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This paper focuses on the lane departure avoidance system for a four in-wheel motors’ drive electric vehicle, aiming at preventing lane departure under dangerous driving conditions. The control architecture for the lane departure avoidance system is hierarchical. In the upper controller, the desired yaw rate was calculated with the consideration of vehicle-lane deviation, vehicle dynamic, and the limitation of road adhesion. In the middle controller, a sliding mode controller (SMC) was designed to control the additional yaw moment. In the lower layer, the yaw moment was produced by the optimal distribution of driving/braking torque between four wheels. Lane departure avoidance was carried out by tracking desired yaw response. Simulations were performed to study the effectiveness of the control algorithm in Carsim®/Simulink® cosimulation. Simulation results show that the proposed methods can effectively confine the vehicle in lane and prevent lane departure accidents.

In the last decade, a large portion of highways traffic accidents lead to heavy casualties [

To realize LKAS or LDAS, several types of control inputs have been pursued in literature. According to active control means, the LDAS can be classified into three types, that is, systems using steering control, systems using differential braking control, and systems using differential driving/braking control.

The steering control, which overlaid a steering torque or a steering angle by a DC motor mounted on steering column, has been deeply and widely investigated [

The control of vehicle’s lateral dynamics using differential braking technique was proposed by Pilutti et al. in 1995 [

The third technique is that differential driving/braking control by the output torque of each wheel motor is individually controlled. A wheel motor can provide more accurate and faster torque response compared with hydraulic system. The distributing driving torque between rear wheels has been used to fulfill the lane keeping functions [

In this paper, a new lane departure avoidance control method using differential driving/braking control for enhancing the active safety of electric vehicles is proposed. In Section

The control architecture for lane departure avoidance system is hierarchical, as shown in Figure

Architecture of the proposed lane departure avoidance control method.

The rotational torque applied by the driver to the steering wheel and the state of vehicle’s steering switch can be combined to identify driver’s intention. If steering torque was greater than 2 Nm or steering switch was turned on, control system will assume that the driver has a clear intention to manipulate vehicle.

Time to line cross (TLC) and distance to lane center (DLC) are used jointly to decide whether to turn on lane departure avoidance control or not.

Lane departure avoidance control will be turned on when either of the following conditions is satisfied:

①

②

Lane departure avoidance control will be turned off when either of the following conditions is satisfied:

①

② Driver’s intention is obvious.

③

④ The lane identification failure.

The desired vehicle dynamics to prevent lane departure is planned by a preview driving model and a 2-DOF linear vehicle model.

Assuming that the motion of the vehicle is constrained by Ackerman geometry, an optimal preview model is used to calculate the desired steering angle (

A linear 2-DOF vehicle model is considered as a reference vehicle model for lane departure avoidance control.

According to the kinemics relations of the vehicle, the slip angles of front wheel (

At large slip angles, the tire model can be no longer linear. The lateral tire force depended on slip angle

Under different vertical loads and tire-road friction coefficients, the calculated lateral forces are compared with test data, as shown in Figure

Lateral tire force comparison: simplified magic formula and test data.

Then, the equivalent cornering stiffness of each tire can be given by

The peak lateral acceleration must be bounded by the tyre-road friction coefficient

The maximum yaw rate must be limited by the friction coefficient of the road. Thus, the desired yaw rate response (

To make a vehicle follow the desired yaw rate, a sliding mode controller is adopted to calculate the additional yaw moment (

Differentiating the above equation:

Combining (

Setting

The deviation between actual speed

A PI controller is designed to determine the sum of longitudinal forces (

The lower controller determines the output torque of the in-wheel-motor at each wheel, so as to meet driver’s desired speed and generate a net yaw moment that tracks the desired value for additional yaw moment determined by the middle controller. Control allocation technology is utilized in this study for torque allocation.

When the condition of front wheel is small, the total longitudinal force and additional yaw moment can be expressed as

The primary objective of the lower controller is to track the desired yaw response and make minimum allocation error. Another objective of the lower controller is to minimize the energy consumption of the in-wheel-motors.

According to the objectives of torque allocation, the optimization problem can be described by Sequence Least Squares (SLS). It is expressed as follows:

A weighting factor

To minimize the allocation error,

Considering the dynamics of each wheel, the relationship between tyre longitudinal force (

The output torque of the in-wheel-motor is limited by motor speed. The relationship of the output torque and motor speed is shown in Figure

Specification of in-wheel motor.

The dynamic response of the in-wheel-motor can be described as a first-order lag:

In order to verify the effectiveness of the proposed method, a high-fidelity four-wheel-independent-drive electric vehicle (4WID-EV) model developed in Carsim and Matlab/Simulink is applied in this study. The single lane change test is chosen as the simulation test maneuver. The target road is designed according to ISO-3888-2-2002 and is shown in Figure

Vehicle parameters.

Definition | Symbol | Unit | Value |
---|---|---|---|

Vehicle mass | | kg | 1231 |

Wheel base | | m | 2.6 |

Track width | | m | 1.481 |

Distance from C.G. to front axle | | m | 1.56 |

Distance from C.G. to rear axle | | m | 1.04 |

Yaw moment of inertia | | kg⋅m^{2} | 2031.4 |

Height of C.G. | | m | 0.34 |

Wheel radius | | m | 0.304 |

Target road for simulation.

Coordinate

Curvature

To evaluate the work load of each tyre, tyre usage (

The vehicle is driven on the target road at the speed of 80 Km/h. The width of lane is 3.5 m and tyre-road friction coefficient

The decision-making is shown in Figure

Decision-making.

TLC

DLC

Decision logic

The control results of Maneuver 1 are shown in Figure

Control results.

Driving/braking torque

Yaw rate tracking

Lateral acceleration response

Tyre usage

Side slip angle

The simulation conditions are the same as Maneuver 1 except the tyre-road friction coefficient

The decision-making is shown in Figure

Decision-making.

TLC

DLC

Decision logic

The control results of Maneuver 2 are shown in Figure

Control results.

Driving/braking torque

Yaw rate tracking

Lateral acceleration response

Tyre usage

Side slip angle

The simulation conditions are the same as Maneuver 1 except the speed of 120 km/h.

The decision-making is shown in Figure

Decision-making.

TLC

DLC

Decision logic

The control results of Maneuver 3 are shown in Figure

Control results.

Driving/braking torque

Yaw rate tracking

Lateral acceleration response

Tyre usage

Side slip angle

The maximum side slip angle on wet road is smaller than that on the dry road. The objective of the stability system is to track a desired yaw rate, which is limited by the friction coefficient of the road and vehicle speed. As shown in Figures

In this paper, a hierarchical method for LDAS has been presented on the basis of differential driving/braking control. The proposed method consists of three parts: an upper-level controller, a middle-level controller, and a lower-level controller. The upper-level controller was designed to monitor driver intention and vehicle-lane deviation and to determine whether an intervention is required. Another task of the upper-level controller is to determine the desired dynamics (desired yaw rate). To tack the desired dynamics, sliding mode control method and PI control method were used in the middle-level controller. The lower-level controller was designed to distribute driving/braking torque between each wheel. To achieve optimal allocation of the output torque of the wheel motors, a control allocation method was adopted. The performances of the proposed method were evaluated via three software-in-loop tests. Simulation results show that the presented method can effectively prevent the lane departure by differential driving/braking control.

The proposed method is verified in SIL test, which is different with hardware-in-loop (HIL) and real driving experiment, for example, signal disturb or delay. To this end, the proposed LDAS will be implemented in HIL platform and a prototype vehicle in the future.

The authors declare that they have no conflicts of interest.

This work was supported by the Natural Science Foundation of Fujian Province, China (2015J01196) and the Scientific Research Foundation of Fuzhou University, China (XRC1430, 2014-XQ-17).