© Wuhan University 2025

0 Introduction

Autonomous vehicles stand as pivotal components in the realization of advanced smart transportation systems and low-carbon transitions, garnering significant interest across various sectors and yielding substantial advancements in research and development. Within autonomous driving frameworks, the intricate and dynamic nature of external environments underscores the ongoing necessity for human oversight, preventing the complete substitution of drivers by intelligent systems in complex scenarios^[1]. Moreover, given China's intricate traffic conditions, autonomous vehicles undergoing road testing are mandated to integrate both automated and manual driving capabilities^[2]. Consequently, exploring the dynamics of authority transition in human-machine cooperative driving holds significant academic merit and practical potential^[3].

When the driver intervenes in the system, how to ensure that the autonomous driving system accurately detects the intervention behavior is a key area of research^[4]. To this end, Furusho et al^[5] proposed using the measurement value of the torque sensor as the basis for judging driver intervention. However, torque sensors are easily affected by steering column damping and friction, which can lead to errors in measurement results. To solve the above problems, Cholakkal et al^[6] designed a fault-tolerant control model for the torque sensor. The signal value of the torque sensor was estimated by the load torque and the total torque, and then the driver's hand torque value was calculated. Nevertheless, these two methods will still significantly impact the detection results when the system fluctuates. To further improve the accuracy, Marouf et al^[7] designed a cascaded synovial observer to estimate the driver's hand torque. The observer inputs motor current and steering angle, verifying its effectiveness through the simulation model. Wang et al^[8] designed an online estimation method for manual steering intervention hand torque using a steering dynamics model and verified the performance of the estimator by simulating three typical steering intervention cases.

During driver takeovers of steering systems, optimal timing and control strategies for transitioning control rights emerge as focal points in scholarly investigations^[9-10]. Nilsson et al^[11] introduced an approach anchored in driver capability assessment to determine the moment for driving mode shifts, enhancing vehicular safety. Regarding the transfer of driving authority, Saito et al^[12] advocated for a haptic shared control technique, mitigating steering angular velocity instability during transitions, albeit with inherent risks due to its reliance on assistant driver system (ADS) integration. Sonoda et al^[13] executed control rights transfer under curvilinear road conditions, achieving steady transitions through simulations and empirical vehicle trials. Song^[14] devised a time-domain transformation weighting mechanism, facilitating smoother takeovers between humans and machines, yet overlooked the torque dynamics between the driver and steering wheel. A common thread in these studies reveals that incorporating a transitional phase significantly bolsters vehicular safety and driver control stability during handover processes.

Addressing the challenges mentioned above, this study focuses on tubular electric power steering systems. We propose the use of an extended state observer estimation algorithm to determine driver intervention during automated steering phases, without the need for additional sensors. A novel steering mode transition module is introduced, in which automatic steering and manual steering cohabits, and each is assigned distinct weighting factors. As these factors dynamically adjust, the shift in driving control becomes seamless. This method of indirect and progressive switching mitigates system disruptions, ensuring smoother transitions and bolstering the safety of steering operations.

This paper is arranged as follows: Section 1 specifies the driver intervention method based on the extended state observer, encompassing hand torque generation and estimation model development. Section 2 involves simulation and implementation of the extended state observer, as well as determination of hand torque and time thresholds. Section 3 explores steering control transfer and designs a steering mode transition unit. Section 4 conducts steering mode switching experiments to verify the transition unit. Section 5 summarizes the research results and highlights the strategy's advantages and practical value.

1 Driver Intervention Method Based on Dilated State Observer

When the auto drive system stops working, control will be returned to the driver. A key issue that needs to be addressed during the transfer of control is to ensure that the driver's operational response is sensitive, comfortable, and that the ride is safe and smooth. The usual steering mode switching process is shown in Fig. 1.

Fig. 1 Steering mode switching flow chart

The problem of determining driver intervention in automatic steering systems has been addressed by Furusho et al^[5], who have suggested using torque transducer measurements as a basis for judging driver steering intervention. However, the use of such a direct judgement method would make the results inaccurate. If the torque sensor is installed on the steering column, it is easily affected by steering column damping and friction during the operation of the steering system. Therefore, this paper proposes the use of an expansion state observer for hand torque estimation. By comparing the estimated hand torque with the pre-set hand torque thresholds and time thresholds, it can accurately determine whether the driver has steering intervention. Figure 2 shows the flow of the steering intervention judgement.

Fig. 2 Steering intervention judgement flow

1.1 Study of Hand Torque Generation During Driver Intervention

There are two factors that affect the torque sensor readings in C-EPS type steering columns: one is the driver's hand torque, and the other is the load acting on the steering column. Therefore, the values measured by the torque sensor are not only related to the hand torque input by the driver but also to the steering wheel's moment of inertia, friction, and damping.

In the stationary state of the vehicle, the influence of the rotational inertia of the steering wheel, friction, and damping on the value collected by the torque sensor can be ignored, and it is approximated that T_s=T_d. When the vehicle is in motion, the moment of inertia of the steering wheel and the load on the steering column have a significant effect on the torque sensor and cannot be ignored. At this time, the driver's hand torque value cannot be directly read from the torque sensor. To verify the above inference, the following experiments were carried out.

When the vehicle speed is zero and the driver's hands are not touching the steering wheel, the sampled value of the torque sensor is shown in Fig. 3(a). When the driver takes both hands off the steering wheel, we set the speed signal to V=5 km/h. The host computer sends the target steering angle of the automatic steering system as a sinusoidal signal with an amplitude of 30° and a frequency of 3 Hz, and the measured value of the torque sensor is shown in Fig. 3(b).

Fig. 3 Comparison of torque sensor measurements

As shown in Fig. 3, when the driver is not touching the steering wheel and both the vehicle and steering wheel are stationary, the measured value is nearly zero. When both the vehicle and the steering wheel are in motion, the torque value fluctuates considerably at this point, even though the applied hand torque is zero. From the experimental results above, it can be seen that the use of the torque sensor to determine the presence of steering intervention is inaccurate and is likely to lead to misjudgment of the vehicle's automatic steering system. Therefore, it is necessary to estimate the driver's hand torque, which is generally estimated based on factors such as the steering torque, steering angle, rotational parameters of the column, and the rotational angular velocity of the column. We estimate the driver's hand torque and make steering intervention judgments. To this end, this paper designs a hand torque estimation algorithm based on the extended state observer and uses it as a decision condition for steering intervention.

1.2 Hand Torque Estimation Model Based on Extended State Observer

The extended state observer is a nonlinear observer whose main function is to consider uncertainties or disturbances in the system as part of the state and to create an extended state space in order to estimate the values of these uncertainties or disturbances by observing the states in this space. Based on the above theoretical foundation, the expanded state observer has been successfully applied to electric power steering systems. Moreillon^[15] used a dilated state observer for driver hand moment estimation and released the steering wheel at 16 s. The measured values of the compensated driver hand moment were in general agreement with the hand moment estimated by the observer. Illán et al^[16] conducted a simulation implementation of the dilated state observer in order to verify its effectiveness in measuring the driver's hand torque, and the experimental results showed that the extended state observer has a good ability to track the driver's hand torque. Therefore, based on the existing research, this paper designs the extended state observer to realise the estimation of hand torque for the characteristics of the C-EPS steering actuator. The simplified model of the steering wheel and steering column of the system is shown in Fig. 4.

Fig. 4 Simplified physical model of the system

The parameters of the system are shown in Table 1.

The state space expression of the simplified model is shown in equation (1).

$\{\begin{array}{c}\begin{array}{l}\dot{\mathit{x}}=\mathit{A}\mathit{x}+{\mathit{B}}_{\mathrm{1}}{u}_{\mathrm{1}}+{\mathit{B}}_{\mathrm{2}}{u}_{\mathrm{2}},\\ \mathit{y}=\mathit{C}\mathit{x}+D{u}_{\mathrm{1}}.\end{array}\end{array}$(1)

In the above equation, x is the state quantity and y is the output quantity. u₁ and u₂ are the known and unknown input quantities, respectively, and the expression is:

$\mathit{x}=\left[\begin{array}{c}{\theta }_s\\ {\dot{\theta }}_s\end{array}\right],u_{\mathrm{1}}={\theta }_c,u_{\mathrm{2}}=T_d,\mathit{y}=T_s,$(2)

$\begin{array}{l}\mathit{A}=\left[\begin{array}{cc}\mathrm{0}& \mathrm{1}\\ -\frac{K_s}{J_s}& -\frac{B_s}{J_s}\end{array}\right],{\mathit{B}}_{\mathrm{1}}=\left[\begin{array}{c}\mathrm{0}\\ \frac{K_s}{J_s}\end{array}\right],{\mathit{B}}_{\mathrm{2}}=\left[\begin{array}{c}\mathrm{0}\\ \frac{\mathrm{1}}{J_s}\end{array}\right],\\ \mathit{C}=\left[\begin{array}{cc}{K}_s& \mathrm{0}\end{array}\right],D=-K_s.\end{array}$(3)

where T_s is the value of the torque sensor as a state space output. θ_c is the lower steering column turn angle as a known input to the state space. T_d is the driver hand torque as an unknown input to the state space. To estimate the driver's hand torque, a new state quantity x_e is constructed by adding it to the state quantity x, which has:

${\mathit{x}}_{\mathit{e}}=\left[\begin{array}{c}\mathit{x}\\ u_{\mathrm{2}}\end{array}\right]=\left[\begin{array}{c}{\theta }_s\\ {\dot{\theta }}_s\\ T_d\end{array}\right]$(4)

The new state space after extension is described as:

$\{\begin{array}{c}{\dot{\mathit{x}}}_{\mathrm{e}}={\mathit{A}}_e{\mathit{x}}_e+{\mathit{B}}_e{u}_{\mathrm{1}},\\ \mathit{y}={\mathit{C}}_e{\mathit{x}}_e+D{u}_{\mathrm{1}}.\end{array}$(5)

Among them, A_e is the system state matrix after expansion, B_e, C_e are the input matrix and output matrix, respectively:

${\mathit{A}}_{\mathit{e}}=\left[\begin{array}{ccc}\mathrm{0}& \mathrm{0}& \mathrm{0}\\ -\frac{K_s}{J_s}& -\frac{B_s}{J_s}& \frac{\mathrm{1}}{J_s}\\ \mathrm{0}& \mathrm{0}& \mathrm{0}\end{array}\right],{\mathit{B}}_{\mathit{e}}=\left[\begin{array}{c}\mathrm{0}\\ \frac{K_s}{J_s}\\ \mathrm{0}\end{array}\right],{\mathit{C}}_{\mathit{e}}=\left[\begin{array}{ccc}{K}_s& \mathrm{0}& \mathrm{0}\end{array}\right]$(6)

The newly constructed extended state space is verified below:

$\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}(\left[\begin{array}{c}{\mathit{C}}_{\mathit{e}}\\ {\mathit{C}}_{\mathit{e}}{\mathit{A}}_{\mathit{e}}\\ {\mathit{C}}_{\mathit{e}}{\mathit{A}}_{\mathit{e}}^{\mathrm{2}}\end{array}\right])=\mathrm{3}$(7)

The energetic matrix of the system is full rank from equation (7), so it is an energetic system. The state observer is designed as follows:

$\{\begin{array}{c}\begin{array}{l}{\dot{\widehat{\mathit{x}}}}_e={\mathit{A}}_{\mathit{e}}{\widehat{\mathit{x}}}_{\mathit{e}}+{\mathit{B}}_{\mathit{e}}{u}_{\mathrm{1}}+\mathit{G}(\mathit{y}-\widehat{\mathit{y}}),\\ \widehat{\mathit{y}}={\mathit{C}}_{\mathit{e}}{\widehat{\mathit{x}}}_{\mathit{e}}+\mathit{D}{u}_{\mathrm{1}}.\end{array}\end{array}$(8)

Define the gain matrix G=[G₁ G₂ G₃]^T, then ${\mathit{A}}_{\mathit{e}}-\mathit{G}{\mathit{C}}_{\mathit{e}}$ is:

${\mathit{A}}_{\mathit{e}}-\mathit{G}{\mathit{C}}_{\mathit{e}}=\left[\begin{array}{ccc}-G_{\mathrm{1}}{K}_s& \mathrm{1}& \mathrm{0}\\ -K_s(\frac{\mathrm{1}}{J_s}+G_{\mathrm{2}})& -\frac{B_s}{J_s}& -\frac{\mathrm{1}}{J_s}\\ -G_{\mathrm{3}}{K}_s& \mathrm{0}& \mathrm{0}\end{array}\right]$(9)

Further there are characteristic equations expressed as:

$f(s)=\mathrm{d}\mathrm{e}\mathrm{t}[s\mathit{I}-({\mathit{A}}_{\mathit{e}}-\mathit{G}{\mathit{C}}_{\mathit{e}})]$(10)

Assuming that the desired observer poles are a₁, a₂, and a₃, there are:

$f\text{'}(s)=(s+a_{\mathrm{1}})(s+a_{\mathrm{2}})(s+a_{\mathrm{3}})$(11)

The specific parameter values of G₁, G₂, and G₃ are obtained by solving the equations in equations (10) and (11).

2 Simulation and Implementation of an Extended State Observer

2.1 Simulation of Extended State Observer

The performance of the state observer is affected by the gain matrix G, while the poles of the observer determine the values of the matrix G. In this paper, we perform pole configurations by building an observer simulation model to determine a reasonable matrix G. Some of the parameters used in the steering column are shown in Table 2.

In order to show the simulation process of the observer more clearly, the following section describes the process of building the simulation model of the observer using Matlab/Simulink, and the simulation flow is shown schematically in Fig. 5, where In-1 and In-2 are the inputs to the model, representing the input turning angle θ_c at the lower end of the steering column and the driver's hand torque T_d, respectively.

Fig. 5 Flow chart of observer simulation

By simulation of several different sets of observer poles, the poles were chosen as: s₁=0, s_2,3=-1±j; at this point G=[-0.013 4 -114.350 5 0.066 2]^T.

On this basis, simulation tests were conducted to evaluate the performance of the observer. The verification of the observer's performance is divided into two parts: the first part assesses the steering wheel's ability to track the lower-end angle, and the second part evaluates the state observer's ability to estimate the driver's hand torque. Firstly, a sinusoidal angle signal (3 rad, 1 Hz) is input to In-1. 0 is input to In-2, that is, T_d = 0. The tracking of the steering wheel angle ${\widehat{\theta }}_s$ with respect to the lower end angle θ_c is observed through s₁, and the error results are shown in Fig.6.

Fig. 6 Steering wheel angle following error graph

From Fig. 6, when the input hand torque is 0, the steering wheel angle and the lower end input angle error value are basically 0. It proves that the steering wheel has good steering tracking ability in the simulation model.

When In-1 input is 0, In-2 inputs a step signal (5 N∙m), that is, T_d = 5. At this point, T_d is used as the input hand torque in the simulation model. The variation of the hand torque is monitored by s₂, as shown in Fig. 7.

Fig. 7 Observations of hand torques

From Fig. 7, the observer has good tracking ability for the input hand torque step signal when the In-1 input is 0. The system has a short fluctuation time and a fast response time when the hand torque tracking the experiment.

In summary, the simulation experiments show that the extended state observer in this paper can achieve the estimation of unknown input quantities. During the estimation of unknown variables, the system exhibits strong tracking ability, fast response, and high accuracy.

2.2 Implementation of Extended State Observer

The extended state observer will vary with response time. When applied to embedded systems, it is necessary to discretize linear time-invariant systems. The commonly used methods are approximation and precision. Although precise methods can ensure high consistency in solutions between continuous and discrete systems, their computational process is relatively complex and requires a significant amount of computing resources and time. In contrast, approximation methods are computationally simpler as they achieve discretization by approximating the state space model of a continuous system. Therefore, in order to optimize computational performance, this paper uses an approximate method to discretize the continuous system, which requires less computation. The results of discretizing the extended state observer are as follows:

$\{\begin{array}{c}\begin{array}{l}{\widehat{\mathit{X}}}_{\mathit{e}}((k+\mathrm{1})T)={\widehat{\mathit{X}}}_{\mathit{e}}(kT)+T({\mathit{A}}_{\mathit{e}}{\widehat{\mathit{X}}}_{\mathit{e}}(kT)\\ +{\mathit{B}}_{\mathit{e}}{u}_{\mathrm{1}}(kT)+\mathit{G}(\mathit{y}(kT)-\widehat{\mathit{y}}(kT))),\\ \widehat{\mathit{y}}(kT)=\mathit{C}{\widehat{\mathit{X}}}_{\mathit{e}}(kT)+D{u}_{\mathrm{1}}(kT).\end{array}\end{array}$(12)

Further, the following formula can be obtained:

$\begin{array}{l}{\widehat{\mathit{X}}}_{\mathit{e}}((k+\mathrm{1})T)={\widehat{\mathit{X}}}_{\mathit{e}}(kT)+T(({\mathit{A}}_{\mathit{e}}-\mathit{G}{\mathit{C}}_{\mathit{e}}){\widehat{\mathit{X}}}_{\mathit{e}}(kT)\\ +{\mathit{B}}_{\mathit{e}}{u}_{\mathrm{1}}(kT)+\mathit{G}(\mathit{y}(kT)-D{u}_{\mathrm{1}}(kT)))\end{array}$(13)

It can be seen from formula (13) that after discretization, the current estimated state variable ${\widehat{\mathit{X}}}_{\mathit{e}}((k+\mathrm{1})T)$ can be derived from the input at the previous moment and the state variable ${\widehat{\mathit{X}}}_{\mathit{e}}(kT)$ estimated at the previous moment. Therefore, the current hand torque can be calculated from the hand torque value estimated at the last moment and the input steering column lower end angle.

To verify the above design, we conducted the following experiment: when the vehicle speed signal is 0, the driver applies a slight hand torque to the steering wheel. We compare the estimated hand torque value by the system with the measured value of the torque sensor. The experimental results are shown in Fig. 8.

Fig. 8 Comparison chart of module estimated and measured values

As shown in Fig. 8, the designed driver hand torque estimation module has fluctuations when the system just starts working, but it can quickly return to the correct estimated value. At the same time, the estimated hand torque value is slightly smaller than the measured value of the torque sensor, which is also consistent with the theoretical study in the previous section. It can be concluded from experiments that the designed extended state observer can estimate the driver's hand torque. Although the estimated value of the designed expanded state observer fluctuates, it is fast and can be used as a condition for judging the intervention of the automatic driving system.

2.3 Determination of Hand Torque Threshold and Time Threshold

After completing the estimation of the driver's hand torque, in order to avoid the hand torque during steering intervention being interfered by the lower end of the torsion bar, it is necessary to determine the time threshold and hand torque threshold. It can also be seen from the above simulation experiment that a small amount of fluctuation will occur when the system estimates the driver's hand torque. By setting the time threshold t₀ and the torque threshold T₀, the accuracy of the system's judgment can be improved. When the driver's hand torque value exceeds T₀ and is maintained for more than t₀, it can be determined that there is human intervention in the automatic steering system.

In this paper, the hand torque threshold T₀ is determined through the following experiment. The host computer sends a steering wheel angle signal, and the hand is lightly placed on the steering wheel to move with the steering wheel. The measured data are shown in Fig. 9.

Fig. 9 Hand torque curve

This paper adopts a simplified torque threshold setting method. As shown in Fig. 9, the absolute value of the maximum hand torque is |T_so| = 0.329 092 N∙m. In the above experiment, the driver did not intervene in the automatic steering system. When setting the torque threshold T₀, it is necessary to ensure that it is greater than |T_so| to avoid false triggering due to noise or small fluctuations. Considering the characteristics of the column electric power steering system, such as fast dynamic response and low noise sensitivity, the torque threshold should not be too large. The range of T₀ was initially set at 0.3-1.0 N∙m, and debugging was performed with an increase of 0.1 N∙m each time. Finally, T₀ was determined to be 0.6 N∙m.

In order to improve the accuracy of the system's judgment, we also set a time threshold t₀. If the torque applied by the driver satisfies the conditions of T₀ and t₀, the intervention state variable is set to 1, otherwise, it is set to 0. For the selection of the time threshold, we send commands to the steering wheel through the host computer and perform 40 experiments for each time threshold to determine whether the driver's hands are on the steering wheel. The experimental results are shown in Fig. 10. We compared the frequency of the system correctly identifying the driver's intervention under different time thresholds. As shown in Fig.10, the accuracy is highest when the time threshold is 50 ms. Therefore, the time threshold selected in this paper is 50 ms.

Fig. 10 Impact of time threshold on system accuracy

3 Transfer of Rights to Steering Control

3.1 Transfer of Control Transition Study

After identifying the driver's intervention in the automatic steering system, the driving rights will be transferred. The methods of transferring rights can be divided into direct transfer and indirect transfer. Direct conversion is the direct switching of drive control. If direct transfer is chosen while the vehicle is in motion, there will be significant shaking when the transfer of rights occurs. This kind of trembling may cause significant safety hazards and have a significant impact on the driver's sense of control and ride stability. Therefore, the ideal transfer of control is to add a conversion module during the switching process. We can set different control weights to distinguish between two driving modes, and can achieve the transfer of driving rights by gradually changing the weight values during the transition phase. This ensures the safety of the vehicle and the smoothness of driving during the transfer of rights. This article proposes a steering mode conversion unit that includes different weights for two driving modes to achieve smooth and seamless control transfer.

3.2 Steering Mode Transition Unit Design

A shared control approach exists in the "human-machine co-driving" model, where the driver and the automated driving system can simultaneously control the vehicle^[17]. This mode is centred on the driver, with the autopilot system providing road warnings and manoeuvre corrections. We apply the idea of shared control to the steering mode transition unit, which gradually transfers the driving control by changing the weights. The transition unit flow is shown in Fig. 11.

Fig. 11 Steering mode transition unit flow chart

When the steering module determines the driver's control intent, it enters the steering mode transition unit. The initial value of the counter T_cnt is 0. The total time of the steering mode transition unit is denoted as T_trans, and the period of calculation of the steering mode weight values is denoted as T_all. Manual steering is weighted as P and automatic steering is weighted as A. Therefore:

$A=\frac{T_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}}-T_{\mathrm{c}\mathrm{n}\mathrm{t}}\times T_{\mathrm{a}\mathrm{l}\mathrm{l}}}{T_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}}}$(14)

$P+A=\mathrm{1}$(15)

From equations (14) and (15), the weight value of the autopilot control mode gradually changes from 1 to 0 as the counter count increases, and the driving control is switched from the autopilot system to the manual steering system. At this point, the weight of the manual steering control mode gradually changes from 0 to 1. The addition of the steering module not only ensures safety when the vehicle is switched, but also reduces the steering wheel's friction, improves the driver's handling experience, and avoids vehicle shake due to the switching of steering modes, improving handling safety.

From Fig. 11, when the driver steers to intervene, the current value I_as to be supplied by the steering executive motor is obtained by querying the linear characteristic curve table, multiplied by the automatic steering weight P, and the weighted output value is obtained. At this point, in the automatic steering system, the target current value I_au output from the speed loop is multiplied by the automatic steering weight A to obtain a weighted output value.

Finally, the weighted current values under manual steering control are added to the weighted current values under automatic steering control to obtain the total target current I_sum as follows:

$I_{\mathrm{s}\mathrm{u}\mathrm{m}}=I_{\mathrm{a}\mathrm{s}}\times P+I_{\mathrm{a}\mathrm{u}}\times A$(16)

In summary, the driver steering intervention module is used to determine whether the driver is intervening in the automatic steering system. When driver steering intervention is detected, the steering mode conversion unit is used to switch driving control. The control process for switching driving modes is shown in Fig.12.

Fig. 12 Driving mode switching flow chart

When the column electric power steering system is in the automatic steering state, the driver's hand torque will be predicted by the expansion state observer. When the driver intervenes in the automatic steering system, the estimated hand torque increases. The system will judge the hand torque if the judgement condition is reached, the steering intervention judgement module will set the intervention state variable to 1, and the system will enter the steering mode transition unit to start the transfer of driving control. The switching from automatic steering mode to manual mode is performed by changing the weighting parameters for a set time T_trans. After the power switch is completed, we set the weighting factor P to 1 and A to 0. At this point, manual driving mode has been entered.

4 Steering Mode Switching Experiment

To verify the designed steering mode conversion unit, we constructed a steering test bench as shown in Fig. 13. The steering test bench mainly comprises a ZYNQ (Zynq-7000 All Pgrammable SoC) control mainboard, data acquisition board, motor drive board, switching power supply, encoder, angle sensor, PC, and signal generator.

Fig. 13 Steering lab bench

We set the speed signal to V=5 km/h, the target rotation angle of the steering wheel to 180°, and simulated different speed signals using square wave signals of different frequencies for the following experiments. The amplitude range of the wave signal is 0 to 5 V, and the corresponding relationship between vehicle speed and frequency is shown in Table 3.

We set the torque threshold T₀ to 0.6 N∙m and the time threshold t₀ to 50 ms. The intervention state variable is set to 1 when the driver's hand moment value estimated by the system satisfies both of these constraints, and 0 otherwise.

We conducted an experiment using two transmission methods to switch driver steering control. In the operation of the automatic steering system, direct switching with drive control and switching with added transition units are used separately. When the driver intervenes and shifts to the right, the collected data is presented in numerical form, as shown in Fig. 14.

Fig. 14 Chart comparing direct and transitional transfer of driving control

As can be seen from Fig. 14(a), the rate of change of the steering wheel angle during the transfer of rights is larger using direct switching of driving control. In the experiment, the driver felt a noticeable sense of frustration from the steering wheel, but it was short in duration. As can be seen in Fig. 14(b), the driver's hand torque increases to 2.25 N∙m during direct switching, which is the main reason for the sense of frustration. At the same time, the weighting factor for the automatic steering control is instantly reduced from 1 to 0, as shown in Fig. 14(c).

With the steering mode transition unit, the maximum driver hand torque is around 1 N∙m when the driver intervenes. The steering wheel angle change curve is smoother than that of the direct switching method, and the steering wheel angle change rate is relatively small without any obvious sense of frustration. The driving weight coefficient gradually changes from 1 to 0 in 1 s, and the whole process is relatively smooth.

Through the above comparison experiment, it can be seen that in the process of driving mode switching, the addition of the steering mode transition unit makes the whole steering weight switching smoother, reduces the sense of frustration of the steering wheel, and effectively improves the driver's handling experience.

5 Conclusion

This paper proposes a hand torque prediction model based on an extended state observer, which adds torque and time thresholds to assist in judgment, and designs a steering mode conversion unit during the steering mode switching process. Firstly, we simulated the extended state observer using sine and step signals, and the results showed that the system has good tracking ability and fast and accurate response. Then, square wave signals of different frequencies are used to simulate vehicle speed signals to test the steering transition unit. Experiments show that when the steering transition unit is used, the maximum value of the driver's hand torque is reduced from the original 2.25 N∙m to 1 N∙m, which effectively avoids the large torque jump during the driving right-switching process and significantly reduces the steering wheel's frustration; Finally, during the driving rights switching process, the driving weight coefficient gradually changes from 1 to 0 within 1 s, and the process is relatively smooth. These results prove that the method designed in this paper can significantly improve the accuracy and stability of the system and meet the needs of practical applications.

References

All Tables

All Figures

	Fig. 1 Steering mode switching flow chart
In the text

	Fig. 2 Steering intervention judgement flow
In the text

	Fig. 3 Comparison of torque sensor measurements
In the text

	Fig. 4 Simplified physical model of the system
In the text

	Fig. 5 Flow chart of observer simulation
In the text

	Fig. 6 Steering wheel angle following error graph
In the text

	Fig. 7 Observations of hand torques
In the text

	Fig. 8 Comparison chart of module estimated and measured values
In the text

	Fig. 9 Hand torque curve
In the text

	Fig. 10 Impact of time threshold on system accuracy
In the text

	Fig. 11 Steering mode transition unit flow chart
In the text

	Fig. 12 Driving mode switching flow chart
In the text

	Fig. 13 Steering lab bench
In the text

	Fig. 14 Chart comparing direct and transitional transfer of driving control
In the text