This paper discusses a concept for enhanced active safety by introducing a driver warning system based on vehicle dynamics that predicts a potential loss of control condition prior to stability control activation. This real-time warning algorithm builds on available technologies such as the Electronic Stability Control (ESC). The driver warning system computes several indices based on yaw rate, side-slip velocity, and vehicle understeer using ESC sensor suite. An arbitrator block arbitrates between the different indices and determines the status index of the driving vehicle. The status index is compared to predetermined stability levels which correspond to high and low stability levels. If the index exceeds the high stability level, a warning signal (haptic, acoustic, or visual) is issued to alert the driver of a potential loss of control and ESC activation. This alert will remain in effect until the index is less than the low stability level at which time the warning signal will be terminated. A vehicle speed advisory algorithm is integrated with the warning algorithm to provide a desired vehicle speed of a vehicle traveling on a curve. Simulation results and vehicle tests were conducted to illustrate the effectiveness of the warning algorithm.
Freeway entrance and exit ramp interchanges are the sites of far more crashes per mile driven than other segments of interstate highways. Crashes most common on exit ramps—run-off-road crashes—frequently occurred when vehicles were exiting interstates at night, in bad weather, or on curved portions of ramps. When the vehicle is driving under these conditions at a higher speed than the surface can allow, the understeer gradient of the vehicle can increase causing the vehicle to plow or decrease and becomes negative causing the vehicle to spinout.
In recent years, electronic stability control systems for motor vehicles have become increasingly popular [
Electronic Stability Control (ESC) helps keep the vehicle on its steered path during a turn, to avoid sliding or skidding. It uses a computer linked to a series of sensors—detecting wheel speed, steering angle, yaw rate and lateral acceleration of the vehicle. During normal driving, ESC works in the background and continuously monitors steering and vehicle direction. It compares the driver’s intended direction (determined through the measured steering wheel angle) to the vehicle’s actual direction (determined through measured lateral acceleration, vehicle rotation (yaw), and individual road wheel speeds). ESC intervenes only when it detects a probable loss of steering control, that is, when the vehicle is not going where the driver is steering. This may happen, for example, when skidding during emergency evasive swerves, understeer or oversteer during poorly judged turns on slippery roads, or hydroplaning. If the vehicle starts to drift, the system momentarily brakes one or more wheels and, depending on the system, reduces engine power to keep the car on the steered course. However, Electronic Stability Control cannot override the laws of physics. If a driver exceeds the friction capabilities of the road surface, ESC cannot prevent a crash. It is a tool to help the driver maintain control.
In this paper, we introduce a driver warning algorithm integrated with the Electronic Stability Control system. The warning system is designed to further assist a driver by warning of an impending ESC activation so that the driver will reduce the vehicle’s speed prior to the need for ESC intervention. It is hoped that the warning system will assist the driver in recognizing and avoiding instances of potential loss of vehicle control and also reduce usage of ESC.
The body of the paper begins first with system architecture including a brief description of the different blocks used in the warning algorithm. Second, we develop the warning signal command for both the transient and the steady-state modes of the vehicle. Third, we calculate a vehicle advisory speed in a curve based on vehicle understeer gradient. Finally, we present simulation results and vehicle tests.
Figure the vehicle and driver block which contains the following: driver inputs (steering, accelerator pedal, and brake pedal), vehicle sensors (lateral acceleration, yaw rate, wheel speeds to estimate the vehicle longitudinal speed, throttle position, and master cylinder pressure sensor); the ESC block: command Interpreter block; the warning and speed advisory block: the driving states, the Lateral Surface Capability Index, the warning Algorithm: the understeer index, the stability index, the arbitration logic, the vehicle speed advisory.
Schematic diagram of the warning algorithm.
The vehicle yaw-plane dynamics can be described by a second-order state [
The transfer functions from the steering input to the vehicle yaw rate and side-slip velocity can be derived from the state
Equations (
When the state approach is employed to generate the commands, the desired vehicle side-slip velocity and desired yaw rate are computed based on the system differentials using nominal values of system parameters defined in (
When the state equation approach is employed to generate the commands, the desired vehicle side-slip velocity and desired yaw rate are computed based on the system differential equations using nominal values of system parameters:
In this reference model, the
The transfer-function approach for obtaining the desired vehicle response is based on the structure of the system input-output transfer function derived in (
Equations (
Therefore, rewriting (
The steady-state value of the vehicle side-slip velocity can be obtained by multiplying the gain with the steering angle; that is,
Equation (
The steady-state desired yaw rate
Therefore, (
Given the steady-state side-slip velocity, the next step is to process such value through a dynamic filter with desired damping ratio and natural frequency representative of the system dynamics described in (
The dynamic filter with desired damping ratio, natural frequency, and zero can be implemented using a set of two first-order differentials
Equations (
The dynamic relationship between the steering angle and desired side-slip velocity can be expressed into the following form:
Using this relationship, a dynamic filter can be established with steering angle as input:
Defining
A block diagram of the command interpreter block is illustrated in Figure
Block diagram of the command interpreter algorithm.
This block reads all available sensor signals, namely, the lateral and longitudinal accelerations, steering wheel angle, and yaw rate to detect the current driving situation. This block distinguishes 11 different driving modes such as cruising, braking, cornering, transient, low speed maneuvering, and reversing.
For the purpose of this study, it is sufficient to distinguish between a transient mode and a steady turn for both linearized and nonlinear relations between lateral tire forces and slip angles. We define four intermediate flags
The transient mode is determined as follows:
The delay mode starts when the input signal becomes false. The variable count is incremented by one as long as the old value of the variable is less than
We define three intermediate flags
Figure
Block diagram of the driving states algorithm.
The lateral surface capability index is determined based on the comparison between actual vehicle motion obtained from sensor inputs and vehicle behavior obtained from a linear vehicle motion model. When the vehicle is in the linear range of operation, the vehicle motion model is close to the actual vehicle motion obtained from the sensor inputs. In this case, the lateral surface index is set to the maximum lateral acceleration that the vehicle can sustain on dry surface. When the vehicle lateral motion approaches the limit of adhesion, the vehicle motion model is substantially different from the actual vehicle motion, and it can be concluded that the lateral surface index must at least equal
The first step in this block is to detect whether the vehicle is in a linear mode of motion or not. To this effect, the linear mode detection evaluates the following three conditions:
The desired yaw rate
The difference between measured and expected lateral accelerations in (
Equation (
We define four intermediate flags
The lateral surface capability index is determined based on input data from the sensors and the flags
Schematic diagram of the lateral surface capability index.
On the other hand, if the linear flag is found to be “false,” this may be due to the fact that the quality of the road surface has deteriorated and its friction coefficient has decreased, or that the vehicle is going at the stability limit. In that case,
If the straight driving flag is found to be “true,” no estimation of lateral surface capability index is possible. In this case, the timer mentioned is enabled; that is, the timer starts to run if the straight flag has just switched to “true,” or it simply continues to run if the straight flag was “true” already in the previous iteration of the procedure. The value of the timer is thus representative of the time in which the vehicle has been going straight. If the timer has exceeded a predetermined limit, the algorithm resets the friction coefficient to
The warning algorithm computes indices based on yaw-rate error, yaw rate dead-band, side slip velocity error, and side slip velocity dead-band, an understeer error, and an understeer dead-band, using various sensors. It consists of 3 major blocks: stability index block; steady state linear/nonlinear understeer index block; arbitration block.
Schematic diagram of stability index implementation.
The stability index block requires the yaw rate error
The yaw rate and the lateral velocity rate dead-band lookup tables store a yaw rate dead-band
From the dead bands
The decision whether the vehicle is in a situation approaching ESC activation or not during a transient maneuver can be based on the yaw rate and lateral velocity derivative indices defined in (
Vehicle in steady turn.
For steady state mode, the dynamic equation of motion in the body-centered coordinate system is given by
The linearized lateral forces are expressed in terms of the tire slip angles
From (
In the linear case
Figure
Steer angle versus
For the nonlinear tire characteristics, in which the tire force-sideslip angle becomes significantly nonlinear, the slopes are not constant and vary with the turn radius when the vehicle speed is constant as illustrated in Figure
Steer angle versus
Since in the nonlinear case there is no constant understeer coefficient, we define a variable coefficient that expresses how the slip angle difference changes as the lateral acceleration changes
By applying Kalman filter technique, it is possible to estimate the linear understeer and nonlinear understeer variable.
The Kalman filter addresses the general problem of trying to estimate the state of a discrete-time controlled process that is governed by the linear stochastic difference equation
We will be using two Kalman filters for the linear and nonlinear operations. Equations (
In the linear range we define
In the nonlinear range we define
The random variables
They are assumed to be independent (of each other), white, and with normal probability distributions
Consider the signal model of (
The linear flag defined in (
When the vehicle is determined to be in non-linear regime, the linear flag becomes zero, filter (
In principle, the two filters might be regarded as a single Kalman filter which swaps
In analogy to what was described earlier for the yaw rate and lateral velocity rate stability indices
Since
Similar to the yaw rate dead band
The structure and operation of the understeer index are depicted in Figure
Schematic diagram of the understeer index implementation.
The operation of the arbitrator is explained referring to the flowchart of Figure
Flow chart of the arbitrator logic.
A general stability index is set equal to the
If the vehicle is in a straight line driving mode, the general stability index determined prior to this step is multiplied by positive factor
Finally, the general stability index is compared to an upper threshold
Very often the road signs indicate the safe speed in a curve. However, on low
When the vehicle is driving in a curve at a higher speed than the surface can allow, the understeer gradient of the vehicle increases causing the vehicle to plow or decreases and becomes negative causing the vehicle to spinout. The warning algorithm described earlier will issue a warning to alert the driver that he/she is traveling faster than the road surface can allow. In this section, we develop an advisory speed algorithm in a curve based on vehicle dynamics in conjunction with the driver warning algorithm. The advisory speed algorithm computes the advisory speed which allows a vehicle to travel around the turn or curve in its travel lane without causing an uncomfortable “side force” to its driver or passengers and helps maintain control of the vehicle. The advisory speed is based on the maximum lateral capability of the surface, the driver steering input, the actual vehicle speed, and the actual understeer of the vehicle. A visual advisory speed can be displayed, for example, in the DCI or a HUD display when the warning signal is issued. The visual advisory HMI is outside the scope of this paper.
Based on the steering input
Finally, the advisory speed is calculated as follows:
The advisory speed is communicated to the driver to allow the driver to make a choice on what action should be taken, or through an intervention system where the engine and/or braking systems are controlled automatically to reduce the vehicle’s speed.
In this section, we present some typical simulation results showing the performance of the driver warning algorithm described in Section
Time trace of the road friction coefficient.
Figure
Warning and ESC flags time trace, driver not reacting to the warning at the time the warning is set.
Vehicle path compared to the target path, driver not reacting to the warning at the time the warning is set.
Vehicle trajectory in the curved section of the road, driver not reacting to the warning at the time the warning is set.
To illustrate the performance of the speed advisory algorithm, the simulation was repeated this time with the driver reacting to the warning signal by reducing the vehicle speed based on the speed advisory algorithm.
Figure
Vehicle advisory speed.
Vehicle path compared to the target path, driver reacting to the warning at the time the warning is set.
Vehicle trajectory in the curved section of the road, driver reacting to the warning at the time the warning is set.
Warning and ESC flags time trace, driver reacting to the warning at the time the warning is set.
To study the effect of the vehicle being on a banked road on the warning algorithm, the previous simulation was repeated with the vehicle traveling at 80 kph on a 40 m radius loop with 200 m straight section of dry surface and variable bank angle. When the vehicle operator is driving on a banked road, the measured lateral acceleration will include the effect of the banked road and therefore affecting the straight driving detection algorithm. In addition, the operator introduces a correction to the steering angle to maintain the vehicle on the road, and therefore the desired yaw rate and understeer commands will indicate that the driver wishes to travel on the bank and not across it. In this case, the warning signal might be triggered unnecessarily especially when the vehicle is in the linear range of operation. Figure
False warning issued on a banked road with uncompensated lateral acceleration.
Vehicle path compared to the target path on a banked road.
True and measured uncompensated lateral acceleration on a banked road.
Therefore, it is important to compensate for the effect of the bank in the lateral acceleration measurement.
When the vehicle is driven on a banked road, the measured lateral acceleration is corrupted by the bank angle of the road given by the following equation:
Define
Next, we will develop a Kalman filter to estimate
Define the following state vector
The random variables
They are assumed to be independent (of each other), white, and with normal probability distributions
The Kalman filter developed in (
The previous simulation was repeated using the compensated lateral acceleration
In Figure
True lateral acceleration and measured uncompensated and compensated lateral acceleration on a banked road.
Warning signal on a banked road with compensated lateral acceleration.
To evaluate the warning algorithm performance, the following results are based on experimental data obtained using an Opel Omega vehicle equipped with ESC sensors. The tests were conducted on low-mu handling track with straight and curved sections to simulate a freeway exit. Time slices from different driving sessions are zoomed in to illustrate the performance of the warning algorithm.
A time slice of 10 seconds (50–60 seconds) is shown in Figure
Vehicle simulating a freeway exit on low
At time
Figure
Warning and ESC signals under transient maneuvers.
Figure
Warning and ESC signals with increasing steering angle at low speed.
Figure
Vehicle simulating a freeway exit on low
In some of the conditions evaluated, the warning signal is issued 3 to 4 seconds prior to ESC activation to allow the driver to react to the warning. If the driver reacts to the warning signal by reducing the vehicle speed in the curve, the vehicle will follow more precisely the road curves with minimum or no ESC intervention. For large and increasing steering angle maneuver at relatively low speed, the warning is issued almost at the same time as the ESC activation. The warning signal is not effective in this case since the driver does not have time to react to the warning signal before the ESC activation. However, at these low speeds, the ESC is very effective and can stabilize the vehicle without heavy brake intervention. When the vehicle is driven on a banked road, the uncompensated lateral acceleration measurement can false trigger the warning algorithm. Therefore, it is important to compensate for the effect of the bank in the lateral acceleration measurement. This warning system should be evaluated in a wider range of road and vehicle conditions to more fully evaluate its usefulness.
Distance from the center of gravity of vehicle to the front axle (m)
Distance from the center of gravity of vehicle to the rear axle (m)
Cornering stiffness of both tires of front axle (N/rad)
Cornering stiffness of both tires of rear axle (N/rad)
Acceleration of gravity (m/
Steering gear ratio
Moment of inertia of entire vehicle about the yaw axis (
Total vehicle mass (kg)
Vehicle weight on the front axle
Vehicle weight on the rear axle
Desired understeer coefficient (deg/g)
Vehicle track width (m)
Lateral velocity of vehicle’s center of gravity (m/s)
Lateral acceleration of vehicle’s center of gravity (m/
Measured lateral acceleration at the vehicle’s center of gravity (m/
Desired lateral velocity of vehicle’s center of gravity (m/s)
Desired lateral velocity rate of vehicle’s center of gravity (m/
Lateral velocity gain (m/s/rad)
Steady sate desired lateral velocity of vehicle’s center of gravity (m/s)
Longitudinal velocity of vehicle’s center of gravity (m/s)
State variables of the second-order filter
Negative of system zero for desired side slip velocity
Negative of system zero for desired yaw rate
Steering angle of the front wheels (rad)
Yaw rate of vehicle (rad/s)
Bank angle (rad)
Desired yaw rate of vehicle (rad/s)
Desired steady state yaw rate of vehicle (rad/s)
Yaw velocity gain (rad/s/rad)
Damping ratio of desired vehicle performance
Natural frequency of desired vehicle performance (rad/s).