Experimental Study of Electric Vehicle YawRate TrackingControl Based on Differential Steering

*is paper investigates the experimental study of differential steering control of a four-wheel independently driven (FWID) electric vehicle (EV) based on the steer-by-wire (SBW) system. As each wheel of FWID vehicle can be independently driven, differential steering is realized by applying different driven torques to the front-two wheels. Firstly, the principle of the differential steering is analyzed based on the SBW system.When the differential steering is activated, the driver’s steering request is sent to the vehicle’s ECU. *en, the ECU gives different control signals to the front-left and front-right wheels, generating an external steering force on the steering components. *e external steering force pushes the steering components to turn corresponding to the driver’s request. Secondly, to test the feasibility of differential steering, a FWID EV is assembled and the vehicle is equipped with four independently driven in-wheel motors.*e corresponding control system is designed. Finally, the field test of the vehicle based on the proposed differential steering control strategy is performed. In the experiment, the fixed yaw rate tracking and varied yaw rate tracking maneuvers are employed. In the fixed yaw rate tracking, the vehicle can track the desired yaw rate well with differential steering. In addition, the vehicle can track the varied yaw rate with proposed differential steering. *e test results confirm the feasibility and effectiveness of the differential steering. By using the differential steering, a backup steering is established without additional components; thus, the costs can be reduced and the reliability of the vehicle steering system can be enhanced, significantly.


Introduction
With the worldwide concerns on energy conservation and environment protection, electric vehicle has attracted great attention with the advantages of energy reduction and emissions reductions [1][2][3][4]. e FWID EV, mounted by in-wheel motors (hub motors), is a promising vehicle architecture for the vehicle maneuverability [5]. On the other hand, to enhance the vehicle handling performance, the SBW system has been equipped on some vehicles. Note that the mechanical connection between the steering wheel and the lower steering assembly in the SBW system is removed; therefore, the reliability of the SBW system becomes more critical, and numerous research studies have been studied on the issue [6][7][8].
As the FWID EV is driven independently by the in-wheel motors, the driven torque of the front-two in-wheel motors can be different to generate a novel steering mechanism: differential steering. Some similar research studies have been published on the issue, such as differential assisted steering and skid steering [9][10][11]. e study in [12] investigated the feasibility of differential drive torque assisted steering and the capability of road feel keeping of the control system. In addition, Wang et al. conducted a study on the assistance quality analysis and robust control of electric vehicle with differential drive assisted steering system in [13]. e study in [14] investigated the differential power-assisted steering system of in-wheel electric vehicle based on a collaborative optimization model. e study in [15] proposed an experimentally validated dynamic model to describe the motion of a skid-steered vehicle in the pivotal steering condition, where the experiments were based on a specific 6 × 6 unmanned skid-steered vehicle, which was driven by six independent in-wheel motors. e study in [16] presented an effective methodology for generating dynamically feasible and energy-efficient trajectories for skid-steered autonomous ground vehicles (AGVs). Reference [17] studied the robust H ∞ Takagi-Sugeno fuzzy output-feedback control for differential speed steering vehicles. e differential drive-based yaw stabilization using MPC for distributed-drive articulated heavy vehicle is presented in [18]. What is more, the integrated hierarchical control strategy of active suspension and differential assisted steering system for electric-wheel vehicle is discussed in [19]. e study in [20] presented the motion tracking control for unmanned ground vehicle, consisting of straight-line driving control and cornering control. e above steering literatures investigated vehicle steering control based on the speed difference between the front-two wheels; and the above differential assisted steering mainly focused on the assisted torque on driver's hands and road feel keeping ability, where no active steering was involved. However, in the SBW system, it is critical to ensure the reliability of the steering system, as well as reducing the additional costs. In addition, compared with the theoretical study of the differential steering, the experimental study of the differential steering is really rare.
To handle the above problems, in this paper, the differential steering is adopted as a backup steering mechanism to enhance the reliability and reduces the external costs in case of the SBW system failure. e main contributions of the paper are as follows. First, the principle of the differential steering is studied based on the analysis of the steering system. en the FWID EV is assembled and the control system is designed. Finally, the field test of the EV based on the proposed differential steering control strategy is performed and the results are analyzed. e rest of the paper is organized as follows. Section 2 studies the mechanism of the proposed differential steering. Section 3 discusses the control schema of the proposed differential steering and the FWID EV. Section 4 gives the field test of the EV with the yaw rate tracking experiments, followed by the conclusion in Section 5.

Vehicle Differential Steering Dynamics
As in Figure 1, the principle of differential steering system based on the FWID EV with SBW system is presented, where there is no mechanical connection between steering wheel and steering actuator. e driver steers the steering wheel and the steering request signal is sent to the vehicle's ECU. e steering request can be realized by the electric power steering (EPS). However, when the steering motor completely fails or the steering signal transmission error occurs, the driver's steering request will not be able to be functioned. Meanwhile, the fault diagnosis system detects the steering fault and activates the differential steering to perform the driver's driving request. Note that the fault diagnosis system of SBW system and electric vehicle has been extensively studied previously and this is not the focus of this paper.
As seen in Figure 1, when the regular SBW system is in complete failure and the differential steering is activated to steer the vehicle, the different driven forces of front-two inwheel motors will yield a moment where r σ denotes the scrub radius, τ ds i (i � 1, 2) denotes the moment around kingpin of the ith wheel, and F xfi (i � r, l) denotes the longitudinal tire force of the ith wheel, respectively. en, the moment will generate a steering angle, which is the focus of the differential steering. In the figure, it is clear that the steering system will turn right when the driven torque of the left wheel is larger than that of the right. e dynamics of the differential steering system is given as follows [9,10]: where J e and b e indicate the effective inertia and damping of the steering system, respectively. δ is the front wheels' steering angle. τ a denotes the tire self-aligning moment.
According to the brush model [21], the self-aligning moment τ a can be expressed as τ a � κ 1 C f α f , where κ 1 is a constant, and C f is front tire cornering stiffness. α f is the front wheel slip angle, which can be expressed as where v x and v y denote the vehicle's longitudinal and lateral velocities, respectively. l f and l r denote the distances from the front axle and the rear axle to the central gravity (CG), respectively.
Assuming that the front wheel steering angle is small, the moment around the center of gravity of the vehicle M z is defined as where l s denotes the half of the vehicle track width. en, the moment M z ′ can be deduced asM z ′ � κ 2 ΔM z , with κ 2 � r σ /l s . en, system (2) can be rewritten as  where /b e denotes small distances termed as v y and € δ are small normally.

The Vehicle Configuration and the Control Schema
To verify the differential steering, a FWID EV is refitted from an All Terrain Vehicle (ATV), which has more convenience in equipping the related components. e vehicle configuration is given in Figure 2. e FWID EV is equipped with four in-wheel motors; each of the front-two motors has 6Kw power, and each of the rear ones has 8Kw power. e inwheel motor is controlled by the Kelly Motor Controller, where control signal is an analog voltage signal within [0, 5] V, and the motor controller works in Torque Mode. It is clear that the Li-ion battery and the MicroAutoBox controller are in the trunk, the dual-antenna GPS is on the roof, and the IMU is near the CG point of the vehicle. e vehicle parameters are listed in Table 1. e GPS/IMU configuration is given in Figure 3. Note that the GPS Real Time Kinematic (RTK) technology is used to improve the positioning accuracy. e signals are received by the GPS base station from the satellites and then transmitted to the vehicle by a high-power transmitter. e vehicle speed, acceleration, heading angle, and yaw rate signal are measured by the IMU component near the CG of the vehicle.
is paper studies the vehicle handling control of a FWID EV based on the differential steering. e yaw rate r, which will influence the vehicle handling performance, should be well regulated in the control system. en control object is to design a controller, with which the yaw rate tracking error can be minimized. e flow chart of the control schema is shown in Figure 4. In the figure, it is clear that the controller receives two signals: the desired yaw rate r d and the actual yaw rate r m . e desired yaw rate signal r d is generated from the driver input, which is an analog voltage signal. For safety reasons, the signal is converted into [− 10, 10], indicating that the desired yaw rate can be modified from − 10 deg/s to 10 deg/s. However, the range can be enlarged in the severe driving conditions. e actual yaw rate r m is measured by the IMU near the CG point of the vehicle. en the yaw rate difference Δ d between r d and r m is minimized with a PID controller.
As seen in Figure 5, a voltage signal dV is obtained from the PID controller corresponding to yaw rate difference Δ d.
en the voltage dV is converted into two parts, the control voltages V 1 and V 2 , to control the front-two in-wheel motors, respectively. Considering the dead zone and property of the in-wheel motor controller, an offset is added to keep the motor running in normal conditions.
In Figure 4, the motor controller receives the control signals V 1 and V 2 and gives driving commends to the frontleft and front-right in-wheel motors; then the desired torques T 1 and T 2 are generated, respectively. Since the steering wheel is released by the driver, the different driven torque between the front-two in-wheel motors will force the fronttwo wheels to rotate around their Kingpin, as well as the steering wheel.
en the vehicle completes the steering maneuver corresponding to the driver yaw rate input. Note that steering wheel angle sensor (SAS) is employed to measure steering angle; then we can obtain the steering wheel angle δ h in the field test. In addition, there is no steering motor on the vehicle. In the following test, the driver will release the steering wheel to simulate the situation when the steering motor fault happens.

Experimental Study of Differential Steering
In this section, field test of the vehicle is presented to validate the effectiveness of the differential steering. In the tests, as seen in Figure 6, the vehicle runs well initially, and then the driver releases the steering wheel. Meanwhile, the copilot activates the differential steering control schema and gives the desired yaw rate signals to the controller. Without steering torque from the driver, the steering wheels are only regulated by the differential steering controller. e controller makes the vehicle track its desired yaw rate with the proposed control schema. ree different driving maneuvers are performed in the experiment and the results are in Figures 7-9, respectively. Note that, in these tests, the vehicle is only driven by the front-two in-wheel motors, and the rear-two in-wheel motors are shut off. e positive yaw rate indicates left steering directions, and vice versa.

Fixed Yaw Rate Tracking.
In this test, the vehicle is supposed to track a fixed yaw rate r d � − 7 deg/s. In Figure 7(a), it is clear that, at the first few seconds, the actual yaw rate is zero, indicting that the vehicle is running in a straight line. en the driver releases the steering wheel, and the copilot activates the differential steering and inputs the desired yaw rate r d � − 7 deg/s. As seen in Figure 7(b), when the differential steering is activated, the control system quickly generates the control signals.
en the control voltage of the two in-wheel motors is separated to the    Figure 6: e field test of the differential steering. opposite direction. e control signal of front-right in-wheel motor V 2 increases and the front-left motor signal V 1 decreases. With the different control signals, the in-wheel motors generate the different torques, and thus the wheel speed is quite different as seen in Figure 7(d). With such signals, the right motor generates larger speed than the left one, making the vehicle turn left and the actual yaw rate r m rapidly reaches − 7 deg/s. Note that, in Figure 7(d), the black solid line indicates the vehicle speed (v x ). In Figure 7(c), the vehicle is approximately running in a straight line at the beginning ( * means starting point; • means ending point) and then in a circle as r m ≈ − 7 deg/s.
In Figure 7(a), it is clear that the overall yaw rate tracking performance is well. Because the driver's steering angle is relatively large compared to the yaw rate signal, we give the scaled steering wheel angle, that is, δ h /8, as the black-dotted line in Figure 7(a). Without the driver intervention, the differential steering can still rotate steering wheel, achieving the similar effect of the electric power steering.

Yaw Rate Tracking with Lane-Change-like Maneuver.
In this test, the vehicle is supposed to track a varied yaw rate with the lane-change-like maneuver. e results are given in Figure 8. As seen in zone A of Figure 8(a), the actual yaw rate is zero at the beginning. At 2 s, the driver releases the steering wheel, and the copilot activates the differential steering and changes the desired yaw rate. When the differential steering is activated, the control system quickly generates the control signals, as in zone A of Figure 8(b). en the control voltage of the two in-wheel motors is separated to the opposite direction. e control voltage signal of the front-right inwheel motor V 2 is larger than V 1 in zone A, indicating the left turning of the vehicle, as shown in zone A of Figure 8(b). As the vehicle turns left, the right wheel has larger speed Journal of Advanced Transportation 5 (v fr ) than the left (v fl ) as in zone A of Figure 8(d). e actual yaw rate tracks the desired value well in zone A. In zone B of Figure 8(a), the driver changes the direction of the yaw rate, trying to amend the heading angle and let the vehicle make an opposite turn. en the control system increases V 1 and decreases V 2 as in zone B of Figure 8(b), generating larger torque in the left wheel than in the right, and thereby the vehicle turns right as in zone B of Figure 8(c). As the vehicle turns right, the left wheel has larger speed (v fl ) than the right (v fr ) as in zone B of Figure 8(d). e actual yaw rate tracks the desired value well in zone B.
In zone C of Figure 8(a), the driver changes the yaw rate direction again to amend the heading angle and let the vehicle move in straight line. en the system increases V 2 and decreases V 1 as in zone C of Figure 8(b), causing larger torque in the right wheel than in the left and thereby stopping the vehicle's right turning trend as in zone C of Figure 8(c). In zone C of Figure 8, the right wheel has larger speed (v fr ) than the left (v fl ). Even though the operations in zone C are not perfect, the actual yaw rate tracks the desired value well in zone C and the lane-change maneuver is still acceptable.

Yaw Rate Tracking with J-Turn-like Maneuver.
In this test, the vehicle is supposed to track a varied yaw rate with the J-turn-like maneuver. In zone A of Figure 9(a), the actual yaw rate is zero at the first few seconds. At 5 s, the driver releases the steering wheel, and the copilot activates the differential steering and inputs the desired yaw rate. In zone A, the desired yaw rate becomes − 3 deg/s. en the system redistributes the control voltage of the front-two in-wheel motors, as in Figure 9(b). e control signal of the frontright in-wheel motor V 2 is larger than V 1 in zone A, indicating the left turning of the vehicle, as in Figure 9(c). As the vehicle turns left, the right wheel has larger speed (v fr ) than  Journal of Advanced Transportation the left (v fl ) as in Figure 9(d). e actual yaw rate tracks the desired value well in zone A. In zone B of Figure 9(a), the driver tries to change the yaw rate direction to amend the heading angle and let the vehicle make an opposite turn. en the system increases V 1 and decreases V 2 as in zone B of Figure 9(b), causing larger torque in the left wheel than in the right, and thereby the vehicle turns right as in zone B of Figure 9(c). As the vehicle slightly turns right, the left wheel has larger speed (v fl ) than the right (v fr ) as in zone B of Figure 9(d). e actual yaw rate tracks the desired value well in zone B.
In zone C of Figure 9(a), the driver tries to amend the heading angle and let the vehicle turn left. en the system increases V 2 and decreases V 1 as in zone C of Figure 9(b), causing larger torque in the right wheel than in the left and thereby stopping the vehicle's right turning trend as in zone C of Figure 9(c). As the vehicle stops turning right, the right wheel has larger speed (v fr ) than the left (v fl ) as in zone C of Figure 9(d).
In zone D of Figure 9(a), the driver tries a J-turn maneuver in right turning. en the system increases V 1 and decreases V 2 as in zone D of Figure 9(b), causing larger torque in the left wheel than in the right, and thereby the vehicle turns right as in zone D of Figure 9(c). As the vehicle turns right sharply, the left wheel has larger speed (v fl ) than the right (v fr ) as in zone D of Figure 9(d).
With the higher speed and sharp steering in the J-turn test, the operations in zone D are not perfect. However, under such circumstance, the performance of yaw rate tracking and the J-turn trajectory in this test is still acceptable. erefore, the feasibility and effectiveness of the differential are proven by the field tests. Journal of Advanced Transportation 7

Conclusion
As the driven torque of the FWID EV between the front-left and front-right wheels can be independently controlled, this paper designs the differential steering as the backup steering power when the SBW system fails its regular function. To test the real performance of the differential steering, a FWID EV is manufactured and the corresponding control schema is designed. e field test of the vehicle yaw rate tracking is performed under the cooperation of the driver and the copilot. e fixed yaw rate tracking and varied yaw rate tracking maneuvers are employed in the tests of the FWID EV. In the fixed yaw rate tracking, the vehicle can track the desired yaw rate well with differential steering. In addition, the vehicle can track the varied yaw rate with proposed differential steering. e test results verify the effectiveness of the proposed differential steering.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare no conflicts of interest.