ground friction becomes a significant portion of contribution to steering effort in this scenario, making EPAS power assist crucial. Report  reveals that excessive steering torque upon EPAS failure may cause driver arm or back injuries and parking lot accidents. Therefore, it is important to evaluate DBAS performance in low speed maneuvers.
The double U-turn path, shown in Figure 6(a) considers minimum turning radius of the vehicle model, i.e., 5.7 m. Two different vehicle speeds result in different lateral acceleration levels, thus different steering effort demands upon EPAS failure. Steering torque results in Figure 6(b) show that DBAS can partially reduce steering torque. Contrary to the previous scenarios, both front and rear wheels of one side apply brakes during U-turns, because braking only one front wheel is found to be less effective in reducing steering torque at lower speeds.
The investigated scenarios demonstrate that DBAS is effective in reducing steering torque to similar levels as EPAS in various steering maneuvers and at different vehicle speeds. The next section provides some insights into why DBAS is able to effectively reduce steering torque; it also discusses side effects of DBAS on vehicle and driver.
PRELIMINARY ANALYSIS OF DBAS
Analysis of DBAS based on Vehicle Dynamics
It is well known that differential braking causes the vehicle to steer to the side that has the larger brake force , which explains why DBAS facilitates steering of the vehicle. However, why DBAS reduces steering torque still remains a question. This subsection focuses on explaining the reasons for steering torque reduction from both steering system and vehicle point of view.
For typical front-wheel drive vehicles without torque vectoring technology  or in-wheel motors, driving torque [T.sub.t] is evenly distributed to both front wheels, shown in Figure 7. Considering the same normal loads and road friction on both sides of the vehicle, this leads to the same longitudinal forces [F.sub.x,LF and [F.sub.x,RF] of left and right front tires. Their resultant torques from scrub radius around kingpin [T.sub.lonLF] and [T.sub.lon,RF] are therefore always canceled out, and no force is transmitted to the steering rack through the mechanical linkages. However, when differential braking torque [T.sub.b] is applied, a difference is developed between [F.sub.x,LF] and [F.sub.x,RF], and [T.sub.lon,LF] and [T.sub.lon,RF] can no longer cancel out each other. The direction of resultant force [F.sub.kp]
transmitted to steering rack turns out to be the same as driver input steering torque, thus making it an assistive force which reduces steering effort demanded from driver.
While differential braking creates an assistive force to help the driver, it also induces other effects on the vehicle. The simplified 7-DOF vehicle model and 2-DOF bicycle model in Figure 8 show that different tire longitudinal forces [F.sub.x,LF] and [F.sub.x,RF] create a yaw moment [M.sub.z,DBAS] on the vehicle. With the same steering angle input from the driver, this extra yaw moment will generate more yaw rate than usual. In other words, DBAS reduces the required steering angle [[theta].sub.sw] and front wheel steer angle [gamma] for the same turn or road curvature. This reduction in steering angle can be seen in the results from CarSim simulations. However, it is noticed that the reduction of steering angle highly depends on the driving scenario and vehicle speed. For instance, shown in Figure 9, on highway exit ramp, only about half of the original steering angle is required when DBAS is working.
Nevertheless, during intersection right turn about the same level of steering angle is required with or without DBAS.
Related to extra yaw moment and reduced steering angle, slip angles of front and rear tires [[alpha].sub.F] and [[alpha].sub.R] are also found to be different before and after differential braking. Generally, those of the front tires decrease and the rear increase; the simulation results of highway exit ramp scenario are shown for instance in Figure 10(a) Tire aligning moments, which is a major component of resistance force against driver steering effort, are mostly determined by slip angles . The decrease of front tire slip angles leads to the reduction of front tire aligning moments [M.sub.z,LF] and [M.sub.z,RF], confirmed by simulation results shown in Figure 10(b) Therefore, not only does the assistive force [F.sub.kp] amplify driver steering input, but the reduction of front tire aligning moments [M.sub.z] also mitigates the resistance force acting against driver. The combination of these two effects is the reason why DBAS manages to reduce driver's steering effort.
Potential Side Effects and Possible Solutions
Since the CarSim vehicle model is quite detailed and capable of demonstrating most kinds of vehicle dynamics effects, it is possible to examine the side effects of DBAS on the vehicle apart from its benefit of steering torque reduction. Steering angle reduction, as illustrated before, may happen in some scenarios and can be a potential issue. Another apparent side effect is vehicle speed reduction, since differential braking inherently slows down the vehicle . Other effects of DBAS turn out to be insignificant, for example, vehicle roll angle stays about the same when DBAS is working, leaving no increased risk of rollover.
Reduced steering angle, together with smaller tire slip angles in the front and larger in the rear, is an apparent sign of oversteer. Oversteer causes the vehicle to be unstable at higher speeds. Electronic Stability Control (ESC) is designed to counter oversteer, which means DBAS is inherently in conflict with ESC. However, at lower speeds where the main working range of DBAS is, oversteer is acceptable if it can be managed by driver. In other words, DBAS can be allowed to override ESC and reduce steering effort at lower speeds in the event of EPAS failure if it is proven safe. Upon EPAS failure, it might be better for drive to oversteer rather than experience a sudden increase in steering torque and feel difficult to steer the wheel.
In all simulations, the virtual driver is designed to follow the path regardless of prevailing conditions, implying that the driver is able to accommodate changes in steering angles between when EPAS is active and DBAS is active. In reality, though, more than 50% reduction of steering angle on highway exit ramp will very likely make driver feel vehicle oversteer severely and may make it difficult to control the vehicle . In report , a 25% difference of steering angle is defined as recognizable by human. Therefore, attention needs to be paid to the highway exit ramp scenario, or relatively high speeds for DBAS, i.e., around or over 30 mph.
Since steering angle and torque reduction go hand-in-hand when DBAS is working, it is possible for a trade-off to be made between them. Partial reduction of steering torque still assists driver in steering the vehicle, while increased effort can alert driver to EPAS failure. At the same time, steering angle reduction becomes less obvious, making driver still feel comfortable in controlling the vehicle. This compromised solution is also simulated in CarSim by adjusting the reference steering torque map in Figure 2, and results are shown in Figure 11. The modified DBAS (denoted as DBAS mod) causes about 30% reduction of steering angle, which is recognizable yet assumed to be manageable, while steering torque reduction from EPAS-off case is 50% less than before. In lower speed maneuvers, such as intersection turns, steering angle reduction is minimal, hence no correction is required in these scenarios.
Vehicle speed reduction is another major side effect of DBAS. However, in the event of EPAS failure, it might not be harmful to slow the vehicle down, since accidents are usually more severe at higher speeds. In CarSim simulations, driver speed control is set as maintaining a target speed. The virtual driver actually applies more throttle to achieve the target speed when DBAS is working. For example, on highway exit ramp, driver throttle input is 35% for DBAS and 7% for EPAS-on, as shown in Figure 12. Although it is possible for a driver to always adjust throttle to maintain the desired speed, allowing the vehicle to slow down when DBAS is active by applying the same throttle as before can be acceptable. In fact, it may be better for driver to maintain the throttle, since slowing down the vehicle reduces lateral acceleration and hence steering torque demands.
In this paper, Differential Braking Assisted Steering (DBAS) is proposed to alleviate excessive steering torque demands on the driver in the event of EPAS failure, so as to reduce crash and injury rate. DBAS makes use of existing resources, i.e., differential braking and measurements from vehicle sensors, instead of adding more devices, which is favorable for a backup system.
The core of the DBAS control strategy is to minimize the difference between actual and reference steering torque through differential braking. A modified torque map which depends on vehicle speed and lateral acceleration is used to determine the reference steering torque. DBAS performance is verified through CarSim simulations of multiple safety-critical driving scenarios. Results show that steering torque can be reduced to similar levels as EPAS at various vehicle speeds and road curvatures. Preliminary analysis reveals that the ability of DBAS to reduce steering torque is linked to assistive force on steering rack and extra yaw moment created by differential braking.
While DBAS is shown to meet its objective of reducing steering torque, there are also undesirable side effects of DBAS like steering angle and vehicle speed reduction. These side effects appear to be much less likely to lead to crashes upon EPAS failure compared to a sudden increase in steering torque, and countermeasures have been proposed to mitigate them. Compared with tackling the key problem and saving the day, these side effects can be viewed as necessary and acceptable costs. To further evaluate DBAS for emergency safety, Hardware-in-the-Loop simulations or actual vehicle testing must be performed in the future. Both methods involve real driver, which is critical for determining whether the side effects are indeed manageable or not. The transition from EPAS-on to EPAS-off, and then DBAS active, simulating the realistic situation, can also be tested to observe driver response. Further improvement of DBAS should be focused on mimicking EPAS torque assist feature and minimizing the differences in vehicle controllability, so that drivers can still maneuver the vehicle comfortably as before and avoid accidents in the event of EPAS failure.
[1.] Kim, J., Song, J., "Control logic for an electric power steering system using assist motor," Mechatronics, Volume 12, Issue 3, April 2002. Pages 447-459, ISSN 0957-4158, doi:10.1016/S0957-4158(01)00004-6
[2.] Safercar.gov, INCLA-PE10005-1480, "ODI Closing Resume." http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[3.] Safercar.gov, INCLA-PE12017-8226, "ODI Closing Resume," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[4.] Safercar.gov, INCLA-PE14030-7526, "ODI Closing Resume," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[5.] Safercar.gov, RCAK-15V144-4682, "Recall Acknowledgement," http://www-odi.nhtsa.dot.gov/owners/SearchSafetylssues, accessed Jul. 2016
[6.] Safercar.gov, RCAK-16V190-6360, "Recall Acknowledgement," http://www-odi.nhtsa.dot.gov/owners/SearchSafetylssues, accessed Jul. 2016
[7.] Safercar.gov, RCAK- 14V282-7519, "Recall Acknowledgement," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[8.] Safercar.gov, RCAK-15V340-6934, "Recall Acknowledgement," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[9.] Safercar.gov, RCAK-10V073-2166, "Recall Acknowledgement," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[10.] Srivastava, P., Karle, M., Shailesh Karle, U., and Deshpande, A., "Development of Electrical Power Assisted Steering (EPAS) Considering Safety and Reliability Aspects as per ISO 26262," SAE Technical Paper 2015-26-0086, 2015. doi:10.4271/2015-26-0086
[11.] Nozawa, T., Shintani, Y, Tamaizumi, T., Hibi, T. , "Development of Brushless Motor EPS Assist Control for Disconnection Failure," JTEKT Engineering Journal English Edition No. 1008E, 2011
[12.] Oprea, C, and Martis, C, "Fault tolerant permanent magnet synchronous machine for electric power steering systems," Power Electronics, Electrical Drives, Automation and Motion, 2008. SPEEDAM 2008. International Symposium on, Ischia, 2008, pp. 256-261, doi:10.1109/SPEEDHAM.2008.4581310
[13.] Lawson, M., and Chen, X., "Fault tolerant control for an electric power steering system," 2008 IEEE International Conference on Control Applications, San Antonio, TX, 2008, pp. 486-491, doi:10.1109/CCA.2008.4629701
[14.] Safercar.gov, INRL-PE12017-52566, "Ford 07/12/2012 Response to ODI," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[15.] Wang, J., Wang, Q., and Jin, L., "Modeling and simulation studies on differential drive assisted steering for EV with four-wheel-independent-drive," 2008 IEEE Vehicle Power and Propulsion Conference, Harbin, 2008, pp. 1-7, doi: 10.1109/VPPC.2008.4677428
[16.] Wang, J., Wang, Q., Jin, L., and Song, C, "Independent wheel torque control of 4WD electric vehicle for differential drive assisted steering," Mechatronics, Volume 21, Issue 1, February 2011, Pages 63-76, ISSN 0957-4158, doi:10.1016/j.mechatronics.2010.08.005
[17.] Leng, B., Xiong, L., Jin, C, Liu, J., "Differential Drive Assisted Steering Control for an In-wheel Motor Electric Vehicle," SAE Int. J. Passeng. Cars - Electron. Electr. Syst.8(2):2015, doi:10.4271/2015-01-1599
[18.] van Zanten, A., "Bosch ESP Systems: 5 Years of Experience," SAE Technical Paper 2000-01-1633, 2000, doi:10.4271/2000-01-1633
[19.] Arndt, S., Arndt, M., and Rosenfield, M., "Effectiveness of Electronic Stability Control on Maintaining Yaw Stability When an SUV Has a Rear Tire Tread Separation," SAE Int. J. Passeng. Cars--Electron. Electr. Syst. 2(1): 120-140, 2009, doi: 10.4271/2009-01-0436
[20.] Pilutti, T, Ulsoy, G., and Hrovat, D., "Vehicle Steering Intervention Through Differential Braking," ASME. J. Dyn. Sys., Meas., Control. 1998:120r3V314-321, doi: 10.1115/1.2805402
[21.] Pilutti, T, Hrovat, D., and Ulsoy, G., "Vehicle steering system and method for controlling vehicle direction through differential braking of left and right road wheels," U.S. Patent 6,021,367, Feb. 1, 2000
[22.] Offerle, T, Tseng, H, and Stephan, C, "Method and apparatus of controlling an automotive vehicle using brake-steer as a function of steering wheel torque," U.S. Patent 7,165,644, Jan. 23, 2007
[23.] Dominguez-Garcia, A., Kassakian, J., and Schindall, J., "Abackup system for automotive steer-by-wire, actuated by selective braking," Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual, 2004, pp. 383-388 Vol.1, doi:10.1109/PESC2004.1355774
[24.] International Organization for Standardization, "Road vehicles--Test method for the quantification of on-center handling--Part 1: Weave test", International Standard ISO 13674-1:2010
[25.] International Organization for Standardization, "Passenger cars--Test track for a severe lane-change maneuver--Part 1: Double lane-change", International Standard ISO/DIS 3888-1
[26.] Safercar.gov, INRD-PE14030-61127P, "Ford 12-19-2014 Appendix," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[27.] Safercar.gov, INRL-PE10005-39793P, "GM 4/14/2010 Letter to ODI," http://www-odi.nhtsa.dot.gov/owners/SearchSafetyIssues, accessed Jul. 2016
[28.] Safercar.gov, INRD-PE10005-39799P, "GM 4/14/2010 Attachment," http://www-odi.nhtsa.dot.gov/owners/SearchSafetvIssues, accessed Jul. 2016
[29.] Kumar, R., Suda, B., Karande, S., Piyabongkarn, D., "Simulation and Experimental Study of Torque Vectoring on Vehicle Handling and Stability," SAE Technical Paper 2009-28-0062, 2009, doi: 10.4271/2009-28-0062
[30.] Pacejka, H, "Tyre and Vehicle Dynamics", ISBN 0750669187
Duanxiang Zhang, Bo Lin, Ahmet Kirli, and Chinedum Okwudire
University of Michigan
Chinedum E. Okwudire
Department of Mechanical Engineering
University of Michigan, Ann Arbor, MI, 48109
Table 1. Selected driving scenarios for CarSim simulation Lateral Scenario Path Speed Ace. Purpose Highway 500 ft. 30 mph 0.25g steady state Exit Ramps diameter response circle Serpentine 200 ft. 30 mph 0.3g transient Driving radius 1/4 response Course circles Intersection 25 to 100 < 20 mph <0.4g most Turns ft. radius common maneuver Parking Lot minimum < 10 mph <0.25g ground U-turns turning friction radius effect
|Printer friendly Cite/link Email Feedback|
|Title Annotation:||Electric Power Assisted Steering|
|Author:||Zhang, Duanxiang; Lin, Bo; Kirli, Ahmet; Okwudire, Chinedum|
|Publication:||SAE International Journal of Transportation Safety|
|Date:||Jul 1, 2017|
|Previous Article:||NHTSA's Proposed Frontal Oblique Impact Test Protocol: Analyses and Evaluation.|
|Next Article:||Validating Google Earth Pro as a Scientific Utility for Use in Accident Reconstruction.|