Keywords

1 Introduction

Unintentional lane departure due to driver inattention or fatigue can cause tragic accidents. According to NHTSA data, 42% of traffic fatalities are caused by lane departure [1]. The Lane Keeping Assistance (LKA) function is now a common feature in new vehicles to help avoid fatal accidents. The European Union has even made LKA mandatory for M1 and N1 vehicles [2].

The Handbook of Driver Assistance Systems published by Springer describes the requirements of LKA to help prevent unintentional vehicle lane departure [3].

  1. 1.

    Inform the driver of imminent lane departure in a timely manner.

  2. 2.

    Steer the departing vehicle back into the lane if possible.

However, unnecessary warning or intervention from the LKA system should be avoided. In addition, intervention should be avoided for intentional lane changes e.g. during overtaking or if the driver intentionally “cuts corners”. LKA intervention on unintentional lane departures should be clearly perceptible without hindering the driver.

The torque overlay method, in which the LKA torque is added on the existing assist torque for manual driving, has often been used as a steering based LKA mechanism. Torque overlay can exist in both open-loop and closed-loop format. The open-loop format adds the LKA torque for an arbitrary period of time when the system detects an imminent lane departure. The amount of torque applied to the steering wheel is small and can be easily overcome so that the driver keeps control of the vehicle. However, the LKA performance is expectedly low because the open-loop system does not consider feedback of the vehicle position and heading with respect to the lane marking. Furthermore, the haptic warning disappears even if the risky situation exists. To resolve this problem, closed-loop torque overlay, also known as blended control, is now widely implemented [4]. Blended control improves the LKA performance by incorporating steering angle feedback and provides continuous risk communication to the driver. However, the overlaid torque is modulated to ensure that the driver does not require excessive steering torque leading to a trade-off between manual and automated driving modes. Hence, a method for switching the control authority between driver and automation is required based on estimating driver intention [3].

We propose an LKA system based on admittance-type haptic shared control [5] which removes the need for complex authority switching controllers. The experiment results, which were performed on a real vehicle, show improved acceptance of intentional lane crossing and LKA performance when the driver is hands-off. Additionally, the risk of lane departure is continuously communicated to the driver via the steering wheel.

2 Requirements Specification of LKA

The main requirements for LKA are haptic risk communication and safe vehicle motion. However, the driver’s steering feel should not be impaired by the LKA function. Additionally, the LKA function must cope with a wide range of operating situations across driver intentions, vehicle states, traffic environments and so on. The LKA specification can be summarized by the flowchart in Fig. 1.

Fig. 1.
figure 1

LKA specification flowchart.

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  1. 1.

    The estimated time until lane crossing \({t}_{LC}\) is calculated by the distance between the vehicle and lane marking \({\delta }_{e}\), heading angle \({\delta }_{h}\), vehicle speed \(v\) and steering column angle \({\theta }_{c}\) as \({t}_{LC}=f({\delta }_{e},{\delta }_{h},v,{\theta }_{c})\). The threshold time \({t}_{th}\) determines when the LKA function is activated. A small \({t}_{th}\) reduces the impact of the LKA function on manual driving while a large \({t}_{th}\) allows more comfortable vehicle motion when the function is activated.

  2. 2.

    Intentional lane crossing by drivers must be accepted by the LKA function which, until now, has required complex driver intention estimation methods. The proposed LKA control scheme shall eliminate this requirement. Therefore, it is sufficient for the controller to observe the indicator as the driver intention.

  3. 3.

    When the driver is hands-on, continuous haptic warning is necessary while high-risk conditions persist. When the driver is hands-off or “out-of-the-loop”, safety features must prevent lane departure ideally in all situations. The maximum lateral acceleration and jerk which may be induced by the LKA function has been specified in ISO 11270 and UN ECE-R79 [6, 7] as 3 \({\text{m}}/{\text{s}}^{2}\) and 5 \({\text{m}}/{\text{s}}^{3}\) respectively. However, this may be insufficient in certain situations. For example, a vehicle travelling at 50 \({\text{km/h}}\) on a road with the minimum curvature of 80 \({\text{m}}\) [8] experiences a lateral acceleration of 2.41 \({\text{m}}/{\text{s}}^{2}\) which is already approaching the limit. The lateral acceleration which would be induced by the LKA function would be even greater as the vehicle must follow a smaller radius of curvature. Therefore, strict LKA in all situations would merit a revision of the current regulations.

  4. 4.

    When Lane Centering Assist (LCA) is available, the LKA function should quickly transition to LCA in order to prevent jerky motion as illustrated by Fig. 2. As LCA is merely a convenience feature, the centering torque is much smaller than the LKA torque which is a safety feature.

    Fig.2.
    figure 2

    Example of jerky motion due to lack of LCA.

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  5. 5.

    Even when LCA is not active, some centering functionality must be present to prevent the vehicle from “bouncing” between lane markings due to the LKA heading correction. A temporary return control is therefore required to obtain smooth vehicle motion once the LKA heading correction is completed.

The proposed LKA based on admittance control will primarily focus on improving point 2 and 3. It is shown to provide high lane keeping performance and continuous haptic warning while being receptive of driver intentional lane crossing.

3 Admittance Control Based LKA

Figure 3a shows the block diagram of LKA based on admittance control. Closed-loop torque overlay based LKA is also shown as a benchmark in Fig. 3b; note the presence of a gain \({k}_{t}\) which modulates the torque command generated by the angle controller. \({\theta }_{LKA}\) is the angle command to prevent lane departure and is generally calculated by \({\theta }_{LKA}=f({\delta }_{e},{\delta }_{h},v)\). \({T}_{tb}\) is the torsion bar torque of the Electric Power Steering (EPS) which is used to measure the driver torque \({T}_{d}\). Upon activation of the LKA function, \({\theta }_{c}\) tracks \({\theta }_{cmd}\) using the angle controller which is implemented by PD control.

Fig. 3.
figure 3

Block diagrams of LKA control schemes.

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In Fig. 3a, the Manual Reference Controller (MRC) is used to estimate the manual deviation angle \({\theta }_{MD}\) created by the driver input. \({\theta }_{MD}\) is then superposed with \({\theta }_{LKA}\) to create the command angle \({\theta }_{cmd}\) for the angle controller, thereby incorporating the driver intention directly into the angle control. The dynamics of the steering column during hands-off situations is given by Eq. 1 and the reaction torque felt by the driver during hands-on situations is given by Eq. 2:

$${J}_{c}{\ddot{\theta }}_{c} ={k}_{p}\left({\theta }_{LKA}-{\theta }_{c}\right)+{k}_{d}\left({\dot{\theta }}_{LKA}-{\dot{\theta }}_{c}\right)+{J}_{c}{\ddot{\theta }}_{LKA}$$
(1)
$${T}_{tb}={k}_{MD}({\theta }_{LKA}-{\theta }_{c})+{c}_{MD}({\dot{\theta }}_{LKA}-{\dot{\theta }}_{c})+{J}_{MD}\left({\ddot{\theta }}_{LKA}-{\ddot{\theta }}_{c}\right)$$
(2)

where \({J}_{c}\) is the moment of inertia of the steering column, \({k}_{p}\) and \({k}_{d}\) are the PD controller gains. \({J}_{MD}\), \({c}_{MD}\) and \({k}_{MD}\) are the MRC parameters.

From Eqs. 1 and 2, it can be seen that the LKA performance in hands-off situations and the driver torque required to intentionally change lanes have been decoupled.

The PD controller gains \({k}_{p}\) and \({k}_{d}\) can be tuned to improve the angle tracking performance independent of the reaction torque. The MRC parameters \({k}_{md}\) and \({c}_{md}\) allow flexible adjustment of reaction torque with respect to distance to the lane marking, as \({\theta }_{LKA}=f({\delta }_{e},{\delta }_{h},v)\). Crucially, \({\theta }_{c}\) can perfectly track \({\theta }_{cmd}\) where \({\theta }_{cmd}={\theta }_{LKA}+{\theta }_{MD}\) and \({\theta }_{MD}=0\) during hands-off situations. Deactivation of the LKA function is unnecessary for intentional lane crossing which means that the system can continuously provide haptic information while high-risk conditions persist.

4 Performance of LKA

In this section, the admittance control based LKA is evaluated on a real vehicle using the closed loop torque overlay as a benchmark. The experiment procedure is shown in Fig. 4. First the driver intentionally steers the vehicle across the lane marking (Fig. 4a). Next, the vehicle approaches the lane marking without driver input and risking unintentional lane crossing (Fig. 4b). Ideally, intentional lane crossing can be achieved without excessive driver torque and unintentional lane crossing is prevented by the LKA function.

Fig. 4.
figure 4

Experimental procedure.

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The torque overlay experiment results are shown in Fig. 5. The blue highlighted area corresponds to the intentional lane crossing scenario and the beige highlighted area corresponds to the unintentional lane crossing scenario. In Fig. 5a, a high value of the gain \({k}_{t}\) is used to prioritize the angle tracking performance and unintentional lane departure is prevented. However, the reaction torque during intentional lane crossing is high at around 6 Nm. In Fig. 5b, a low value of \({k}_{t}\) is used and the reaction torque during intentional lane crossing has been reduced to around 2 Nm. However, angle tracking performance is reduced, and unintentional lane departure is observed.

Fig. 5.
figure 5

Performance of torque overlay based LKA.

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Figure 6a shows the experiment results using the proposed admittance control based LKA. The high angle tracking performance derived from the admittance control structure prevents unintentional lane departure. In addition, the reaction torque observed during intentional lane crossing is comparable to that from Fig. 6b at around 2 Nm. Thus, the requirements of LKA outlined in Sect. 2 have been achieved without the need for complex authority switching mechanisms which rely on estimation of driver intention. Figure 6b demonstrates how the reaction torque may be easily tuned using the MRC parameter \({k}_{MD}\). The reaction torque grows linearly until the vehicle has crossed the lane marking at which point it plateaus. The LKA function is never turned off and continuous risk information is communicated to the driver even when driving along the lane marking. Exploring the optimal MRC parameters is an important step in combining appropriate haptic risk communication and driver acceptance.

Fig. 6.
figure 6

Performance of admittance control based LKA.

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5 Conclusion

This paper has proposed an LKA system based on admittance-type haptic shared control. The admittance control scheme has been shown to allow high lane keeping performance when the driver is hands-off while being receptive of driver intentional lane crossing. Figures 5 and 6 demonstrate how the trade-off required of conventional torque overlay LKA has been resolved using the proposed admittance control based LKA.

Maintaining a comfortable steering feel and smooth vehicle motion when the LKA function is activated are the primary challenge to driver acceptance of the function in the future. The requirements of LKA outlined in Sect. 2 aim to improve driver acceptance rates by addressing both of these issues.